Description
Factor Adjustment Dynamics
ABSTRACT
Title of dissertation: ESSAYS ON FACTOR ADJUSTMENT
DYNAMICS
Juan M. Contreras, Doctor of Philosophy, 2006
Dissertation directed by: Professor John P. Rust
Professor John C. Haltiwanger
Department of Economics
This study analyzes dynamic production input factor decisions using the an-
nual Census of Manufacturing ?rms from Colombia and monthly production data
from a glass mould ?rm. It proposes a model that is able to explain the empiri-
cal evidence about capital and employment adjustment observed in these data-sets,
namely the mix of smooth and lumpy adjustment, and both the static and dy-
namic interrelation in capital and employment adjustment. The key points of the
explanation are the joint analysis of capital and employment adjustment and the
existence of adjustment costs for capital and labor. These adjustment costs take the
form of disruption in the production process and reallocation of internal resources
to adjust the input factors, ?xed costs of adjusting factors and congestion e?ects
in the adjustment costs, meaning that it is more costly for ?rms to adjust capital
and employment at the same time. The study uses a structural approach and a
simulated minimum distance algorithm to estimate the adjustment cost parameters
in the case of the Census of Manufacturing Firms and a calibration procedure to
explore the ?t of the model in the speci?c case of the glass mould ?rm
ESSAYS ON FACTOR ADJUSTMENT DYNAMICS
by
Juan M. Contreras
Dissertation submitted to the Faculty of the Graduate School of the
University of Maryland, College Park in partial ful?llment
of the requirements for the degree of
Doctor of Philosophy
2006
Advisory Committee:
Professor John P. Rust, Co-Chair/Advisor
Professor John C. Haltiwanger, Co-Chair/Advisor
Professor John Shea, Advisor
Professor Michael J. Pries, Advisor
Professor Vojislav Maksimovic
c Copyright by
Juan M. Contreras
2006
DEDICATION
To my father, mother, brother and wife
ii
ACKNOWLEDGMENTS
I want to thank ?rst and foremost John Rust, who took the time and had the
patience to teach me how to think and work as an economist. It has been a pleasure
and an honor to have learned from such a ?ne person and professional.
I also want to give special thanks to John Haltiwanger, who helped me enor-
mously with the data and guided me through all the dissertation process giving me
constant and good advice. It has been a privilege having him as advisor.
I am thankful to John Shea, who gave extensive comments for all my drafts
and helped me to improve greatly this paper, to Mike Pries and Alex Whalley who
also helped me with his comments and to Marcela Eslava, who very kindly made
possible for me to access the Colombian Census of Manufacturing Firms. I also
acknowledge the ?nancial support from the Central Bank of Colombia.
Special mention deserves the owner of the glass mould ?rm, who allow me to
get access to the production records of his company. My brother and manager of
the plant, Luis Fernando Contreras, also deserves my deepest gratitude for helping
me to collect and organize the data from this ?rm. I thank also Bandy S. who gave
access to excellent computer resources and support.
Finally, I can not thank enough the help and care of my wife and colleague,
Ignez Tristao, whose many ideas and discussions are re?ected in this dissertation.
iii
INTRODUCTION
Along the years, managers, economists and engineers have shared a common
question: how to maximize the gains from an industry operation. This simple
question has stimulated a broad range of research, ranging from the development
of mathematical tools and computer algorithms for the solutions of the problem, to
applications in speci?c industries and the analysis of the aggregate implications for
the overall economy.
Maximizing the pro?ts is equivalent to choosing optimally production input
factors, a problem that has received a lot of attention in the economic literature.
This research has lead to remarkable developments in production theory, in indus-
trial organization and in business cycles analysis. At the ?rm level, starting with
the work of Holt et al. (1960), the standard approach has been to ?t quadratic
cost functions to the production problem in order to obtain linear decision rules for
the amount of inputs to use. More recently, in order to get closer to the discrete
decisions observed at the micro level, other line of research has considered di?erent
types of non quadratic adjustment costs functions and di?erent types of non-linear
(i.e. discrete) decision rules as the key to determine optimal operation decisions, as
in Rust (1987) and Hall (2000).
At the aggregate level, the neoclassical model of investment and labor demand
had also used quadratic adjustment costs functions in order to match the smooth
iv
adjustment observed at the aggregate level. Hall and Jorgenson (1967), Abel (1979)
and Hamermesh and Pfann (1996) are examples of this approach. Nadiri and Rosen
(1969) also uses convex adjustment costs to explain the aggregate interrelation be-
tween capital and labor adjustment. These explanations for the investment and
labor demand rely on the representative agent paradigm according to which the
aggregate economy can be described by a single representative agent and the het-
erogeneity across agents comes from pure luck, because they receive di?erent shocks
in productivity and demand.
The problem with this approach is that recent studies using ?rm level data
such as Caballero et al. (1995), Caballero et al. (1997),Narazani (2004) and Sakel-
laris (2004) have shown that the representative agent does not act according to the
convex cost model. In particular, three key facts about investment and dynamic
employment demand emerge from this evidence: ?rst, there are a lot of inaction pe-
riods when ?rms do nothing and some periods when the ?rms adjust continuously;
second, when ?rms adjust there is a mix of very large and small adjustments; and
third, there is an interrelation between capital and labor adjustment, which means
signi?cant dynamic correlations and a higher probability of investing when the ?rm
is hiring more workers and viceversa.
Building in part over this empirical evidence and over single-agent decision
studies
1
, Caballero and Engel (1999), Cooper et al. (1999), Cooper and Haltiwanger
(2005) and Cooper et al. (2004), to mention a few, have proposed models which
do not rely only on quadratic adjustment costs and are able to generate discrete
1
Like the Bus replacement problem in Rust (1987)
v
and non smooth adjustment. They are dynamic in nature and match both the
micro evidence and the macro facts. However, these models do not explain the
interrelation between employment and capital adjustment since they analyze each
factor by separate. Also, they have been subject to criticism because of the lack of
direct empirical support for the existence of adjustment costs.
This dissertation addresses directly those two criticisms and continues this line
of research exploring ?rm’s behavior with a focus on the real rigidities that ?rms face
when they desire to optimally adjust the combination of production input factors.
Speci?cally, it analyzes from an empirical and theoretical point of view the costs
that ?rms have to pay when adjusting capital and the number or workers, together
with the patterns of energy and materials adjustment. The ?rst chapter uses an
annual census of manufacturing ?rms while the second one focuses in a single ?rm
with monthly data on production. The implications of a model that explain their
behavior are compared when applied to both cases.
In the ?rst chapter, I analyze the empirical evidence about factor adjustment
dynamics using the Colombian Annual Manufacturing Census from 1982 to 1998,
and propose a model able to account for the three facts mentioned above and ob-
served in this data set (i.e. mix of smooth and lumpy adjustments, mix of small
and large adjustments and interrelation in capital and employment adjustment).
The main feature of this chapter’s dynamic model of ?rms’ factor demand
decisions is the existence of adjustment costs for capital and employment. The
adjustment cost structure captures key features of the data such as reductions in
output during adjustment (disruption cost), the costs of installing capital and cre-
vi
ating or destroying a job vacancy (?xed costs), a convex cost component introduced
to capture the observed mix of smooth and lumpy adjustment, and an extra cost of
adjusting capital and labor simultaneously (congestion e?ects).
The adjustment cost structural parameters of the model are estimated by ap-
plying a minimum distance algorithm. The structural methodology allows me to
reject statistically the existence of ?xed costs and to accept the existence of disrup-
tion costs for capital and labor, the convex costs for capital and the existence of
congestion e?ects. The conclusions of the analysis are that (i) there exist signi?-
cant dynamic interrelations between factor adjustments; (ii) both interaction e?ects
in the adjustment cost parameters and the convex and non convex nature of the
adjustment costs appear to be important in explaining ?rms’ mix of smooth and
lumpy adjustments on the one hand and small and large adjustments on the other
hand, in capital and employment; and (iii)depending on their capital to labor ratio,
?rms either do not adjust or adjust only capital, only labor or both capital and
labor simultaneously.
The second chapter presents direct evidence of the adjustment costs that a
glass mould ?rm has to pay when adjusting capital and employment in response
to the arrival of new orders using detailed monthly data on production. At this
frequency, it is observed a disruption in the production process due to the installation
of small units of capital represented by speci?c tools with limited life (usually less
than one year). This cost is measured in man hours and quanti?ed as an average of
1.6% of the total sales. Hiring a worker also increases the average production time
(decreases productivity) by 1.02%
vii
The existence of a powerful union also creates a high cost of adjusting the
number of workers through established fees for ?ring and hiring in addition to the
high legal ?ring costs. These costs are asymmetric and quanti?ed in US$53,000 and
US$1,320 dollars respectively. Given the high technology involved in the process,
hiring a new worker implies an extra cost of training for the speci?c process and
a cost in the lower productivity this new worker has while learning quanti?ed in
US$1,534 dollars. Moreover, the adjustment of one worker increases the disruption
cost in the adjustment of capital by 1.17%, the same congestion e?ect observed in
the case of the colombian data.
I describe these adjustment costs and the production process using the model
from the previous chapter to understand the e?ect on the factor adjustment dy-
namics, comparing the results with the ones in the previous chapter. Overall, the
higher frequency of the data and the particularities of the ?rm help to understand
the nature of the adjustment costs observed at the ?rm level.
viii
TABLE OF CONTENTS
List of Figures xi
List of Tables xii
1 An Empirical Model of Factor Adjustment Dynamics 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Factor Adjustment: An Exploration of the Facts from the Micro-data 8
1.2.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.2.2 Basics About Factor Adjustment: Distributions and Correla-
tions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.2.3 Factor Adjustment Interrelation: Dynamic Dependence . . . . 22
1.2.4 The Role of Heterogeneity . . . . . . . . . . . . . . . . . . . . 25
1.3 A Dynamic Model of Firms’ Factor Adjustment . . . . . . . . . . . . 32
1.3.1 Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
1.3.2 Analysis of the Model . . . . . . . . . . . . . . . . . . . . . . 38
1.4 Capital and Labor Adjustment: A Numerical Analysis of the Pro-
posed Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
1.4.1 Numerical Methods . . . . . . . . . . . . . . . . . . . . . . . . 45
1.4.2 About the Parameters: Estimation and Calibration . . . . . . 47
1.4.3 Decision Rules for Capital and Employment Adjustment . . . 50
1.4.4 Congestion E?ects and Adjustment Costs: A Simulation ex-
ploration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
1.5 Structural Estimation of the Adjustment Cost Parameters . . . . . . 69
1.5.1 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
1.5.2 Adjustment Costs Parameters: Fitting the Data . . . . . . . . 71
1.5.3 Non-formal Tests of Goodness of Fit . . . . . . . . . . . . . . 74
1.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
2 Costs of Adjusting Production Factors: The Case of a Glass Mould Company 80
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
2.2 Description of the ?rm and the production process . . . . . . . . . . . 83
2.2.1 History of Moldes Medellin . . . . . . . . . . . . . . . . . . . . 83
2.2.2 The Production Process . . . . . . . . . . . . . . . . . . . . . 85
2.3 Data: Production process, Factor Adjustment Dynamics and Adjust-
ment Costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
2.3.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
2.3.2 A First look at the Production and Factor Adjustment Dynamics 87
2.3.3 A Description and Calculation of the Adjustment Costs faced
by the Company . . . . . . . . . . . . . . . . . . . . . . . . . 93
2.4 How Well the Model from Chapter One Can ?t this Particular Firm? 100
2.4.1 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
2.4.2 Calibration/Estimation of the Parameters . . . . . . . . . . . 104
2.4.3 Simulations Results . . . . . . . . . . . . . . . . . . . . . . . . 109
ix
2.5 Conclusions and Future work . . . . . . . . . . . . . . . . . . . . . . 111
3 Conclusions and Final Thoughts 114
1 Appendix Chapter 1: Complementary Analysis of the Variables Around
Spikes in Capital and Employment 119
x
LIST OF FIGURES
1.1 Factor Adjustment for a Particular Firm from the Colombian Census
of Manufacturing Firms. . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.2 Distributions of Factor Adjustment. Percentage of observations (y-
axis) in a range of adjustment (x-axis) . . . . . . . . . . . . . . . . . 14
1.3 Distribution of Factor Adjustment in High and Low Capital Intensive
Firms. % of observations (y-axis) in a range of adjustment (x-axis) . . 27
1.4 Value functions: lateral view, labor. . . . . . . . . . . . . . . . . . . . 52
1.5 Decision rules. All costs in K,L. . . . . . . . . . . . . . . . . . . . . . 54
1.6 Decision rules. Comparison among Adjustment costs. Low shock. . . 54
1.7 Decision rules. Comparison among Adjustment costs. Intermediate
shock. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
1.8 Decision rules. Comparison among Adjustment costs. High shock. . . 55
1.9 Time Series: All Costs Present. . . . . . . . . . . . . . . . . . . . . . 58
1.10 Time Series: Investment Rate, Adjustment Costs Comparison . . . . 58
1.11 Time Series: Labor Growth, Adjustment Costs Comparison . . . . . . 59
1.12 Labor and Capital Adjustment Levels. Intermediate Shock, High and
Low values for Capital and Labor . . . . . . . . . . . . . . . . . . . . 60
1.13 Labor and Capital Adjustment Levels. Intermediate Shock, Mix of
High and Low values for Capital and Labor . . . . . . . . . . . . . . 61
1.14 Distributions of Factor Adjustments for the Simulated Series. Per-
centage of observations (y-axis) in a range of adjustments (x-axis). . . 75
2.1 Production Factors Series . . . . . . . . . . . . . . . . . . . . . . . . 89
2.2 Production Factors Adjustment . . . . . . . . . . . . . . . . . . . . . 90
2.3 Setup Costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
2.4 Cost Shares . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
2.5 Residual Production Function . . . . . . . . . . . . . . . . . . . . . . 108
xi
LIST OF TABLES
1.1 Distribution of factor adjustment(%) . . . . . . . . . . . . . . . . . . 16
1.2 Factor adjustment contemporaneous correlation . . . . . . . . . . . . 18
1.3 Correlations among incidence of episodes (dummies for inaction/spikes) 19
1.4 Probability of inaction/adjustment conditional on Inaction/adjustment
of the other factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
1.5 Dynamic relations in factor adjustment . . . . . . . . . . . . . . . . . 23
1.6 Factor adjustment contemporaneous correlation: Low Capital Inten-
sive Firms (Lower quartile in
K
L
ratio) . . . . . . . . . . . . . . . . . . 26
1.7 Factor adjustment contemporaneous correlation: High Capital Inten-
sive Firms (Upper quartile in
K
L
ratio) . . . . . . . . . . . . . . . . . 26
1.8 Probability of inaction/adjustment conditional on Inaction/adjustment
of the other factor: Low Capital Intensive Firms . . . . . . . . . . . . 28
1.9 Probability of inaction/adjustment conditional on Inaction/adjustment
of the other factor: High Capital Intensive Firms . . . . . . . . . . . 29
1.10 Dynamic relations in factor adjustment: Low Capital Intensive Firms 30
1.11 Dynamic relations in factor adjustment:High Capital Intensive Firms 31
1.12 Parameters Adjustment Costs . . . . . . . . . . . . . . . . . . . . . . 50
1.13 Basic simulated statistics . . . . . . . . . . . . . . . . . . . . . . . . . 66
1.14 Correlation(
I
K
, ?L) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
1.15 Simulated V AR(1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
1.16 Simulated Moments . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
1.17 Calculated Adjustment Cost Parameters . . . . . . . . . . . . . . . . 73
1.18 Probability of inaction/adjustment conditional on Inaction/adjustment
of the other factor: Simulated data . . . . . . . . . . . . . . . . . . . 76
2.1 Basic Statistics. Monthly values . . . . . . . . . . . . . . . . . . . . . 91
2.2 Correlation among the levels of the variables . . . . . . . . . . . . . . 92
xii
2.3 Correlation among the Growth of the variables . . . . . . . . . . . . . 92
2.4 VAR for Growth of the variables . . . . . . . . . . . . . . . . . . . . . 93
2.5 Legal Firing Costs in the Colombian Legislation . . . . . . . . . . . . 97
2.6 E?ect of a Change in the Number of Workers on the Capital Disrup-
tion Adjustment Cost . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
2.7 Adjustment Cost Parameters . . . . . . . . . . . . . . . . . . . . . . . 105
2.8 Production Function Estimates . . . . . . . . . . . . . . . . . . . . . 107
2.9 Benchmark Moments (Monthly Values From the Data) . . . . . . . . 109
2.10 Simulations Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
xiii
Chapter 1
An Empirical Model of Factor Adjustment Dynamics
1.1 Introduction
It was not until a decade ago, with the availability of new ?rm-level datasets,
that lumpiness and infrequent adjustment in capital and labor
1
could be observed
in ?rms’ behavior; this was in stark contrast to the smooth adjustment shown in
aggregate data for those factors
2
. At the same time, models attempting to explain
the aggregate behavior of these variables had to be revised to account for the mi-
croeconomic facts if models with micro foundations were to be useful in terms of
policy and predictions at the ?rm and aggregate levels. However, previous studies of
adjustment have tended to analyze one factor at a time, which has made it di?cult
to understand the joint adjustment of capital and labor at the micro level and its
macroeconomic implications.
Looking for a better understanding of ?rms’ factor adjustment behavior, this
paper analyzes to what extent it is important to consider joint capital and labor de-
cisions at the ?rm level from an empirical and theoretical point of view. Speci?cally,
1
The term labor is used in this paper to indicate the number of workers which can also be
referred to as employment.
2
In order to clarify terms, lumpiness refers to coexistence of inaction and large adjustments with
little in between; this is the opposite of a smooth adjustment that occurs when the adjustment
is done in a continuous way. The main distinctive feature between them is the existence of long
inaction periods and large adjustments in the case of lumpy adjustments and the non existence of
inaction periods in the case of smooth adjustments; note, however, that one could observe large
and smooth adjustments at the same time.
1
it asks whether ?rms adjust labor independently of capital, if there exist interaction
in this adjustment and what the nature of this interrelation is. Although capital
and labor movements are the main focus, I also incorporate materials and energy
adjustments into the analysis.
The implicit view in the early investment
3
and labor demand literature was
that pro?t-maximizing ?rms would adjust factor demand constantly in response to
shocks in demand and productivity. It was natural to think that way since the
aggregate series were smooth, and the literature instead focused on issues such as
the role of the cost of capital, the serial correlation in investment and the aggregate
dynamics of labor demand. Recent ?rm-level empirical studies have shown, however,
that ?rms do not adjust as often as they should under convex costs, and when they
do adjust, this response comes often simultaneously from adjustment in several
margins. Moreover, new emerging evidence, such as that presented in this paper,
shows that capital and labor adjustment distributions have fat tails, a mix of small
and large adjustments and a mass point around the inaction region, which has been
taken as evidence of lumpy adjustment
4
; the recent evidence also shows that their
adjustments are interrelated
5
.
Subsequent models of investment and labor demand made e?orts to incor-
porate this emerging empirical evidence and specially the lumpy and infrequent
3
See Hall and Jorgenson (1967), Tobin (1969), Abel (1979) and Hayashi (1982) among others.
4
Davis and Haltiwanger (1992), Davis et al. (1996), Caballero et al. (1995, 1997) and Cooper
and Haltiwanger (2005), have shown the mentioned patterns in the separate analysis of labor and
capital adjustment distributions using micro-level data. Rust (1987) shows the lumpy nature of
the adjustment for a single agent in the case of machine replacement.
5
Nadiri and Rosen (1969) using aggregate data and Sakellaris (2004), Eslava et al. (2004) and
Narazani (2004), using micro data, ?nd that the adjustment processes for capital and labor are
interrelated.
2
adjustment
6
. An important point they neglect, however, is that ?rms adjust not
just along one but along several margins, particulary for capital and labor. The few
studies that consider capital and labor together do so at a very aggregate level, which
does not exploit the rich and heterogeneous adjustment observed at the micro level
and does not account for the correlation among adjustments
7
. As a consequence,
estimated parameters governing the adjustment of capital and labor in response to
shocks may be biased
8
.
The lack of understanding of factor adjustment at the ?rm level has important
implications. For example, increasing ?ring costs may a?ect capital formation. Or
a policy aiming to increase investment may not be as e?ective as expected if labor
hiring/?ring costs are una?ected or if the elasticity of factor use with respect to its
relative price is not properly estimated. Non-convexities arising from adjustment
costs, understood as infrequent and lumpy movements, may lead to very di?erent in-
dustry responses to public policies aimed at job creation, destruction or investment.
There is a need to estimate those responses in a consistent and realistic way, not
6
These facts were incorporated in the early theoretical literature as models of infrequent ad-
justment, while later models also attempted to reproduce the lumpiness in such adjustments. See
for example Dixit and Pindyck (1994), Abel and Eberly (1994, 1998) in the case of investment
and Hamermesh (1989), Hamermesh and Pfann (1996) in the case of labor. More recent work
includes Cooper and Haltiwanger (2005) and Cooper et al. (2004), who consider also the small
and smooth adjustments present in such distributions in conjunction with episodes of large and
infrequent adjustments.
7
At the macro level, see Shapiro (1986), Hall (2004) for analysis of capital and labor adjustment
assuming convex costs . Caballero et al. (1995, 1997), Cooper and Haltiwanger (2005), Cooper et al.
(2004) analyze capital and labor adjustment in a separate way. Rust (1987) analyzes investment
for a single ?rm. Abel and Eberly (1998) model capital and labor adjustment but do not take into
account the interactions between them. Rendon (2005) features a model with a simpler adjustment
cost structure, to answer if liquidity constraints restrict job creation.
8
The biases arise because the models analyze the response of either capital or labor to shocks,
incorporating all the other factor decisions into the shocks. For example, movements in one factor,
such as, capital would a?ect the shock in a labor adjustment model, and the real response of labor
to shocks would be overstated.
3
only for the sake of predicting the e?ects of public policies, but also because the be-
havior of aggregate investment and job creation and destruction is directly a?ected
by the microeconomic response of ?rms to shocks in demand and technology.
In exploring these issues, this paper uses ?rm level data from the Colombian
Annual Manufacturing Census, covering the period 1982 to 1998. This is a unique
data set because it contains ?rm level data on the value of production, energy and
materials, prices for each product and each material used, the number of workers
and payroll and book values of equipment and structures. The existence of ?rm level
prices opens a wide range of empirical possibilities
9
; in this paper they are useful
because they allow the precise identi?cation of technology and demand shocks and
of input factor elasticities and considerably reduce the measurement error in factor
demand due to confusion between prices and quantities
10
.
In line with recent studies, the empirical analysis reveals the mix of small
and large adjustments in the capital and labor adjustment distributions, which
also present fat tails and large inaction periods; the analysis also uncovers their
interrelated nature. In addition to these studies, the analysis reveals the adjustment
patterns in energy and materials and their relation to capital and labor adjustment.
The picture that emerges is that in response to shocks, ?rms adjust capital and labor
in a non-trivial, interrelated way. Firms also adjust energy and materials when they
9
With the existence of ?rm level prices for the whole Census of manufacturing ?rms, issues that
before could not be clearly analyzed because of identi?cation problems or simply because of lack of
data, can be analyzed better. Among them we could mention the comprehensive analysis of price
stickiness or the e?ects of technology shocks in the business cycle.
10
Note that while other studies, dealing with di?erent issues, have used a similar Colombian
dataset, all but Eslava et al. (2004) and Eslava et al. (2005) use a shorter period (up to 1991) and
they do not have price information. I follow Eslava et al. (2004) in the Total Factor Productivity
(TFP) and demand shocks estimation.
4
are hit by demand and technology shocks. This is not surprising if we think that
?rms face a pro?t maximization problem over all inputs. What is interesting is the
observed dynamics of the adjustment.
The data analysis motivates the main contribution of this paper, which is to
propose, analyze and estimate a theoretical model of ?rm behavior that combines
a labor decision problem with a machine replacement problem along with a rich
speci?cation of adjustment costs. None of the previous models in the literature
have been able to explain the interrelation between capital and labor adjustment,
in part because the existence of this type of empirical evidence is very recent and
not complete for all the production factors, and in part because of the di?culty in
the analysis and estimation of such a model (analytically or numerically).
The proposed adjustment cost structure captures key features of the data such
as reductions in output during adjustment (disruption costs), the cost of installing
capital and creating or destroying a job vacancy (?xed costs) and a convex cost com-
ponent introduced to capture the observed mix of smooth and lumpy adjustment
11
.
One of the key features in the model is the presence of interaction e?ects in
the adjustment of capital and labor. Interaction e?ects are precisely de?ned as the
11
An important point not addressed here relates to the current debate about the production fac-
tors’ response to technology shocks. Besides the serious identi?cation issues faced in the literature
trying to estimate technology shocks (where IV methods or other identifying assumptions attempt
to di?erentiate technology shocks from other shocks given the lack of rich enough ?rm level data
and especially of ?rm level prices), previous work has not considered the possibility that, while
adjusting, ?rms decrease production (as it is shown later in this paper), suggesting the presence of
an adjustment cost in productivity shock estimates that may lead to misleading conclusions about
the e?ects of pure technology shocks on factor adjustment. This is an important insight that may
be worth exploring in future work. See for example Shea (1998), Gali (1999), Basu et al. (2004),
Christiano et al. (2003), and Alexopoulus (2004). I thank Martin Eichenbaum for highlighting this
point.
5
extra cost or bene?t
12
of jointly adjusting capital and labor. If the interaction e?ect
is a cost I call it congestion e?ect, and if it is a bene?t I call it complementarity
e?ect. For example, the interaction e?ect may be present as congestion if ?rms
have to train new workers to operate new machines, incurring in this way in an
extra cost; or in the opposite way, the interaction may be present in the form of
a complementarity e?ect, for example, if the incorporation of a new process in a
production plant requires a new physical space for the machines or the workers, and
this space can be shared by them; another example of the congestion e?ect would
be if disruption in the production process occurs while incorporating new workers
and machines simultaneously, incurring production losses that may be greater or
less than if hiring new workers or making new investments independently.
Once the key parameters such as factor elasticities, productivity shocks and
demand shocks are estimated, the theoretical model is compared with the data in
two ways. First, the adjustment cost parameters from the model are arbitrarily cho-
sen in order to give an example of the implications for ?rm behavior. In a second
stage, these adjustment cost parameters are estimated with a minimum distance
algorithm in order to match key moments that comprehensively describe ?rms’ ad-
justment patterns in capital and employment. The decision rules and the time series
implications that emerge from the model are also analyzed. This part of the paper
is the core analytical contribution because it gives an idea of how labor and capital
adjustments are potentially interrelated and how they interact (or not) at the ?rm
12
It is important to note that the model does not restrict this e?ect to be a cost but it also can
be a bene?t. It is the empirical analysis which determines it as a cost.
6
level, depending on the capital to labor ratio a particular ?rm has.
The model is indeed a good representation of ?rm behavior: it is able to
reproduce the mix of smooth and lumpy adjustments in the one hand, and the mix
of large and small adjustments in the other hand observed empirically for capital and
labor. Moreover, the dynamic relationships observed in the data are also reproduced.
The model that best ?ts the data includes the interaction term in the adjustment
costs for capital and labor and it is present as a congestion e?ect, which suggests
that investment in?uences hiring decisions in an important way (and viceversa)
because the extra cost that this joint decision implies. The congestion e?ects are
key, especially to match the contemporaneous correlation between capital and labor
adjustment. It turns out that, according to the model, the type of real rigidity
(represented by the type of adjustment cost the ?rms face) is as important as the
interaction between capital and labor adjustment, which appears as an extra cost
(congestion e?ect). The structural methodology allows me to reject statistically the
existence of ?xed costs and to accept the existence of disruption costs for capital and
labor, the existence of convex costs for capital but not for labor and the existence
of congestion e?ects. Finally, the benchmark model of convex costs, widely used in
the macroeconomic literature, is not able to explain by itself the type of behavior
observed in ?rm investment and dynamic employment demand decisions.
The paper proceeds as follows. Section 2 presents the empirical evidence,
which is descriptive and with minimal structure imposed on the data. Section 3
presents the model used to explain the empirical patterns and discusses the adjust-
ment cost assumptions. Section 4 discusses some important numerical issues dealing
7
with the model and analyzes the decision rules that emerge from an illustrative pa-
rameterization of the model. Section 5 recovers the parameters governing the joint
adjustment of capital and labor from the model and carries on some experiments in
order to give an idea of the goodness of ?t in the estimated parameters. Section 6
concludes and gives directions for further research.
1.2 Factor Adjustment: An Exploration of the Facts from the Micro-
data
The ?rst task is to analyze empirically whether capital and labor adjustments
are interrelated. Because the variables of interest are adjustments, I look at the gross
investment rate and at the growth in demand for labor, energy and materials. I start
by showing the distribution of factor adjustments, then presenting basic correlations
among them. Given the low (but statistically di?erent from zero) correlation among
factor adjustments, I analyze the behavior of the variables during large adjustment
and inaction episodes.
13
I use again basic correlations of the incidence of adjustment,
also analyzing the conditional probability of inaction or adjustment.
14
I also run a
VAR(1) for factor adjustments to get a sense of the magnitude of the dynamic
interactions between factor adjustments at the ?rm level for the whole range inputs.
Finally, I explore if di?erent types of ?rms exhibit di?erent patterns in the capital
and labor adjustments. Speci?cally, I divide Census of Manufacturing ?rms in
high and low capital intensive ?rms. The analysis reveals that the adjustment
13
The criteria used to de?ne inaction and large episodes is discussed later in the paper.
14
To give continuity to the argument in the main text, I present in the appendix an additional
analysis of the interrelations between labor and capital during periods of large adjustments. In
particular, I use a variation of the methodology of Sakellaris (2004) and Letterie et al. (2004) to
analyze the interrelated adjustment between capital, labor, energy and materials.
8
distributions present very similar patterns across ?rms and the contemporaneous
correlations keep the signi?cance and low variation in all types of ?rms; the dynamics
of adjustments, however, is heterogenous depending on the ?rms characteristics, at
least in the dimension considered here. Even if this analysis is beyond the scope
of the present paper, it suggests that it is worth to explore more the di?erences by
sector in capital and employment adjustments.
These empirical exercises are built around the issue of interest, which is the
interrelation in capital and employment adjustment. The distributions show a mix
of small and large adjustments of capital and labor with large inaction periods at
the ?rm level; this has been interpreted in the literature as lumpy adjustment, but
it misses the point that infrequent adjustment periods can be followed by smooth
and small adjustment periods. In the case of materials and energy, the adjustment
is more continuous, but they show also a mix of small and large adjustments; in
this sense, their adjustment can not be called lumpy as the capital and labor ad-
justment; these distributions also show di?erences in the frequency of adjustment
across factors. This micro evidence is in contrast to the smooth aggregate series that
have been extensively analyzed in the literature. The contemporaneous correlations,
and the analysis of the episodes of large adjustments and inaction, show that these
adjustments indeed have a statistically signi?cant degree of interrelation.
15
The
VAR(1) aims to show that the dynamic interrelation between factor adjustment
holds during all episodes of adjustment, not just spikes, which are important and
15
The analysis of these episodes, found in the appendix, reinforces the view that adjustments are
interrelated, that there is a mix of small and large adjustments and a mix of smooth and lumpy
factor adjustments, and that there exists evidence of adjustment costs based on the observation of
the decrease in productivity and output after the adjustment, especially in the case of capital.
9
also statistically signi?cant.
While the main focus of this paper is the adjustment of capital and labor, I
also consider energy and materials adjustment in order to motivate the assumption
below that these factors are adjusted at no cost. The distributions of adjustment
presented later on justify this claim, as will become clear.
This section is in the same spirit as other recent work showing evidence on
the interrelation between capital and labor adjustment using micro data. Narazani
(2004) focuses on a small subset of large Italian ?rms to study capital and labor ad-
justment. Sakellaris (2004) shows evidence on the interrelation in factor adjustment
in episodes of considerable adjustment in capital and labor. Letterie et al. (2004) an-
alyze this adjustment for Denmark ?rms and Polder and Verick (2004) compare the
adjustment dynamics in Denmark and Germany. Eslava et al. (2004) use the same
dataset used in this paper and employ Caballero, Engel and Haltiwanger’s (1995,
1997) methodology to analyze the nonlinear interrelation between capital and labor
adjustment. None of these studies, however, contain the structural approach and
comprehensive analysis that this paper presents.
One of the most important points to note is that the analysis is carried over
the whole Census of manufacturing ?rms, and not just for a subset as most previous
studies have done. It is also important to note the high quality of the capital
measure, something not common in this type of panel, and the fact that the existence
of prices at the ?rm level reduces measurement error in factor adjustment, a unique
characteristic of this dataset. This initial exploration of the facts is the basis for the
factor adjustment model presented later.
10
1.2.1 Data
The data come from the Colombian Annual Manufacturing Census (AMS)
during the period 1982 -1998. The AMS is an annual unbalanced panel of around
13,000 ?rms per year containing ?rms with more than 10 employees or sales above
a certain limit. It contains the values of production, materials and energy con-
sumption; physical quantities of energy; prices for each product and material used;
production and non-production workers and payroll; and book values of equipment
and structures. I use the panel of pairwise continuing ?rms constructed by Eslava
et al. (2004), which accounts for a total of 2,167 ?rms in the period 1982-1998. I
choose to work with a balanced panel because I do not analyze the e?ects of ?rm
entry or exit. In this section I describe how the variables were constructed. For
more information about the construction of the variables, see Eslava et al. (2004).
Price level indices are constructed for output and materials using Tornqvist
indices. Tornqvist indices are the weighted average of the growth in prices for all
individual products (or materials) generated (used) by the plant. The weights are
the average of the shares in the total value of production (or materials used). More
formally, the index for each plant j producing outputs (or using materials) h in year
t is:
ln P
jt
= ln P
jt?1
+ ?P
jt
with P
j1982
= 100 as the base year, ?P
jt
=
H
h=1
¯ s
hjt
?ln(P
hjt
) representing the
weighted average of growth in prices for all products h, and ¯ s
hjt
=
s
hjt
+s
hjt?1
2
as
the simple average of the share of product (material) h in plant j’s total value of
11
production (materials usage).
Quantities of materials and output are constructed by dividing the reported
value by the prices. Energy quantities and number of workers are reported by the
plants. Investment represents gross investment and is generated from the informa-
tion on ?xed assets reported by the plants. More speci?cally, gross investment is
calculated recursively with the formula
I
jt
= K
NF
jt
? K
NI
jt
+d
jt
??
A
jt
where K
NF
jt
?K
NI
jt
is the di?erence in the value of the ?xed assets reported by plant
j at the end and beginning of year t and d
jt
? ?
A
jt
is the depreciation minus the
in?ation adjustment reported by plant j at the end of year t. In the rest of the
paper, all the variables are in logs unless indicated. The reported growth is the log
di?erence, and the observations are considered outliers if they are greater than 10
(adjustment of 1000%) or lower than -1 (adjustment of -100%).
1.2.2 Basics About Factor Adjustment: Distributions and Correla-
tions
Distributions of Factor Adjustments
Before showing the complete distributions of factor adjustment for the whole Census
of Colombian Firms during the period from 1982 to 1998, it is useful to introduce
the behavior of one particular ?rm during this period. The selected ?rm is from
the food sector and satis?es no particular criteria other than illustrating of how
12
Figure 1.1: Factor Adjustment for a Particular Firm from the Colombian Census of
Manufacturing Firms.
individual ?rms adjust input factors . Figure 1.1 shows the time series behavior
for this ?rm in the case of capital, employment, energy and materials adjustments.
This ?gure illustrate the basic patterns observed in the panel. In particular, for this
?rm there is no negative investment; there exist some periods of inaction in capital
and labor; the ?rm continuously adjusts energy and materials; and there are periods
of large adjustment in all the factors mixed with periods of small adjustment.
Figure 1.2 shows the distribution of factor adjustments for all plants in my
sample. The factors are capital, employment (number of workers), energy and ma-
terials. Table 1.1 summarizes ?gure 1.2. In Table 1.1, the inaction zone is de?ned
as an adjustment lower than 1% in absolute value, while the spikes are de?ned as
13
Figure 1.2: Distributions of Factor Adjustment. Percentage of observations (y-axis)
in a range of adjustment (x-axis)
Gross Investment Rate
0
5
10
15
20
25
-
0
.
5
-
0
.
4
-
0
.
3
-
0
.
3
-
0
.
2
-
0
.
1
-
0
0
.
0
6
0
.
1
4
0
.
2
2
0
.
3
0
.
3
8
0
.
4
6
I/K
%
o
f
o
b
s
e
r
v
a
t
i
o
n
s
Wks growth
0
5
10
15
20
25
-
0
.
5
-
0
.
4
-
0
.
3
-
0
.
3
-
0
.
2
-
0
.
1
-
0
0
.
0
6
0
.
1
4
0
.
2
2
0
.
3
0
.
3
8
0
.
4
6
Workers growth (log difference)
%
o
f
O
b
s
e
r
v
a
t
i
o
n
s
Energy Growth
0
5
10
15
20
25
-
0
.
5
-
0
.
4
-
0
.
3
-
0
.
3
-
0
.
2
-
0
.
1
-
0
0
.
0
6
0
.
1
4
0
.
2
2
0
.
3
0
.
3
8
0
.
4
6
Energy growth (log difference)
%
o
f
o
b
s
e
r
v
a
t
i
o
n
s
Materials Growth
0
5
10
15
20
25
-
0
.
5
-
0
.
4
-
0
.
3
-
0
.
3
-
0
.
2
-
0
.
1
-
0
0
.
0
6
0
.
1
4
0
.
2
2
0
.
3
0
.
3
8
0
.
4
6
Materials Growth (log difference)
%
o
f
O
b
s
e
r
v
a
t
i
o
n
s
adjustments above 20% in either direction.
16
An observation is de?ned as the adjust-
ment of ?rm j in year t. I will analyze these distributions in terms of the frequency,
symmetry and size of the adjustments.
With respect to the size of adjustments, there is no standard de?nition for
large or small adjustments, but a visual inspection of the capital and labor adjust-
ment distributions shows a combination of small and large values with a mass point
16
The inaction and spike zones are de?ned with this arbitrary criteria to give a sense of “small”
and “large” adjustment and to be consistent with previous literature on factor adjustment.
14
around the inaction region(i.e. zero adjustment). The existence of these mass points
around zero adjustment and the fat tails of the distributions can be interpreted as
lumpy adjustment; for example, in table 1.1, the lumpy pattern can be observed in
the proportion of the adjustments above 20%, considering this number as a large
adjustment indicator, compared to the proportion of the adjustments lower than
1% in absolute value, considering this as the inaction region; in the other hand, the
smooth adjustment can be observed in the proportion of adjustments below 20%
and above the inaction region. The materials and energy adjustment distributions
fail to be considered lumpy under this criteria since the percentage of observations
in the inaction region is not very high; what these distributions show is more a
continuous adjustment with jumps in the size of the adjustments.
Perhaps a more standard measure of how many extreme observations are ob-
served in a distribution is the excess kurtosis. In the case of input factor adjustments,
all distributions have large excess kurtosis, indicating that many observations are
far away from the mean.
17
Speci?cally, excluding outliers greater than 10 in each
distribution (which is an adjustment of 1000%) the excess kurtosis measures are 59,
35, 11 and 92 for capital, employment, materials and energy adjustment respectively.
Excluding the outliers greater than 2 (adjustment of 200%) the excess kurtosis mea-
sures remain large and equal to 7.65, 7.96, 2.2 and 3.85, respectively. These numbers
indicate fat tails in the distributions of adjustment and a clear lumpy adjustment
pattern for capital and labor because of the existence of a mass point around the
17
The normal distribution has an excess kurtosis of zero. The fatter the tails of a distribution,
the bigger the excess kurtosis.
15
Table 1.1: Distribution of factor adjustment(%)
I
K
?L
L
?m
m
?e
e
Inaction (abs
< 1%) 18.9 13.4 3.2 5.6
Positive Spike (y > 20%) 29.8 11.6 28.4 23.7
Negative Spike (y < 20%) 1.8 11.1 18.8 15.8
?(y, y
?1
) 0.025 -0.057 0.0 -0.298
Number of Obs 24467 34243 31977 34597
inaction region; in the case of materials and energy, as it was said before, it indicates
the existence of large adjustments but not of a lumpy pattern since there is no mass
point around the inaction region.
With respect to the symmetry of the adjustments, ?gure 1.1 suggests that the
investment distribution is very asymmetric: there is very little negative investment.
This suggests irreversibility of capital in Colombia. The labor adjustment distrib-
ution is much more symmetric. Putting together those two distributions, we can
conclude that it is easy for ?rms to adjust employment negatively but not capital,
perhaps because of di?erences in the adjustment costs involved for each input fac-
tor (the selling price of capital is lower than the buying price) due in turn to the
physical nature of the factors re?ecting the irreversibility of capital. Materials and
energy distributions are also symmetric, though not as much so as the employment
adjustment distribution.
With respect to the frequency of adjustments, we observe that ?rms often leave
capital and employment essentially ?xed, but adjust materials and energy more fre-
quently. This is the justi?cation for the assumption later in the model that materials
and energy are not subject to adjustment costs. Firms adjust them in an almost
16
continuous fashion. The evidence for Colombia is in line with the evidence for the
U.S. using the LRD (Longitudinal Research Database), where lumpiness in capital
and employment is also present together with signi?cant periods of smooth adjust-
ment. This evidence alone suggests the presence of adjustment costs and, as many
others have pointed out, may indicate (S,s) behavior in capital and employment
adjustment.
Summarizing the information observed in the distributions, we can conclude
that: (i) the distributions of input factor adjustment have fat tails; (ii) the invest-
ment distribution is asymmetric, showing a large degree of irreversibility, while the
labor adjustment distribution is highly symmetric; (iii) Capital and employment ad-
justments are infrequent (large mass point around zero adjustment) but materials
and labor adjustment are much more frequent (no mass points around zero). Points
(i) and (iii) signal the existence of lumpiness in the adjustment of capital and labor
due to non-convex costs in capital and labor adjustment; and (iv) small and large
values coexist in the distributions of adjustment for all the factors.
Correlations of Factor Adjustments
Table 1.2 shows the contemporaneous correlations among factor adjustments
18
The
highest correlation coe?cients are for employment and materials growth, followed
by the correlations between materials and energy growth and employment and en-
ergy growth. The correlation between the investment rate and employment growth
18
The correlations are calculated regressing adjustment on time dummies to take out business
cycle e?ects, and I consider only the residuals which re?ect ?rm-level shocks. Another interesting
possibility would be to consider the business cycle e?ects as well, but this is left for future work.
17
Table 1.2: Factor adjustment contemporaneous correlation
I
K
?L
L
?m
m
?e
e
I
K
1
?L
L
0.057 1
?m
m
0.026 0.175 1
?e
e
0.041 0.107 0.147 1
All correlations are statistically
di?erent from zero at 1% signi?cance
is small but nonzero. All the correlations are statistically di?erent from zero. More-
over, even if the correlation coe?cient for capital and employment growth hides a
considerable amount of sectoral heterogeneity, many sectors
19
share a similar coe?-
cient, which is near the one reported in Table 1.2.
The contemporaneous correlations give a sense that capital and employment
adjustment periods are interrelated. However, given the low correlation between
capital and employment, it is worth analyzing the correlation of adjustment during
inaction periods, during spike episodes and during a combination of both.
20
The
questions here are whether inaction or spikes in employment are correlated with
inaction or spikes in capital, and whether inaction or spikes in one factor increase
the probability that ?rms adjust the other factor. Equivalently, we could ask if ?rms
stagger capital and labor adjustments. If ?rms stagger, we would observe a negative
correlation between the incidence of adjustments in investment and employment
and an increase in the probability of adjustment conditional on inaction in the
19
The sectors present in the data are Food, Drinks and Beverages, Tobacco, Textiles, Wood,
Paper, Chemicals and Rubber, Oil, Glass and Non-metallic, Metals and Metal products, Machinery
and others. Of these, just the Oil sector, the Drinks and Beverages sector and the Tobacco sector
have a negative correlation coe?cient.
20
The inaction and spike episodes are de?ned as above: less than 1% in absolute value for
inaction and more than 20% in absolute value for the spikes.
18
Table 1.3: Correlations among incidence of episodes (dummies for inaction/spikes)
Investment Rate:
I
K
Employment Growth:
?e
e
Dummies for: Inaction Spike Pos Spike Inaction Spike Pos spike
Inaction 1
I
K
Spikes -0.335* 1
Pos. Spike -0.241* 0.719* 1
Inaction 0.081* -0.035* -0.030* 1
?e
e
Spike 0.006 0.030* 0.006 -0.229* 1
Pos spike -0.041* 0.055* 0.024* -0.231* 0.361* 1
Neg spike 0.040* 0.01 0.026* -0.216* 0.364* -0.325*
The correlations are among 0/1 dummies during large adjustment episodes
*: statistically di?erent form zero at 1% of signi?cance. Dummies for inaction
are de?ned as 1 if abs(x) < 0.01 and dummies for spikes are de?ned as 1 if x > 0.2
other factor.
To further explore these issues, and to characterize ?rms’ adjustments dur-
ing inaction and spike episodes, the rest of the subsection explores the correlation
between the incidence of zeros and spikes in capital and employment and the prob-
abilities of inaction/spike in one factor conditional on inaction/spike in the other
factor.
21
Even though the de?nition of inaction and spikes given above may be some-
what arbitrary and may be capturing adjustments that are not small or large for
certain types of capital,
22
it is useful to characterize the behavior of capital and em-
ployment around “small” and “large” episodes of adjustment. Table 1.3 shows the
correlation of the incidence of inaction and spikes in investment and employment
adjustment.
21
The appendix has a more extensive analysis of the behavior of several variables around inactions
and spikes in capital and employment adjustment.
22
For example, many ?rms need small tools important for production which signal a positive
investment but lower than 1% of their capital stock.
19
After a closer look at table 1.3, several facts emerge
23
.First, the correlation
between investment and employment adjustment is positive and higher during inac-
tion times than during spike times for both factors. Moreover, the only statistically
signi?cant correlation during spikes in employment is with spikes in investment, due
to positive employment spikes and not negative ones. Also, the negative correlation
between the incidence of positive spikes in employment and inaction in capital sug-
gests that after a positive spike in employment, there is inaction in capital. All this
would suggest that during some periods, ?rms increase capital and employment in
large amounts at the same time, and have inaction periods for the two factors after
the adjustment.
There is also a positive correlation between negative spikes in employment and
both inaction and positive spikes in investment. This suggests that sometimes ?rms
substitute one factor for another (increasing capital and decreasing employment)
and at other times ?rms choose to adjust only employment down given the high
irreversibility of capital. Table 1.3 suggests that capital and labor tend to move
together during inaction and spike episodes.
Table 1.4 shows the results of estimating four di?erent logit models, each one
for investment and employment and inaction and spikes respectively, where the
dependent variable is the probability of adjustment or inaction in one factor and
the independent variables include the adjustment and inaction
24
status in the other
23
Two clarifying points: ?rst, observe that the correlation between Inaction and spikes episodes
is not -1 because these episodes are not consecutive and instead there exist adjustments larger than
1% and smaller than 20% in between; second, the “spikes” are di?erent from “positive spikes” in
the sense that they include negative spikes.
24
both dummies are included at the same time
20
factor. The logit estimation includes controls for ?rm-speci?c variables such as Total
Factor Productivity (TFP) and demand shocks
25
and the adjustment of energy and
materials. It is important to control for the shocks in this context since they lessen
the chances that the comovement between employment and investment is merely
due to an omitted third factor. Moreover, controlling for the TFP and demand
shocks identify the movements in employment and capital as dependent not only
from shocks but from other sources, in this case interpreted later as adjustment
costs.
From table 1.4, it can be observed that the probability of inaction in invest-
ment increases if there is inaction in employment. The same is true in the case of
employment, but the e?ect is not statistically signi?cant. At the same time, the
probability of an investment spike increases if there is an employment spike, and
the probability of an employment spike increases when there is an investment spike.
These numbers con?rm the conclusions drawn from table 1.3: capital and labor tend
to move together. The probability of inaction in employment decreases when there
is an investment spike. The other e?ects are not statistically signi?cant. All these
numbers suggest that, on the one hand, when there is a large adjustment in either
capital or employment, it is more likely that ?rms are having large adjustments in
both factors; on the other hand, when ?rms do not adjust employment, it is more
likely that they do not adjust capital, but when ?rms do not adjust capital, it does
not mean necessarily that they do not adjust labor.
As further evidence of the interrelation of capital and labor adjustment, other
25
The estimation of these shocks is explained later in the paper in the calibration section.
21
Table 1.4: Probability of inaction/adjustment conditional on Inaction/adjustment
of the other factor
Investment Employment growth
Variable x P(inaction/x) P(Spike/x) P(inaction/x) P(Spike/x)
0.057 0.012
Inaction
(0.071) (0.061)
Investment
-0.11† 0.205**
Spike
(-0.06) (0.048)
0.143* -0.033
Employment
Inaction
(0.067) (-0.058)
Growth -0.033 0.208**
Spike
(-0.059) (0.046)
Observations 12864 17055 12410 14459
†/*/** signi?cant at 10%, 5% and 1%. TFP, demand shocks and year e?ects in regression
Dummies for inaction are de?ned as 1 if abs(x) < 0.01 and dummies for spikes are de?ned as 1 if
x > 0.2
interesting results on the dynamic behavior of the input factors around episodes of
spikes and inaction in capital and labor are reported in the appendix. In particular,
there is evidence that TFP and output fall after periods of adjustment, especially
in the case of capital, suggesting a cost in terms of foregone pro?ts.
The analysis in tables 1.3 and 1.4 examines the case of large changes in capital
and labor. A natural question that follows is whether this analysis extends to all
adjustments in a dynamic context. I discuss the basic empirical approach for this
problem next.
1.2.3 Factor Adjustment Interrelation: Dynamic Dependence
In this subsection, I present the coe?cients of a simple VAR with one lag,
intended to describe how ?rms’ factor adjustments are dynamically interrelated.
22
The VAR variables of interest are gross investment and growth in employment,
energy and materials. The coe?cients and their statistical signi?cance are quite
robust to several controls. The reported VAR is estimated controlling for shocks in
demand and productivity
26
and for year e?ects. Table 1.5 shows the results for this
estimation procedure.
Table 1.5: Dynamic relations in factor adjustment
I
K
?L/L ?m/m ?e/e
-0.008 -0.008 0.023 -0.038
(
I
K
)
?1
0.006 (0.003)** (0.004)** (0.006)**
0.037 -0.147 0.049 0.091
(
?L
L
)
?1
(0.017)* (0.007)** (0.012)** (0.017)**
-0.007 0.024 -0.247 0.036
(
?m
m
)
?1
0.01 (0.004)** (0.007)** (0.010)**
0.013 0.009 0.006 -0.345
(
?e
e
)
?1
-0.007 (0.003)** (0.005)* (0.007)**
Observations 17653 17653 17653 17653
R-squared 0.03 0.07 0.26 0.23
Standard errors in parentheses; **/* signi?cant at 1% and 5%;
year e?ects and shocks in regression
Table 1.5 shows that an increase in labor demand signals a posterior investment
episode (the coe?cient of the e?ect of lagged labor growth on investment is positive
and statistically signi?cant). Moreover, the coe?cient of lagged investment in the
labor equation is negative and signi?cant. F-tests for the cross coe?cients of labor
and capital in this VAR with 4 variables and in a simpler version with just capital
and employment were run to verify Granger causality. Both coe?cients are di?erent
from zero, which does not give much more information since it is not conclusive about
which one causes the other.
26
Later in the paper I explain how these shocks are estimated using the price information
23
It is important to note that the other factors exhibit large coe?cients and
small standard errors, indicating that the ?rms use several margins of adjustment
in capital, labor, materials and energy. Moreover, the diagonal elements (the auto-
correlation) for all factors are negative, suggesting that if ?rms adjust in one period
it is very likely that either they will not do so the next period or that they will adjust
in the opposite direction. The negative autocorrelation in the VAR is a re?ection
of the patterns from the distribution of adjustments. Capital is the factor with
smaller negative autocorrelation in adjustment, which may signal inaction in the
following periods since the distributions show a mass around zero and the negative
coe?cient signals inaction or adjustment in the opposite direction, as mentioned
above. Materials and energy are the factors with higher negative autocorrelation in
adjustment, which may signal instead free adjustment in the opposite direction the
following period.
An interesting point with respect to the autocorrelation coe?cient in the in-
vestment rate is that it changes sign when controlling for individual ?rm charac-
teristics through ?xed e?ects (being positive when ?xed e?ects are not present,
showing a similar coe?cient to that of the simple contemporaneous correlations).
This suggests that unobservable characteristics are important and that the simple
autocorrelation observed before in table 1.2 may be a result of aggregation e?ects
more than ?rm-level e?ects
27
.
27
Exploring this issue even further, this autocorrelation coe?cient for the investment rate main-
tains a consistently positive sign in 2 sectors (Wood and Paper), and maintains the negative sign
in the Chemicals sector for both cases. Moreover, the size of the coe?cient and the statistical sig-
ni?cance is important in 8 out of 12 sectors when controlling for ?xed e?ects, and it is statistically
signi?cant in just 2 sectors when ?xed e?ects are not present, the two with a consistently positive
sign.
24
1.2.4 The Role of Heterogeneity
One question that emerges after the empirical exercises above is if the same
adjustment patterns repeat for all types of ?rms. In particular, this subsection
asks if the interrelation between capital and labor adjustment, if the fat tails and
the mix of small and large adjustments present in the distributions of adjustments,
and if the dynamic correlations among adjustments, are present for all types ?rms.
The characteristic chosen to answer this question is the capital intensity a ?rm has,
dividing the data in high and low capital intensive ?rms. The following empirical
exercises take the high capital intensive ?rms as the ones in the upper quartile of
the capital to labor ratio; the low capital intensive ?rms are in the lower quartile in
that ratio.
Figure 1.3 shows the distributions of adjustments for capital, labor, energy
and materials in the case of low and high intensive capital ?rms. Even if the pat-
terns are the same in both groups, the main di?erence is present in the investment
rate distributions, since low capital intensive ?rms adjust in a more lumpy way: the
percentage of observations with zero adjustment in capital is more than 30%, while
in the case of the high capital intensive ?rms is 15%; in the other hand, the per-
centage of observations with an investment rate of 50% or more is 15% for the low
capital intensive ?rms, while it is less than 10% in the case of high capital intensive
?rms. In the case of labor, materials and energy adjustment, they are very similar.
Based on these distributions of adjustments, we can conclude that there is not much
heterogeneity and that the patterns of interest observed in the previous sections are
25
Table 1.6: Factor adjustment contemporaneous correlation: Low Capital Intensive
Firms (Lower quartile in
K
L
ratio)
I
K
?L
L
?m
m
?e
e
I
K
1
?L
L
0.063* 1
?m
m
0.031 0.170* 1
?e
e
0.019 0.078* 0.093* 1
*signi?cant at 1%
Table 1.7: Factor adjustment contemporaneous correlation: High Capital Intensive
Firms (Upper quartile in
K
L
ratio)
I
K
?L
L
?m
m
?e
e
I
K
1
?L
L
0.039 1
?m
m
0.032 0.143 1
?e
e
0.079 0.103 0.139 1
All correlations are statistically
di?erent from zero at 1% signi?cance
very similar across ?rms, suggesting adjustment costs in capital and labor adjust-
ment for all types of ?rms, perhaps with a higher in?uence of non-convexities(i.e.
disruption and ?xed costs in the sense explained later as opposite to convex costs)
in the case of ?rms with a low capital to labor ratio.
Tables 1.6 and 1.7 show the contemporaneous correlations among factors for
low and high capital intensive ?rms respectively. The most important point these
tables show is that the correlation in capital and labor adjustment is statistically
signi?cant for both groups and not very di?erent; in this case, we also observe that
both groups are not very di?erent and that heterogeneity is not very important.
This heterogeneity in the contemporaneous correlations is more important
26
Figure 1.3: Distribution of Factor Adjustment in High and Low Capital Intensive
Firms. % of observations (y-axis) in a range of adjustment (x-axis) .
HIGH CAPITAL INTENSITY FIRMS (Upper quartile in K/L ratio)
LOW CAPITAL INTENSITY FIRMS (Lower quartile in K/L ratio)
Gross Investment Rate
0
5
10
15
20
25
30
-
0
.
5
-
0
.
4
-
0
.
3
-
0
.
3
-
0
.
2
-
0
.
1
-
0
0
.
0
6
0
.
1
4
0
.
2
2
0
.
3
0
.
3
8
0
.
4
6
I/K
%
o
f
o
b
s
e
r
v
a
t
i
o
n
s
Wks growth
0
5
10
15
20
25
30
-
0
.
5
-
0
.
4
-
0
.
3
-
0
.
3
-
0
.
2
-
0
.
1
-
0
0
.
0
6
0
.
1
4
0
.
2
2
0
.
3
0
.
3
8
0
.
4
6
Workers growth (log difference)
%
o
f
O
b
s
e
r
v
a
t
i
o
n
s
Energy Growth
0
5
10
15
20
25
30
-
0
.
5
-
0
.
4
-
0
.
3
-
0
.
3
-
0
.
2
-
0
.
1
-
0
0
.
0
6
0
.
1
4
0
.
2
2
0
.
3
0
.
3
8
0
.
4
6
Energy growth (log difference)
%
o
f
o
b
s
e
r
v
a
t
i
o
n
s
Materials Growth
0
5
10
15
20
25
30
-
0
.
5
-
0
.
4
-
0
.
3
-
0
.
3
-
0
.
2
-
0
.
1
-
0
0
.
0
6
0
.
1
4
0
.
2
2
0
.
3
0
.
3
8
0
.
4
6
Materials Growth (log difference)
%
o
f
O
b
s
e
r
v
a
t
i
o
n
s
Gross Investment Rate
0
5
10
15
20
25
30
-
0
.
5
-
0
.
4
-
0
.
3
-
0
.
3
-
0
.
2
-
0
.
1
-
0
0
.
0
6
0
.
1
4
0
.
2
2
0
.
3
0
.
3
8
0
.
4
6
I/K
%
o
f
o
b
s
e
r
v
a
t
i
o
n
s
Wks growth
0
5
10
15
20
25
30
-
0
.
5
-
0
.
4
-
0
.
3
-
0
.
3
-
0
.
2
-
0
.
1
-
0
0
.
0
6
0
.
1
4
0
.
2
2
0
.
3
0
.
3
8
0
.
4
6
Workers growth (log difference)
%
o
f
O
b
s
e
r
v
a
t
i
o
n
s
Energy Growth
0
5
10
15
20
25
30
-
0
.
5
-
0
.
4
-
0
.
3
-
0
.
3
-
0
.
2
-
0
.
1
-
0
0
.
0
6
0
.
1
4
0
.
2
2
0
.
3
0
.
3
8
0
.
4
6
Energy growth (log difference)
%
o
f
o
b
s
e
r
v
a
t
i
o
n
s
Materials Growth
0
5
10
15
20
25
30
-
0
.
5
-
0
.
4
-
0
.
3
-
0
.
3
-
0
.
2
-
0
.
1
-
0
0
.
0
6
0
.
1
4
0
.
2
2
0
.
3
0
.
3
8
0
.
4
6
Materials Growth (log difference)
%
o
f
O
b
s
e
r
v
a
t
i
o
n
s
27
Table 1.8: Probability of inaction/adjustment conditional on Inaction/adjustment
of the other factor: Low Capital Intensive Firms
Investment Employment growth
Variable x P(inaction/x) P(Spike/x) P(inaction/x) P(Spike/x)
0.35 -0.08
Inaction
(0.13)** (0.11)
Investment
0.17 0.06
Spike
(0.13) (0.10)
0.41 -0.06
Employment
Inaction
(0.13)** (0.13)
Growth -0.06 0.16
Spike
(0.11) (0.10)
Observations 3269 3839 2800 3372
†/*/** signi?cant at 10%, 5% and 1%. TFP, demand shocks and year e?ects in regression
Dummies for inaction are de?ned as 1 if abs(x) < 0.01 and dummies for spikes are de?ned as 1 if
x > 0.2
when considering the probability of adjustment given inaction/adjustment in the
other factor. Table 1.8 and 1.9 illustrate this point. None of the coe?cients esti-
mated for the high capital intensive ?rms is statistically signi?cant and many signs
are di?erent to the estimated considering all types of ?rms; for example, for the
high capital intensive ?rms, the probability of inaction in investment decreases with
inaction in employment growth, while it increases in the estimation with all the
?rms; in the same way, the probability of a spike in employment growth increases
with inaction in investment, which is the opposite when. considering all types ?rms
in the estimation. The coe?cients are closer to the obtained for all types of ?rms
in the case of the low capital intensive ?rms and some are statistically signi?cant as
well. We can say from these tables that the low capital intensive ?rms tend to move
more together than in the case of the high capital intensive ?rms.
28
Table 1.9: Probability of inaction/adjustment conditional on Inaction/adjustment
of the other factor: High Capital Intensive Firms
Investment Employment growth
Variable x P(inaction/x) P(Spike/x) P(inaction/x) P(Spike/x)
0.02 -0.20
Inaction
(0.18) (0.15)
Investment
-0.13 0.08
Spike
(0.12) (0.10)
-0.1 -0.12
Employment
Inaction
(0.19) (0.12)
Growth -0.24 0.04
Spike
(0.17) (0.11)
Observations 1898 3520 2612 3034
†/*/** signi?cant at 10%, 5% and 1%. TFP, demand shocks and year e?ects in regression
Dummies for inaction are de?ned as 1 if abs(x) < 0.01 and dummies for spikes are de?ned as 1 if
x > 0.2
In the case of the dynamic correlations, heterogeneity seems to play a more
important role and ?rms seem to show a di?erent behavior. Tables 1.10 and 1.11
show a VAR(1) estimated for low and high capital intensive ?rms respectively. With
respect to the dynamic interrelation between capital and labor adjustment, the only
sign consistent in all the estimations is the e?ect of the lagged investment rate in
the labor adjustment, even if not signi?cant for each subgroup but signi?cant for
all the Census of Manufacturing ?rms. In the case of the e?ect of lagged labor
growth in the investment rate, the high capital intensive ?rms have a slightly higher
coe?cient than that estimated for all the ?rms and it has the same sign, which does
not happen in the case of the low capital intensive ?rms The low capital intensive
?rms present. The other coe?cient look similar in general, but the autocorrelation of
investment rates is positive in contrast to the coe?cient obtained when all the ?rms
29
Table 1.10: Dynamic relations in factor adjustment: Low Capital Intensive Firms
I
K
?L/L ?m/m ?e/e
0.023 -0.002 0.038 -0.135
(
I
K
)
?1
0.037 0.011 0.021 (0.030)**
-0.055 -0.167 0.071 0.083
(
?L
L
)
?1
0.044 (0.013)** (0.025)** (0.035)*
0.002 0.019 -0.281 0.055
(
?m
m
)
?1
0.025 (0.008)* (0.014)** (0.020)**
0.009 0.006 -0.013 -0.412
(
?e
e
)
?1
0.016 0.005 0.009 (0.013)**
Observations 4540 4540 4540 4540
R-squared 0.04 0.1 0.29 0.31
Standard errors in parentheses; **/* signi?cant at 1% and 5%;
year e?ects and shocks in regression
are considered. In general, we can say that the dynamic correlation coe?cients
estimated for the high capital intensive ?rms look more similar to the estimates
considering all the ?rms; this suggests some room to explore with respect to the
dynamic behavior across heterogeneous ?rms.
The empirical evidence presented above indicating the infrequent nature and
the mix of smooth and lumpy adjustment in capital and labor, indicates a dynamic
dependence in these adjustments. There is some heterogeneity in the dynamic rela-
tions and in the case of inaction and large adjustment episodes, but the interrelation
pattern is present across all types of ?rms. In the following section, I set up a model
that aims to explain the patterns observed in the data, in particular, the infrequent
and lumpy adjustments, and the interrelation among factor adjustment. The main
features of the model are the presence of convex and non-convex adjustment costs
in capital and labor (but not in the other factors) and the possibility of mutual
interaction e?ects in the form of congestion (if more costly) or complementarities (if
30
Table 1.11: Dynamic relations in factor adjustment:High Capital Intensive Firms
I
K
?L/L ?m/m ?e/e
0.023 -0.002 0.006 -0.026
(
I
K
)
?1
(0.007)** 0.004 0.007 (0.009)**
0.042 -0.182 0.011 0.044
(
?L
L
)
?1
0.029 (0.015)** 0.028 0.038
0.019 0.032 -0.249 0.06
(
?e
e
)
?1
0.016 (0.008)** (0.015)** (0.021)**
0.01 0.007 0.034 -0.357
(
?m
m
)
?1
0.011 0.006 (0.011)** (0.015)**
Observations 4231 4231 4231 4231
R-squared 0.06 0.08 0.25 0.22
Standard errors in parentheses; **/* signi?cant at 1% and 5%;
year e?ects and shocks in regression
cheaper) in the adjustment process through di?erent adjustment costs if the ?rms
adjust capital and labor independently or at the same time. As stated previously,
non-convexities in the decision problem coming from the adjustment costs cause
jumps or infrequent movements in ?rms’ factors and interaction e?ects are de?ned
as changes in cost due to joint adjustment.
The driving forces of factor adjustment in the model are technology and de-
mand shocks, but not factor price shocks; this is assumed for simplicity. Simplicity
also leads me to assume symmetry in the adjustment costs, an assumption that
can be tested in the data. This assumption seems very plausible in the case of
labor adjustment, as the analysis in the appendix reveals a marked symmetry in
the behavior of all variables around bursts of job creation and destruction. Another
important assumption is the lack of inventories as an adjustment variable. This
could be an argument for using only sectors without signi?cant inventories in the
estimation procedure. Factor price e?ects, inventory adjustments and asymmetry
31
of the adjustment costs are interesting and are left for future work.
1.3 A Dynamic Model of Firms’ Factor Adjustment
This model must capture the existence of small and large adjustments and
the mix of smooth and lumpy adjustments and allow for several margins of factor
adjustment as described in section 2. At the same time, the model must also cap-
ture the observed interrelation between capital and labor adjustment. This section
describes the model and analyzes its main implications. For notation purposes, the
subscript it is dropped, but is implicitly applied to all the variables.
1.3.1 Basics
Demand and Production Function
There is imperfect competition and ?rms face a downward sloping demand
curve
Q
d
=
_
P
X
_
??
(1.1)
where X is a stochastic shock to demand, ? is the price elasticity of demand and P
is the price level.
The production function incorporates capital, labor, materials and energy.
Capital and labor are costly to adjust, while materials, energy and hours
28
per
worker can be adjusted at no cost. In this context, hours can be thought of as a
28
In some range, ?rms adjust employment instead of hours because they pay wage premia for
overtime.
32
form of labor utilization, and while this is not explored in the model, energy is likely
to be correlated with capital utilization. The assumption here is that all ?rms have
the same Cobb-Douglas production function and that elasticities and factor shares
vary by sector
29
. This function does not represent an aggregate production function
but instead the production function of each ?rm. If we were to assume heterogeneity
in the production function, it would introduce too much complexity in the problem
and a separate analysis would have to be done for each ?rm or industry. Since I am
interested here in the average behavior of ?rms, this functional form seems to be
the one that can characterize the greatest number of ?rms. Formally,
Q
s
= Bk
?
(lh)
?
e
?
m
?
= Ak
?
l
?
(1.2)
where ?, ?, ? and ? are the input factor elasticities for capital, labor, energy and
materials, A = Be
?
m
?
h
?
, B is a productivity shock, k is the capital level, l is the
stock of workers, h represents hours per worker, e is energy consumption and m
is the materials level. It is convenient for notation to cluster the terms for hours,
energy, materials and productivity in the term A, since they are optimally chosen
period by period in a static maximization problem and there are no intertemporal
links in their case.
Revenue Function and pro?t
Putting together (1.1) and (1.2) we get the revenue function:
R(¯ z, k, l) = ¯ zk
ˆ
?
l
ˆ µ
(1.3)
29
In future work I plan to explore the role of heterogeneity in the elasticities.
33
where: ¯ z = XA
(
1?
1
?
)
,
ˆ
? = ?
_
1 ?
1
?
_
, ˆ µ = ?
_
1 ?
1
?
_
. This type of revenue func-
tion is used by most of the literature because of the lack of ?rm-level information
on prices. It has a demand component that is hard to identify separate from the
technology shock, even if estimated at the ?rm-level. For the Colombian Census
of Manufacturing, however, ?rm-level prices are observed. In equation(1.3), ?rms
implicitly account for the e?ects of their input choices on output prices when maxi-
mizing pro?t. The existence of ?rm-level prices allowed Eslava et al. (2004) to obtain
arguably unbiased estimates of the input elasticities and the elasticity of demand,
which I utilize in this paper.
Before de?ning the ?rm’s intertemporal decision problem, it is useful to de?ne
the pro?t level. Pro?t incorporates the cost of all the inputs, including the adjust-
ment cost which will be de?ned more formally later in this section. For now, pro?t
is given by ?(z, l
?1
, l, k, k
) = zk
?
l
µ
?w(l) ?C(z, l
?1
, l, k, k
) where w(l) is the pay-
ment to employment, C(•) is the adjustment cost, z is a term that incorporates the
technology and demand shocks, together with materials and energy price shocks.
Note that the input factor elasticities are given by ? =
ˆ
? ? M and µ = ˆ µ ? N, where
M and N are terms that incorporate the elasticities of materials and energy coming
from the static optimal ?rm choice for hours, materials and energy.
30
30
Without this simplifying notation, the complete expression including materials and energy
would be ?(•) = ¯ zk
ˆ
?
l
ˆ µ
?l(w
0
+ w
1
h
?
) ?C (z, l
?1
, l, k, k
) ?p
e
e ?p
m
m. Note the functional form
assumed in the wage equation representing a base payment plus a payment for the hours, where
? is the hours wage elasticity. The main di?erence in both equations is the term for the shocks,
¯ z, and the explicitness of the energy and material prices, p
e
e ? p
m
m.. In the text, the term z
captures all of them since the ?rm solves a static optimization problem in energy and materials
every period that can be characterized in the term z.
34
Firms’ Decision Problem
I start by discussing the timing of the decisions and the outcomes.
31
Firms
choose employment taking into account the employment level in the previous period.
Newly hired workers become productive in the same period. However, new invest-
ment becomes productive only in the next period. In this sense there is a “time to
build” for capital but not a “time to hire” for employment. Firms also chose hours,
energy and materials and can adjust them at no cost. Formally, the ?rm’s problem
is given by:
32
V (z, k, l
?1
) = max
k
,l
_
?(z, l
?1
, l, k, k
) + ?
_
V (z
, k
, l)f(z
/z)dz
_
= max
k
,l
{zk
?
l
µ
?w(l) ?C(z, l
?1
, l, k, k
)
+?
_
V (z
, k
, l)f(z
/z)dz
} (1.4)
where I = k
? (1 ??) k represents investment and ? represents depreciation. C(•)
is the cost of adjustment, which takes di?erent parameter values depending on
whether the ?rm adjusts employment, capital or both. ? is the discount factor
and the integral term represents the expected value of the ?rm subject to shocks z.
This shock distribution f(z
/z) includes the joint distribution of the demand and
productivity shocks h(x
/x) and g(A
/A) respectively. I assume these shocks are
independent.
33
31
The model proposed is similar in several dimensions to the ones used by Abel and Eberly
(1998), Cooper et al. (1999), Cooper and Haltiwanger (2005) and Cooper et al. (2004).
32
The notation implicitly states that ?rms optimally choose energy, materials and hours in a
static maximization problem. These values are embedded in the term z.
33
This assumption would not hold if the productivity shocks were not idiosyncratic but instead
common, since in this case TFP would be correlated with demand. Since the estimations of the
shocks in this paper take out the aggregate e?ects, this e?ect is mitigated. This assumption
has been used before by Syverson (2005) to estimate production functions using demand shift
35
The cost of adjustment C(•) potentially includes disruption costs, ?xed costs
and convex costs. The existence of a disruption cost taking the form of lower pro-
ductivity in adjustment periods is justi?ed by the ?ndings of Power (1998) and
Sakellaris (2004). In the appendix, I show that production and TFP decrease when
adjustment takes place, especially after investment spikes. In an additional em-
pirical exercise not shown here, I regressed TFP against a dummy of adjustment
(separately for capital and employment), obtaining a negative and signi?cant co-
e?cient for both factors, giving more support for the inclusion of this disruption
cost. The disruption cost can also be associated with the stochastic adjustment cost
present in Caballero and Engel (1999).
The convex cost term does not have a clear micro-foundation but has been
assumed to exist in previous literature because of the smooth adjustment observed at
the macro level. The distributions shown in section 2 also present regions of smooth
and lumpy adjustments as discussed previously. In the analysis in the appendix,
some ?rm-level adjustments look smooth
34
and the convex cost is incorporated into
the model to capture this fact. This mix of smooth and lumpy adjustment is more
pronounced in the evidence for the U.S. in Sakellaris (2004) than in the evidence
shown in the appendix of this paper. One of the main advantages of the modeling
mechanism taken in this paper is the ability to identify the importance of such a
cost at the ?rm level.
The ?xed adjustment cost can be seen as representing installation costs (in
instruments to calculate productivity and in the recent discussion about the relevance of VAR to
business cycles analysis.
34
Lumpy adjustment is observed in the peaks for the growth variables and smooth adjustment
is observed in the smooth slope of the coe?cients for these adjustments.
36
both time and resources) in the case of capital and ?ring and hiring costs in the
case of labor.
35
Speci?cally, the functional form assumed for the adjustment costs when ?rms
adjust l (labor), k (capital) or kl (capital and labor), is the following:
C (z, k, I, l, l
?1
) =
_
¸
¸
¸
¸
¸
¸
¸
¸
¸
¸
¸
¸
¸
_
¸
¸
¸
¸
¸
¸
¸
¸
¸
¸
¸
¸
¸
_
C
l
= ?
l
R(•) +F
l
l
?1
+
?
l
2
_
?l
l
?1
_
2
l
?1
if ?l = 0
C
k
= ?
k
R(•) +F
k
k +
?
k
2
_
I
k
_
2
k + p
I
? I if I = 0
C
lk
= C
l
+ C
k
+ ?
lk
R(•) + F
lk
?
l
?1
k
+
?
lk
2
_
I
k
_ _
?l
l
?1
_
?
l
?1
k if ?l ? I = 0
(1.5)
In the case of labor or capital adjustment, (C
l
and C
k
respectively) the ?rst term
?
j
R(•) represents the disruption cost, the second term involving F
j
represents
the ?xed cost and the third term involving ?
j
represents the convex cost, with
j=k(capital) and l(labor). In the case of capital adjustment, there is an extra cost
which represents the investment price and it can take values of p
I
= {p
buy
, p
sell
} de-
pending on if the ?rm buys or sells capital. The asymmetry in the price for buying
and selling capital implies that capital is not fully reversible, which is easily observed
in the distribution for capital adjustment shown at the beginning of the paper.
If the ?rm adjusts capital and employment at the same time, the adjustment
cost is the sum of the cost of adjusting capital (C
k
), plus the cost of adjusting
employment independently (C
l
), plus a collection of terms that represent the extra
cost of the joint adjustment. The parameters are then {?
k
, ?
l
, ?
kl
} for the disruption
cost, {F
k
, F
l
, F
kl
} for the ?xed cost, {?
k
, ?
l
, ?
kl
} for the convex cost and p
I
for the
35
The set up of the model and, speci?cally, the setup of the adjustment cost model, will allow
the estimation procedure below to distinguish which component is more important in the factor
adjustment process.
37
investment price.
To check for the existence of interaction e?ects in the adjustment of capital and
employment, the cost function for joint capital and employment adjustment is as-
sumed to be a linear function of the adjustment cost for employment, the adjustment
cost for capital and an interaction term. That is, C
kl
= C
k
+ C
l
+ C
joint adjustment
.
To be more precise, if interaction e?ects exist, the terms re?ecting joint adjustment,
(?
lk
,?
lk
and F
lk
), will be di?erent from zero. This interaction will be in the form of
a congestion e?ect if the cost is positive or in the form of a complementarity if the
cost is negative (i.e. it is a bene?t). Intuitively, interaction e?ects in the disruption
cost mean that forgone pro?ts due to interruption in the production process, or de-
creases in productivity while adjusting capital and labor, may be higher (congestion)
or lower (complementarities) than when adjusting just one factor. For example, the
learning process for new workers operating new machines maybe more expensive
than the cost of training new workers and of buying new machines separately, in-
ducing a congestion e?ect. Congestion e?ects in the ?xed cost may be due to higher
installation costs for workers speci?c to certain machines, and congestion e?ects in
the convex costs may be due to a longer adjustment period in the plants.
1.3.2 Analysis of the Model
The approach in this paper di?ers from previous analysis in the modeling
of the adjustment cost for capital and labor together and in the possibility for
interaction e?ects in this adjustment. These features may lead to behavior di?erent
38
from traditional models, where ?rms have just one factor that is costly to adjust.
In particular, even with convex costs, in our model ?rms may have inaction regions
because of corner solutions in the optimization problem. The economics of joint
adjustment can be summarized as “adjust if the marginal bene?t is bigger than the
marginal cost of adjustment.” In this sense, the relative values of the adjustment
costs play a key role, since they determine which factor to adjust.
The subsections that follow will highlight the main di?erences between this
model and the conventional models, and the new implications of considering joint
adjustment of capital and labor when they are costly to adjust. As a ?nal point,
the ?rm’s optimization problem assumes that ?rms have already optimally chosen
hours, energy and materials as a function of the state space composed of the shocks
in demand and technology, the capital stock and number of workers.
Case 1. No Adjustment Costs
I will start with the case where no adjustment costs are present. In this case, the ?rm
faces a static optimization problem for capital and labor, in addition to the static
optimization problem faced for energy and materials and captured in the term z.
39
The FOCs are:
36
k
: ?
_
V
k
(z
, k
, l) f (z
/z) dz
= p
I
(1.10)
l : µzk
?
l
µ?1
= w
l
(l) (1.11)
It can be seen that labor and capital are very sensitive to shocks. Without adjust-
ment costs, the correlation between investment and demand and technology shocks
is very high, and the same is true for employment adjustment. It is clear that
in order to reproduce the main features of the data some nominal or real rigidity
is needed. The initial candidate in the literature was the convex cost component,
later adding non convex costs to account for inaction and lumpiness. This topic is
analyzed next.
Case 2. Adjustment Costs for Capital and Employment
If ?rms face any type of adjustment costs, the analysis changes. The FOCs and
envelope conditions of the problem in the general case are:
k
: C
k
(z, l
?1
, l, k, k
) + ?
_
V
k
_
z
, k
, l
_
f
_
z
/z
_
dz
? 0 (1.12)
l : µzk
?
l
µ?1
?w
l
(l) ?C
l
(z, l
?1
, l, k, k
) + ?
_
V
l
_
z
, k
, l
_
f
_
z
/z
_
dz
? 0 (1.13)
C
l
?1
(z, l
?1
, l, k, k
) ?V
l
?1
(z, k, l
?1
) ? 0 (1.14)
?zk
??1
l
µ
+ (1 ??) ? C
k
(z, l
?1
, l, k, k
) ?C
k
(z, l
?1
, l, k, k
) ?V
k
(z, k, l
?1
) ? 0 (1.15)
36
The FOCs for labor, energy, materials and hours under the full speci?cation of the model using
the pro?t function in footnote (30) are:
l : µ¯ zk
ˆ
?
l
ˆ µ?1
e
?
m
?
= w
0
+ w
1
h
?
(1.6)
h : ˆ µ¯ zk
ˆ
?
(lh)
ˆ µ
h
?1
e
?
m
?
= ?w
1
lh
??1
(1.7)
e : ? ¯ zk
ˆ
?
(lh)
ˆ µ
e
??1
m
?
= p
e
(1.8)
m : ?¯ zk
ˆ
?
?(lh)
ˆ µ
e
?
m
??1
= p
m
(1.9)
In this case, hours are independent of shocks, as can be seen from (1.7) and (1.6): h =
_
w
0
w
1
(??1)
_1
?
.
40
These FOCs and envelope conditions reveal that the functional form of the adjust-
ment costs is crucial to understanding ?rm’s factor adjustment. These expressions
are inequality conditions because of the possibility of corner solutions. Equations
(1.12), (1.13), (1.14) and (1.15) will hold with equality only when the adjustment in
both factors is nonzero. The ?rm will adjust one factor if the net gain of adjustment
is higher than if the ?rm adjusts the other factor or both employment and capital
together. This opens the possibility of staggered adjustment, even if the adjustment
cost is convex, which di?ers from previous models where convex adjustment costs
imply continuous adjustment.
Another point to notice is that the discounted marginal value of labor ad-
justment depends on investment, and the discounted marginal value of investment
depends on labor adjustment, whenever ?rms decide to adjust both factors or when-
ever the adjustment cost re?ects interaction e?ects.
Convex Adjustment Costs
With convex costs, hours depend on shocks and are negatively related to employ-
ment.
37
As mentioned above, if ?rms face convex costs in both factors, there is a
possibility of inaction if adjusting one factor gives a higher net marginal bene?t
than adjusting both factors at the same time. It has been thought that convex costs
guarantee continuous adjustment, but that is not the case in the setting presented
37
To show this, take the full speci?ed model and assume a convex cost model where the inter-
action term in the adjustment cost for capital and labor is not present. In that case, the FOCs
for labor and hours imply h =
_
µzk
?
e
?
m
?
?w
1
l
1?µ
_ 1
??µ
. Since ? > 1 > µ, hours are negatively related to
employment. However, this feature of the convex cost model with the functional forms assumed
would not be supported by the data, since the correlation between hours growth and labor growth
with ?rm-level data is positive, in contrast to the U.S.
41
in this model.
If both equations hold with equality(i.e., when adjustment is nonzero in both
factors), an interesting result can be seen, assuming a convex cost only for the
interrelation term: ?
kl
(l ? l
?1
)
_
I
k
_
. Updating (1.14) and plugging the result into
(1.13), we ?nd:
E
_
I
k
_
=
1
??
kl
_
w
0
+ ?
kl
_
I
k
_
?µzk
?
l
µ?1
_
(1.16)
From (1.16) we can see that investment rates are positively correlated in time, which
is a common feature of convex cost models of investment. Moreover, since µ < 1, it
can be shown that the investment rate in period t+1 is positively correlated with the
change in labor in period t. Also, because investment and labor are simultaneously
determined,
d(
I
k
)
dl
does not have a clear meaning unless we can assume some causality.
If causality were the case (for example, if ?rms adjust labor ?rst and then decide
investment according to capacity constraints) we would have a negative relationship
between the change in labor and the change in the investment rate.
38
Convex and Non-Convex Adjustment Costs
When hit by a demand or productivity shock, the ?rm decides whether to adjust
capital, labor or both, and at the same time decides the optimal level of materi-
als, energy and hours.
39
The ?rm’s problem is given by (1.4) and the optimality
38
This comes from applying the implicit function theorem where
d(
I
k
)
dl
= ?
dE
_
I
k
_
/dl
dE(
I
k
)/d(
I
k
)
.
39
The FOCs for the static optimization problem are conditional on ? and, under the full speci-
?cation of the model, given by:
h : ˆ µ(1 ??
j
)¯ zk
ˆ
?
(lh)
ˆ µ
h
?1
e
?
m
?
??w
1
lh
??1
= 0 (1.17)
e : ?(1 ??
j
)¯ zk
ˆ
?
(lh)
ˆ µ
e
??1
m
?
= p
e
(1.18)
m : ?(1 ??
j
)¯ zk
ˆ
?
(lh)
ˆ µ
e
?
m
??1
= p
m
(1.19)
42
conditions for capital and labor are given by equations (1.12), (1.13), (1.14) and
(1.15).
If we de?ne V
K
as the value of adjusting only capital, V
L
as the value of
adjusting only labor, V
LK
as the value of adjusting both labor and capital and V
N
as the value of nonadjustment, we can rede?ne the problem as a continuous choice
problem nested in a discrete choice framework. Given the ?rms decision problem in
(1.4), we can express it as V (•) = max[V
N
, V
K
, V
L
, V
LK
], where ?rms choose the
action that gives it the highest V . That is
• Firms do not adjust if V
N
> [V
K
, V
L
, V
LK
]
• Firms adjust labor if V
L
> [V
N
, V
K
, V
LK
]
• Firms adjust capital if V
K
> [V
N
, V
L
, V
LK
]
• Firms adjust capital and labor if V
LK
> [V
N
, V
L
, V
K
]
As will become clear later in the numerical analysis, the ?rms follow an (S,s) policy
in both capital and labor. An interesting issue left for future work is to prove the
validity of this result analytically. The di?culty of this proof comes from the joint
determination of capital and labor, making an (S,s) rule dependent not only on the
shocks and states but on the choice variables.
The model presented cannot be solved analytically because of the non-convex
nature of the decision rules. Therefore, a numerical solution is needed. It is in this
sense that the main di?culty associated with the model is the state space: there
?(z, k, l) and j = labor, capital, capital and labor (adjustment type) and ?
j
= 0 if there is no
adjustment.
43
are three
40
continuous state variables (shocks, capital and labor) and one discrete
choice variable (margin of adjustment). In the next section I show an illustrative
calibration, explain the numerical procedure used to solve the model, numerically
analyze the decision rules, and explore the quantitative implications that emerge
from this model.
1.4 Capital and Labor Adjustment: A Numerical Analysis of the
Proposed Model
The purpose of this paper is ultimately to analyze how ?rms make dynamic
joint decisions about capital and employment. Given the evidence and the model
presented above, this section describes the ?rms’ decision rules with respect to cap-
ital and employment adjustment, and numerically analyzes whether these decision
rules are able to generate simulated economies that reproduce the facts observed
in the data. Speci?cally, I look at inaction periods, lumpy adjustment and the dy-
namic interrelation of capital and labor, and the correlation between factor inputs.
Importantly, I want to determine what is the main force generating these behaviors;
speci?cally, whether it is the interaction e?ects in the adjustment process or the
type of the adjustment costs faced by ?rms.
I use numerical simulations of the model as the main tool to answer to these
questions. First, I explain the computational methods used to solve the model
numerically. Second, I parameterize the model with adjustment cost parameters
that appear to be ex-ante reasonable, illustrating the di?erent behavior the ?rm-level
model exhibits with respect to capital and labor dynamic adjustment when demand
40
Four if the shocks are di?erentiated between demand and productivity.
44
and productivity shocks are the main source of perturbation in the modeled economy.
Third, I show and analyze the decision rules that the model implies, presenting time
series realizations under several con?gurations of adjustment costs, in order to give
an idea of the ergodic distribution of the state variables and which decision rules
the ?rms visit more often. Finally, I analyze the quantitative response of the model
using di?erent adjustment cost con?gurations.
1.4.1 Numerical Methods
The equation to solve is the Bellman equation given in (1.4). The solution
must give the ?rm’s optimal choices for hours, energy, materials, investment and
employment given the vector of shocks z, capital k and previous employment level
l
?1
. The optimal level of hours, energy and materials are a function of the state space
(z, k, l
?1
) and this problem can be solved analytically every period as a function of
this state space conditional on the disruption cost ?
j
as is shown in footnote (39).
The variables left to solve are capital and labor, for which a numerical procedure
should be used given the dynamic links and non convexities that they exhibit in the
model.
In the solution of this equation, three basic choices should be made: (i) the
procedure for maximization over the state space, (ii) the procedure to solve the
unknown value function V (z, k, l
?1
) and (iii) the procedure to solve for the integral
over the shocks that represents the ?rm’s expectation about the future value V (•)
For (iii), I integrate using quadrature methods as in Tauchen and Hussey
45
(1991). This quadrature is solved with Hermite polynomials, which are the best for
this situation since the shocks are assumed (and estimated from the data) as AR(1)
log-processes with lognormal error terms. I discretize the shock distribution into
3 states for the productivity shock and 2 states for the demand shock. I assume
independence of both shocks such that the shock calibrated in the model is the result
of the multiplication of those two.
For (ii) I use value function iteration. While I also solved the model with
policy iteration, the existence of kinks in the value function did not assure reliable
results for the full range of parameters.
The simplest method for (i) would be a grid search, restricting the values
that the state space variables can take to the points in the grid; however, this
method is very imprecise given the large state space faced in this speci?c problem.
Moreover, since I am looking at inaction periods and spikes in investment and capital
adjustment, this grid would need to be very ?ne, which would soon result in the
curse of dimensionality. Instead, I choose a small number of points for the state
space (3 for the productivity shock, 2 for the demand shock, 70 for the capital
stock and 30 for the number of workers) and use a golden section search method
to determine the maximum over the entire state space, bracketing ?rst the optimal
region and then using linear interpolation of the optimal values to the values in the
grid. This method allows very precise calculations for the value function in each
grid point and also allows faster simulation of the model. The code is written in
Matlab and C, linking the programs through MEX-?les.
46
1.4.2 About the Parameters: Estimation and Calibration
There are two sets of parameters: those that can be directly estimated without
imposing an economic model (reduced form parameters) and those that need to be
calibrated or estimated with some simulation procedure (structural parameters).
In the ?rst group we have: the production function coe?cients ?, ?, ?, and ? for
capital, labor, energy and materials respectively; the demand shock process X
it
; the
technology shock process A
it
; and the elasticity of demand ?. In the second group
we have the adjustment cost parameters (?
j
for the convex cost, F
j
for the ?xed
cost, ?
j
for the disruption cost and {p
I
, p
sell
} for the price of capital), the discount
factor ?, the depreciation rate ? and the hours wage elasticity ?. The dataset does
not contain capital prices. Although I can calculate the mean input prices from the
data in the case of employment, energy and materials, I choose to calibrate them
because of the lack of capital prices in order to put all the factor prices on equal
footing. The calibrations come very close to the relative prices calculated from the
data for energy and materials. I do not compare the wage calibration with the data,
and capital prices are not available.
The estimates for production function coe?cients, the demand and technology
shock processes and the elasticity of demand are taken from Eslava et al. (2004).
They use information on prices to estimate an output-based KLEM production
function with demand shift instruments
41
in order to ?nd the production function
41
They use the Syverson (2005) insight that using demand as an instrument for input factors
in production function estimation can get rid of the endogeneity problems that are well known in
such situations. They do so by creating downstream demand shift instruments selected with Shea
(1997) relevance and exogeneity criteria.
47
coe?cients and the technology shock process. An advantage of their methodology
is that the price information allows them to isolate a ?rm speci?c price de?ator,
so that TFP estimations do not use a common price de?ator that, as Klette and
Griliches (1996) and Foster et al. (2005) illustrate, would bias the estimates of the
production function coe?cients. The estimations are carried over for all ?rms in
Colombia and are not di?erentiated by industry as a simplifying assumption, even if
the factor shares may di?er by industry. The coe?cients are 0.213 for capital, 0.303
for labor, 0.176 for materials and 0.2752 for energy. Next, Eslava et al. (2004) take
advantage of the price information and estimate a downward sloping demand curve
similar to the one assumed here, instrumenting output using the calculated TFP,
obtaining the demand elasticity ? = 2.28 and the demand shocks as the residuals
of the regression.
In the calibration of the model, I assume that the demand shocks and the
technology shocks follow an AR(1) lognormal process such that (with lower case
letters meaning logs and dropping the subindex i):
a
t
= ?
a
a
t?1
+ u
t
(1.20)
x
t
= ?
x
x
t?1
+ ?
t
(1.21)
Equations (1.20) and (1.21) are estimated as in Eslava et al. (2004) using year e?ects.
The coe?cients obtained are ?
a
= 0.922, ?
x
= 0.985 and ?
a
= 0.77, ?
x
= 0.89. Given
that ?
a
2
=
?
u
2
1??
a
2
and ?
x
2
=
?
2
?
1??
x
2
, we get ?
u
= 0.297 and ?
?
= 0.151. I normalize the
mean values of the shocks to one (this normalization also a?ects the input prices).
The discount factor ? is set as 0.95, the depreciation rate ? as 0.1 and the hours
48
wage elasticity as 1.1.
Before I discuss the calibration of the input prices, I want to emphasize that
even though those prices can be an important source of ?uctuations and relative
changes in input adjustment, this paper focuses on the ?rm’s responses to demand
and productivity shocks. This is the reason to look for an “average” input price in
each case, and this guides the calibration of the prices.
Energy and materials prices are calculated by solving the FOCs of the problem
without adjustment costs (equations (1.8) and (1.9) respectively). The values for
capital, labor, energy and materials plugged into these equations are the means of
the actual values. It is interesting to note that the implied prices are very close to
those obtained by dividing energy expenditure and materials expenditure by physical
amounts. The labor payment parameters w
0
and w
1
are obtained by solving the
system composed of the FOC for hours and labor in the problem without adjustment
costs (equations (1.6) and (1.7)) and using again mean values. The investment price
is obtained by solving the dynamic problem in the case of no uncertainty and no
adjustment costs.
42
Finally, I treat investment as reversible, but with the capital
resale price equal to 70% of the price of buying capital.
For this illustrative parameterization, I chose the adjustment cost parameters
in an arbitrary manner such that the adjustment costs are the same for all types
of costs and collectively account for either 4% or 20% of average pro?t. From this
point on, I focus on the congestion e?ect because it is the one that is later supported
42
The implicit assumption for the calculation of the prices is that the frictionless FOCs hold “on
average”.
49
by the data. Table 1.12 shows the chosen parameters for the adjustment costs and
the average adjustment cost as a proportion of the contemporaneous pro?t. These
costs do not increase proportionally from one column to the next because they were
obtained with simulations and re?ect an approximate rather than exact value. I
calculate the policy function under the parameterizations discussed above for later
simulations under di?erent realizations of the shocks
43
.
Table 1.12: Parameters Adjustment Costs
Adjustment Cost Cost/?
Adjusted Factor
Type 4% 20%
Fixed (F
l
) 0.22 1
Labor Convex (?
l
) 0.05 0.15
Disrupt (?
l
) 0.01 0.035
Fixed (F
k
) 0.01 0.044
Capital Convex (?
k
) 0.0007 0.006
Disrupt (?
k
) 0.01 0.045
Interaction E?ects: Congestion/ ? =30%
Joint Fixed (F
lk
) 5 5
Adjustment Convex (?
lk
) 0.11 0.11
(Congestion) Disrupt (?
lk
) 0.07 0.07
1.4.3 Decision Rules for Capital and Employment Adjustment
I now present the numerical results for the value function, the decision rules
(or policy functions) and its implications for ?rm behavior, given by the chosen
parametrization. The ?rm has the option to not adjust, adjust only capital, adjust
only employment or adjust both capital and employment. The decision rules are
presented in a graphical analysis over the space determined by the values of capital
43
This policy rule is invariant.
50
and labor. As expected, there is a region of inaction whose size depends on the
value of the shocks, on the type of adjustment costs and on the existence or not of
congestion e?ects in adjustment. This region of inaction determines a bi-dimensional
(S,s) policy in capital and labor depending not only on the shocks and the other state
variables, but also on the other choice variables. However, some regions are more
likely to a?ect ?rm behavior than others since the ergodic distribution of the state
space is an important point to take into account. That is the reason to consider
several time series realizations of ?rm’ behavior under di?erent con?gurations of
adjustment costs.
To illustrate the objective functions, ?gure 1.4 shows that in fact the value
function is concave with some kinks at lower values of employment(this is, L
t?1
on the x-axis). This e?ect on the value functions is due to the scale of the graph.
The decision rules are shown in Figures 1.5, 1.6, 1.7 and 1.8. With these decision
rules and the time series realizations, I will analyze the e?ects of the shocks, the
congestion e?ects and the adjustment costs. Figure 1.5 shows the policy functions
for the case where all costs are present for capital and labor (and equal to 4%) and
there are congestion e?ects in adjustment. The ?rst thing to note is that there is an
inaction region whose shape and size depends on the shock and the value of both
factors. This inaction region de?nes a bi-dimensional (S,s) policy for capital and
labor. The optimal (S,s) policy depends on the shock and the choice of the other
variable (either capital or labor).
Even though some adjustment regions for capital and labor are not convex
sets, there are de?ned zones in which it is optimal to adjust only labor and others in
51
Figure 1.4: Value functions: lateral view, labor.
0 500 1000 1500
1.37
1.375
1.38
1.385
x 10
7
low shock
Labor
0 500 1000 1500
1.38
1.4
1.42
1.44
x 10
7
shock 2
Labor
0 500 1000 1500
1.38
1.4
1.42
1.44
x 10
7
shock 3
Labor
0 500 1000 1500
1.45
1.5
1.55
x 10
7
shock 4
Labor
0 500 1000 1500
1.4
1.45
1.5
x 10
7
shock 5
Labor
0 500 1000 1500
1.7
1.8
1.9
2
x 10
7
high shock
Labor
which it is optimal to adjust only capital, especially for small values of the shock (see
?gure 1.5). In some of the policy rules there exist disjoint sets in the space capital-
labor for a given shock. For example, for the same capital to labor ratio may exist
inaction or adjustment depending on the level of capital and labor, opening the
possibility of multiple optimal regimes. According to the optimal rule, ?rms adjust
capital and labor together only if the shock is big enough (in this case, above the
mean shock). This implies that there is an implicit target for a relationship between
capital and labor, and that target changes with the shock.
With just one factor, a standard (S,s) rule would hold, with the shock being
52
the only determinant of the optimal adjustment policy. With the possibility of
adjusting capital and labor, ?rms make decisions depending on where they are with
respect to the optimal target of not just one isolated factor but a composite of capital
and labor. This is an important improvement over previous models that analyzed
just one factor at a time. This result is also related to Eslava et al. (2005), when
implement the gap approach by Caballero et al. (1995) and Caballero et al. (1997);
their empirical results suggest that ?rms adjust labor and capital depending on the
gap between desired and actual employment and labor. The structural analysis here
implies that this gap is implicitly a?ected by the gap in the other factor, resulting
in this bivariate (S,s) policy.
Figures 1.6, 1.7 and 1.8 compare the decision rules implied by the di?erent
types of adjustment costs considered one-by-one in the presence (or absence) of
congestion e?ects in the case of a bad shock, an intermediate shock and a good
shock.
With respect to the adjustment cost types, the convex cost implies a larger
region of adjustment in both capital and employment than the ?xed cost and the
disruption cost. It is important to note, as the theoretical analysis of the model
revealed above, that even with convex costs, there is a region of inaction, though
much smaller than the one present under non-convex costs.
The biggest inaction zone corresponds to the disruption cost. The ?xed cost
implies more staggered adjustment than the disruption cost, under which simulta-
neous adjustment of both factors is more frequent. The behavior implied by the
53
Figure 1.5: Decision rules. All costs in K,L.
Figure 1.6: Decision rules. Comparison among Adjustment costs. Low shock.
54
Figure 1.7: Decision rules. Comparison among Adjustment costs. Intermediate
shock.
Figure 1.8: Decision rules. Comparison among Adjustment costs. High shock.
55
disruption cost looks more in line with the empirical evidence, where positive co-
movement between capital and employment adjustment is observed.
For low values of the shock (?gure 1.6) the behavior under convex or disruption
costs does not depend much on the existence of congestion e?ects, and the only
di?erence between the behavior under convex cost and that under disruption costs
is the adjustment of only labor in a small region under convex costs. For the low
shock case, ?xed costs generate a more di?erentiated behavior, since there is no joint
adjustment of capital and employment in the case of congestion e?ects.
In the intermediate shock case (Figure 1.7) , we observe that without conges-
tion e?ects, there is more joint adjustment of capital and employment. This does
not necessarily imply a higher correlation of adjustments under this regime, how-
ever, since capital and labor can move in opposite directions. The inaction zones are
de?ned as double (S,s) bands. Interestingly, there is more joint adjustment in the
convex cost case with congestion e?ects than without them. The pattern for ?xed
costs observed in the low shock case repeats itself here: joint adjustment is rare in
the presence of congestion e?ects.
If ?rms face a high value of the shock (Figure 1.8), there is much more joint
adjustment and the behavior under convex costs and disruption costs is very similar,
with a larger inaction zone in the disruption case as expected. Again, ?xed costs
present the most di?erent pattern: in the presence of congestion e?ects, ?rms will
adjust only labor under certain circumstances.
Other important implications of di?erent con?gurations of the adjustment
costs can be seen plotting the time series realizations that the policy rules imply as
56
a way of visualizing the regions that the ?rms spend more time in. For example,
we could try to ?nd if bigger inaction regions imply less variability of investment,
or if bigger inaction regions are compensated by larger adjustments. Figure 1.9
shows the time series realization of one shock series when a ?rm faces all types of
adjustment costs comparing the case of congestion vs. no congestion e?ects, ?gure
1.10 shows the labor growth when the ?rm faces di?erent types of adjustment costs
with and without congestion e?ects and ?gure 1.11 shows the investment responses
of the same.
These time series realizations show that the presence of congestion e?ects
increases the inaction in both capital and labor adjustments in all the cases. In
the other hand, ?xed costs and disruption costs have the same e?ect on investment
rates when there is congestion e?ects, even if the decision rules are di?erent. When
congestion e?ects are not present, ?xed costs increase inaction and volatility in both
capital and labor with respect to the convex and disruption cases. When congestion
e?ects are present and ?rms face all types of adjustment costs, the volatility of labor
growth increases and the volatility of the investment rate decreases; Also, when the
congestion e?ects are present, convex costs increase the volatility of the investment
rate and decrease the volatility in labor growth compared with the case when either
?xed or disruption costs are present.
The decision rules as presented above do not say anything about the direction
of size of the adjustments. For example, capital and labor can move at the same time
57
Figure 1.9: Time Series: All Costs Present.
0 50 100
0.5
1
1.5
Shocks series
0 50 100
0
10
20
All costs, I/K, Congestion
0 50 100
0.5
1
1.5
Shocks series
0 50 100
?10
0
10
All costs Labor growth, Congestion
0 50 100
0
10
20
All costs, I/K, No Congestion
0 50 100
?10
0
10
All costs Labor growth, No Congestion
Figure 1.10: Time Series: Investment Rate, Adjustment Costs Comparison
0 50 100
0
10
20
Convex, I/K, Congestion
0 50 100
0
10
20
Convex, I/K, No Congestion
0 50 100
0
10
20
Fixed, I/K, Congestion
0 50 100
0
10
20
Fixed, I/K, No Congestion
0 50 100
0
10
20
Disruption, I/K, Congestion
0 50 100
0
10
20
Disruption, I/K, No Congestion
58
Figure 1.11: Time Series: Labor Growth, Adjustment Costs Comparison
0 50 100
?10
0
10
Convex, Labor growth, Congestion
0 50 100
?10
0
10
Convex, Labor growth, No Congestion
0 50 100
?10
0
10
Fixed, Labor growth, Congestion
0 50 100
?10
0
10
Fixed, Labor growth, No Congestion
0 50 100
?10
0
10
Disruption, Labor growth, Congestion
0 50 100
?10
0
10
Disruption, Labor growth, No Congestion
but in di?erent directions. There exist enormous non linearities in the decision rules.
Figures 1.12 and 1.13 show the decision rules for labor adjustment and investment
for several values for capital and labor and in the case of an intermediate shock with
low adjustment costs. From Figure 1.12, we observe that at low values of capital and
labor, the adjustments are in the same direction (positive), but for higher values,
?rms stagger depending on the state of (l, k); that is, under some combinations of
capital and labor, ?rms reduce capital and do not adjust labor, and under other
values they do the opposite. Figure 1.13 shows that factors can adjust in opposite
directions when the ?rm has high values of capital and low values of employment or
vice versa(higher or lower relative to their frictionless optimum). This means that
at low values for both capital and labor the correlation between their adjustments is
59
Figure 1.12: Labor and Capital Adjustment Levels. Intermediate Shock, High and
Low values for Capital and Labor
0
10
20
30
0
2000
4000
6000
0
50
100
150
200
Employment
Intermediate shock, Labor Adjustment,low L,K
Capital
L
a
b
o
r
A
d
j
u
s
t
m
e
n
t
0
10
20
30
0
2000
4000
6000
0
1
2
3
4
x 10
4
Employment
Intermediate shock, Investment,low L,K
Capital
I
n
v
e
s
t
m
e
n
t
1
1.1
1.2
1.3
1.4
x 10
4
1
1.2
1.4
1.6
x 10
7
?15000
?10000
?5000
0
Employment
Intermediate shock, Labor Adjustment,high L,K
Capital
L
a
b
o
r
A
d
j
u
s
t
m
e
n
t
1
1.1
1.2
1.3
1.4
x 10
4
1
1.2
1.4
1.6
x 10
7
?15
?10
?5
0
x 10
6
Employment
Intermediate shock, Investment,high L,K
Capital
I
n
v
e
s
t
m
e
n
t
likely to be positive, while at higher values this correlation is likely to be negative.
Thus, we have di?erent possibilities of ?rm behavior depending on if ?rms
face good or bad shocks, whether they face congestion e?ects in the adjustment and
depending on the type of dominant adjustment cost. In summary, the main features
of these decision rules are:
i. The decision rules for capital and employment adjustment exhibit a non-linear
pattern with inaction zones, zones of joint adjustment and zones of single factor
adjustment. That is, the decision rules present a non linear (S,s) rule in both
capital and labor. Adjustment or inaction in capital and labor depend not only
60
Figure 1.13: Labor and Capital Adjustment Levels. Intermediate Shock, Mix of
High and Low values for Capital and Labor
0
5
10
15
20
1
1.2
1.4
1.6
x 10
7
0
50
100
150
200
Employment
Intermediate shock, Labor Adjustment, high K low L
Capital
L
a
b
o
r
A
d
j
u
s
t
m
e
n
t
0
5
10
15
20
1
1.2
1.4
1.6
x 10
7
?15
?10
?5
0
x 10
6
Employment
Intermediate shock, Investment, high K low L
Capital
I
n
v
e
s
t
m
e
n
t
1
1.2
1.4
1.6
x 10
4
0
2000
4000
6000
?15000
?10000
?5000
0
Employment
Intermediate shock, Labor Adjustment, high L,low K
Capital
L
a
b
o
r
A
d
j
u
s
t
m
e
n
t
1
1.2
1.4
1.6
x 10
4
0
2000
4000
6000
0
1
2
3
4
x 10
4
Employment
Intermediate shock, Investment, high L,low K
Capital
I
n
v
e
s
t
m
e
n
t
on the states, such as the productivity and demand shocks and the capital to
labor ratio, but also on the choices of capital and labor.
ii. Persistent bad shocks and ?xed costs lead to a less frequent joint adjustment
in capital and employment. Good persistent shocks increase the joint employ-
ment and capital adjustment.
iii. In general, the presence of convex costs tends to increase the likelihood of
joint adjustment for capital and labor, while the presence of ?xed costs tends
to reduce this joint adjustment. Disruption costs can accommodate a richer
type of adjustment, depending on the capital to labor ratio a ?rm has. This
does not translate directly into measures of correlation since the adjustment
61
of capital and labor can occur in opposite directions.
iv. Under intermediate or high shocks, congestion e?ects in the adjustment in-
crease the likelihood of joint adjustment. Under low shocks, this is only true
if ?xed costs are dominant.
v. Even under convex costs, there may be inaction regions. These inaction zones
are also present and larger when ?rms face disruption or ?xed costs. How-
ever, in the case of ?xed costs, inaction zones can present disjoint sets, which
opens the possibility for multiple optimal regimes of capital and labor for the
same capital to labor ratio. Inaction zones are more important in the case of
intermediate shocks, being almost non existent for bad shocks and smaller for
good shocks.
vi. Congestion e?ects increase the inaction in both capital and labor adjustments
in all the cases; when congestion e?ects are not present, ?xed costs increase
inaction and volatility in both capital and labor with respect to the convex
and disruption cases; when congestion e?ects are present, convex costs increase
the volatility of the investment rate and decrease the volatility in labor growth
compared with the case when either ?xed or disruption costs are present; how-
ever, when congestion e?ects are present and ?rms face all types of adjustment
costs, the volatility of labor growth increases and the volatility of the invest-
ment rate decreases.
vii. It is straightforward to conclude that the decision rules presented show a model
62
that can accommodate at the same time smooth, lumpy, and infrequent ad-
justment, depending on the value of the shocks, the state of the ?rms in terms
of capital and labor, the type of adjustment costs di?erent ?rms face and
the presence or absence of congestion e?ects. The model is able to incorpo-
rate di?erent types of behavior depending on the combination of the variables
above.
Since the decision rules imply a wide range of possibilities of adjustment, the
next section simulates the response of ?rms to a speci?c realization of the technology
and demand shocks in order to analyze the types of adjustment observed under the
current parameterization.
1.4.4 Congestion E?ects and Adjustment Costs: A Simulation ex-
ploration
Given the parameters and the average e?ects they produce in the model, I show
in this subsection the results of some simulation exercises for a particular realization
of the shocks extending the analysis started in the previous section. I choose to
analyze one simple realization because this is not a formal calibration, but instead
an example of the di?erent possibilities that the adjustment costs can accommodate
with respect to ?rm behavior. In particular, I look at the inaction zones and spikes
in investment and employment adjustment, at the correlation among factor inputs
and at the dynamic interrelations expressed in a one-lag VAR across di?erent sets
of parameters. The idea behind the numerical simulations is to complement the
analysis of the decision rules and to understand, given the model and a speci?c
63
realization of the shocks, how ?rms respond to shocks in technology and demand,
how input factors move and comove and what is the role of congestion e?ects. Along
the way, we will see how well the model replicates the stylized facts observed in the
data.
I do not analyze the behavior of materials, hours and energy because they are
not the main focus of this paper. However, the model does a mixed job in replicating
the hours, materials and energy movements observed in the data. Inaction in these
factors occurs on average 20% of the time and spikes occur 30% of the time, and
the correlation between labor and hours is always negative because of the functional
form assumed in the model (see footnote (30) for the wage function assumption and
footnote (36) for the FOCs for labor and hours in the case of no adjustment costs).
The correlation between materials and energy is always above 90% and their VAR
coe?cients in the investment equation are larger than 100. The other statistics are
more reasonable. The positive side of this is that ?rms in the model adjust along
several margins and are not restricted to adjust only capital and employment.
The ?rst simulated statistics are presented in Table 1.13, which shows the per-
centage of inaction episodes, the percentage of positive and negative spike episodes,
and the di?erent responses of capital and employment to shocks. The time series
have 500 periods and I drop the ?rst 50. In this table we can see that the congestion
e?ects have an e?ect on ?rms’ adjustment behavior, making inaction more likely in
the case of low adjustment cost value and when costs are high, in most cases, at
least for capital. The increase in cost when ?rms adjust both factors may prevent
?rms from adjusting either factor as often as they would like.
64
In general, the model can replicate the basic features of inaction and spikes
in investment and labor adjustment. As seen in Table 1.13, the magnitude of the
?xed and disruption costs have a greater e?ect on capital than on employment
adjustment. This means that capital is more sensitive to the adjustment costs in the
model. Finally, with respect to the response of the variables to shocks, labor growth
has a very stable response to shocks when no congestion e?ects are present, but
the response is higher when congestion e?ects exist. Investment growth responds
negatively to shocks in some cases, which may indicate that ?rms over-invest in
some periods, that they replace capital with labor in some good periods or that
they simply sometimes disinvest once they receive a bad shock.
It is also interesting to note that even with convex costs, the percentage of
simulated observations that display inaction in both capital and labor is positive
and high, but not nearly as high as in other cases. This implies that ?rms have the
possibility of staggering adjustment of capital and employment, as discussed before.
This is left to future work.
Table 1.14 shows the simulated contemporaneous correlations between labor
and capital adjustment. It is interesting to note that the best ?t comes from the
high congestion e?ect-low adjustment cost case when all costs are present in capital
and labor. It is also important to note that the correlation between labor and
capital is negative in the case of high convex costs and low congestion e?ects, as
the analysis of the model predicted as a theoretical possibility. Moreover, when
only labor adjustment is costly, this correlation is also negative in the case of low
adjustment costs. The correlation between investment and labor growth increases
65
Table 1.13: Basic simulated statistics
Investment Labor
Adj. Inaction Pos Neg ?(
I
K
, z) Inaction Pos Neg ?(
?L
L
, z)
Cost C/? data 0.189 0.298 0.018 0.10 0.134 0.12 0.11 0.05
Type
NC 0.30 0.25 0.18 -0.03 0.23 0.18 0.11 0.13
K
0.04
C 0.34 0.29 0.16 -0.09 0.29 0.11 0.10 0.14
and NC 0.47 0.27 0.14 0.01 0.38 0.08 0.06 0.15
L
0.2
C 0.60 0.21 0.08 -0.05 0.21 0.17 0.12 0.10
NC 0.14 0.07 0.02 -0.11 0.23 0.00 0.00 0.15
0.04
C 0.03 0.12 0.08 0.08 0.00 0.12 0.09 0.21
Convex
NC 0.09 0.03 0.06 -0.12 0.18 0.02 0.02 0.16
0.2
C 0.09 0.04 0.02 0.07 0.10 0.06 0.05 0.23
NC 0.44 0.21 0.15 0.15 0.31 0.10 0.11 0.16
0.04
C 0.58 0.12 0.09 0.27 0.30 0.10 0.12 0.13
Fixed
NC 0.65 0.08 0.07 0.25 0.35 0.09 0.08 0.17
0.2
C 0.67 0.06 0.06 0.28 0.38 0.07 0.07 0.17
NC 0.43 0.20 0.15 0.18 0.29 0.13 0.10 0.17
0.04
C 0.64 0.15 0.11 0.21 0.34 0.09 0.10 0.18
Disrupt
NC 0.60 0.09 0.11 0.24 0.35 0.08 0.09 0.16
0.2
C 0.55 0.10 0.08 0.26 0.36 0.08 0.08 0.15
NC 0.20 0.30 0.22 0.10 0.28 0.15 0.10 0.19
K but
0.04
C 0.38 0.28 0.17 -0.02 0.25 0.15 0.10 0.14
not L NC 0.48 0.15 0.16 0.07 0.32 0.10 0.11 0.23
0.2
C 0.56 0.18 0.08 -0.10 0.21 0.15 0.13 0.12
NC 0.13 0.28 0.24 0.02 0.26 0.14 0.13 0.11
L but
0.04
C 0.32 0.30 0.20 0.04 0.23 0.16 0.12 0.16
not K NC 0.23 0.26 0.15 -0.08 0.23 0.17 0.13 0.13
0.2
C 0.37 0.26 0.16 0.08 0.26 0.14 0.11 0.13
NC: No Congestion E?ects present. C: Congestion E?ects present (30%). C/?: Adjustment
cost/Pro?t
a lot when ?xed and disruption costs are present.
Table 1.15 shows the coe?cients of a VAR(1) for the investment rate and
labor growth. Several parameterizations perform well, among them the one with all
costs in capital and labor and with low adjustment costs but high congestion e?ects.
Congestion e?ects do not seem to have much e?ect on the convex cost speci?cation,
but they do in the other cases, switching the signs at times. This suggests that
congestion e?ects may be important in determining the dynamic behavior of the
66
Table 1.14: Correlation(
I
K
, ?L)
Data 0.057
(Adj cost)/? 4% 20%
(Congestion E?ects)/? 4% 30% 4% 30%
All Costs in K,L 0.039 0.054 -0.030 0.005
Convex 0.035 0.203 -0.033 0.385
Fixed 0.205 0.313 0.429 0.466
Disrupt 0.325 0.365 0.421 0.421
Adj. Costs in K, not in L 0.193 0.016 0.107 0.002
Adj. Costs in L, not in K -0.058 -0.070 0.015 -0.080
Table 1.15: Simulated V AR(1)
Data C/? = 4% C/? = 20%
-0.008 -0.008 No Compl. Compl=30% No Compl. Compl=30%
0.037 -0.147 I/K ?L I/K ?L I/K ?L I/K ?L
(I/K)
?1
0.008 0.137 -0.055 0.019 -0.005 -0.005 -0.002 0.002
All Cost
?L
?1
0.013 -0.551 0.048 -0.320 -0.020 -0.387 0.480 -0.077
(I/K)
?1
-0.025 -0.061 -0.004 0.000 -0.007 -0.03 0.032 0.000
Convex
?L
?1
0.017 -0.269 0.012 0.065 0.026 -0.272 0.007 -2.918
(I/K)
?1
-0.005 0.000 0.005 0.000 -0.011 0.001 0.054 0.000
Fixed
?L
?1
1.088 -0.431 -0.465 0.341 0.408 -0.329 -3.812 -0.165
(I/K)
?1
0.001 0.001 0.006 0.001 0.037 0.000 -0.006 0.001
Disrupt
?L
?1
-1.010 -0.644 -0.254 -0.197 -3.496 -0.244 0.324 -0.210
(I/K)
?1
-0.016 0.000 -0.020 -0.013 0.000 0.000 -0.010 0.009
All K
?L
?1
-0.062 -0.233 0.085 -0.111 0.001 -0.239 0.018 -0.028
(I/K)
?1
-0.005 0.004 0.009 0.000 -0.009 0.024 0.030 -0.006
all L
?L -0.051 -0.330 0.233 -0.355 0.023 -0.435 0.687 -0.318
?rms’ factor adjustment. Congestion e?ects may act by letting the ?rm adjust one
input at a time, creating other types of dynamics in the economy. It is important
to note that even if the coe?cient on lagged capital is small in the employment
equations, very small movements in capital have a huge e?ect on the number of
workers because of scale e?ects.
What conclusions can we draw from this calibration exercise? First, this pa-
rameterization shows that considering capital and labor interrelation in adjustment
67
costs a?ects the dynamic behavior of labor and capital adjustment. Second, none of
the adjustment costs taken alone can completely explain the moments observed in
the data, and in fact, it is the combination of these costs that allows one to match
the facts. Third, this model also presents a high number of negative investment
spikes and. It seems that a higher degree of non-reversibility than the one assumed
here is needed to match the rarity of negative spikes in the data. Fourth, even with
a model of only convex costs we can have inaction zones due to the existence of
other margins of adjustment. Fifth, the combination of parameters that best ?ts
the data is the low adjustment cost-high congestion e?ects case with all forms of
adjustment costs present in capital and labor.
Sixth, the model calibrations show di?erent results if the costs are present in
one factor alone; this point is important because it suggests that considering one
factor at a time may lead to misleading estimates of adjustment costs, since the es-
timated costs for one factor may incorporate information on costs from the omitted
factors. The estimations of models with one factor which is costly to adjust, may
incorporate costs from the other in the productivity shocks or in the estimated para-
meters. And, ?nally, congestion e?ects in adjustment costs are important and they
imply, according to the model, di?erent behavior in capital and labor adjustment
than that observed when each input is considered separately.
The next section will calculate these adjustment cost parameters in a more
formal way. This will give a clearer idea of the questions asked here; this is, if
there are congestion e?ects in capital and labor adjustment and if the nature of this
interrelation comes from non-convexities in the adjustment cost process.
68
1.5 Structural Estimation of the Adjustment Cost Parameters
In this section, I estimate the adjustment cost parameters from the model.
Speci?cally, I use a minimum distance algorithm to match the moments from the
data to the moments from a simulated panel generated with the model. My main
assumption is that the model is a good approximation of the way ?rms make de-
cisions about labor and capital. I discuss the methodology and then present the
results.
1.5.1 Methodology
The methodology to apply is the Method of Simulated Moments, in the spirit of
McFadden (1989), Pakes and Pollard (1989), and (1996) and Hall and Rust (2003)
among others. The choice of this estimation method is made for computational
feasibility, given that other methods, such as maximum likelihood, would require an
enormous amount of computing power.
The parameter set to be estimated is composed of ?xed, convex and disruption
costs for capital, labor and joint capital-labor adjustment, and the resale price of cap-
ital. These are represented by a vector ? = [(F
k
, F
l
, F
lk
), (?
k
, ?
l
, ?
lk
), (?
k
, ?
l
, ?
lk
), p
i
]
The algorithm consists of solving the dynamic programming problem given a
set of parameters ?, getting the policy functions for that speci?c parametrization,
simulating a panel of plants, calculating the chosen moments from that panel and
comparing them with the moments from the data. The function that depends on
69
the parameters and must be minimized is given by:
min
?
J(?) = {M
data
?M
simulated
(?)}
W {M
data
?M
simulated
(?)} (1.22)
where M is a vector of moments, W is a weighting matrix and ? is a vector of
parameters to be estimated. To ?nd standard errors, there are two options. The
?rst option is to carry on a Montecarlo simulation, repeating the procedure under
di?erent realizations of the stochastic shock. The second option to calculate the
standard errors is by obtaining the asymptotic distribution of the estimator, like
in Hall and Rust (2003); this is the method that I use which is simpler and much
faster. I construct the simulated panels with 1000 plants over 500 periods. At the
moment, I set W to the identity matrix in order to estimate the parameters, which
gives consistent but not e?cient estimates; however, in a second stage, I recalculate
W as in Hall and Rust (2003) in order to calculate the standard errors. In future
work, I plan to re-estimate the parameters with this optimal weighting matrix to
get e?cient estimates. See Hall and Rust (2003) for more details; To solve for
parameters I use the Nelder-Mead simplex algorithm.
Regarding the moments to match, the main questions are which moments re-
?ect variation in the parameters and which moments are worth matching given their
relevance in understanding ?rm behavior. The empirical evidence in the second sec-
tion presented characteristic distributions for capital and labor. In particular, the
distributions showed highly irreversible capital and lumpy adjustment and inaction
zones for both capital and labor. However, given the arbitrary de?nition of inac-
tion and the implications for di?erent types of capital
44
, I choose not to match this
44
For example, a hammer, some special cutting tools and a milling machine are capital goods,
70
feature. Instead, I focus on the lumpiness of the distributions and match the adjust-
ments above the 90
th
and below the 10
th
percentile in the distribution of capital and
labor adjustment (i.e. the fraction of positive and negative spikes). The VAR(1)
illustrates the dynamic interrelations of capital and labor and it is an important fea-
ture to consider. On the other hand, the model highlights the importance of shocks
in the movements of capital and labor; the correlation between adjustments and
shocks is therefore the other important moment. Finally, the correlation between
capital and labor adjustment is of prime interest in the paper and it completes the
set of moments I attempt to match (11 total).
1.5.2 Adjustment Costs Parameters: Fitting the Data
In order to analyze whether congestion e?ects in the adjustment for capital
and labor are important, I ?rst match the moments assuming that all parameters are
present, including the congestion e?ects parameters (F
kl
, ?
kl
, ?
kl
), and compare the
results with those obtained not including the congestion e?ect terms in the model.
In order to analyze which type of adjustment costs are important, I compare the
results of the full speci?cation model with the results of models that shut down a
particular type of adjustment cost. It is worth emphasizing that since I am not
using the optimal weighting matrix but instead the identity matrix, this value is
understated. The calculated moments are presented in table 1.16, and table 1.17
presents the calculated parameters with the standard errors for the full speci?cation.
and de?ning an investment rate lower than 1% as inaction would not considered the investment in
small but important units of capital.
71
Table 1.16: Simulated Moments
Simulated Moments
MOMENTS DATA Convex+Fixed+Disruption Convex
Complem. No complem.
Positive Spikes 0.61 < (I/K) 0.1 0.181 0.3 0.38
(90
th
percentile) 0.23 < (?L/L) 0.1 0.133 0.27 0.25
Negative Spikes 0 > (I/K) 0.1 0.152 0.21 0.26
(10
th
percentile) ?0.22 > (?L/L) 0.1 0.105 0.19 0.21
bkk -0.008 -0.009 -0.014 -0.003
bkl -0.008 -0.016 0.21 0.065
VAR coe?cients
blk 0.037 0.068 0.045 0.005
bll -0.147 -0.203 -0.073 -0.866
?
(
I
K
,
?L
L
)
0.057 0.049 0.139 0.203
Correlations ?
(
I
K
,z)
0.1 0.089 0.03 0.074
?
(
?L
L
,z)
0.05 0.135 0.154 0.297
J(?) N.A. 0.022 0.152 0.745
Two important facts emerge from table 1.16:
45
First, the model that considers
congestion e?ects does better in several dimensions than the model that does not. In
particular, one of the ?tted VAR coe?cients in the case without congestion e?ects
has the wrong sign relative to the data, and the contemporaneous correlation be-
tween capital and employment adjustment is too high in the case without congestion
e?ects. This suggests that when ?rms adjust both factors they pay a price instead of
having a bene?t of adjusting them together. It is important to emphasize that even
if the ?rms pay an extra cost of adjusting capital and labor together, the discounted
expected net bene?t can still be higher than if ?rms adjust one factor each period.
The second important fact from table 1.10 is that the model that considers convex
costs as the only cost faced by ?rms when adjusting does the worse job in explaining
the data moments.
45
These results should be taken with care, however; the minimization routine is susceptible to
getting local minima as solutions. More starting points for the algorithm are needed to con?rm
the ?ndings presented here.
72
Table 1.17: Calculated Adjustment Cost Parameters
Convex+Fixed+Disruption Convex
Congestion E?ects No Congestion E?ects
P
sell
0.42*pi (0.7307) 0.57*pi pi
F
k
0.0002 (0.0021014) 0.0065 NA
F
l
0.007 (0.090392) 0.013 NA
F
lk
0.14 (0.40376) NA NA
?
k
0.000006 (0.0000004)** 0.000016 0.092
?
l
0.0009 (0.0045079) 0.0000571 0.0134
?
lk
0.016 (0.0065368)* NA 0.024
?
k
0.0002 (0.0000182)** 0.00065 NA
?
l
0.0215 (0.0043362)** 0.092 NA
?
lk
0.046 (0.0199720)* NA NA
Standard errors in parentheses; **/* signi?cant at 1% and 5%
Table 1.17 has important information about the size of the adjustment costs
and about the statistical signi?cance of the estimates.With respect to the size of the
estimates, the high degree of irreversibility of the capital in Colombia is observed in
the lower selling price of capital for all the models except in the benchmark convex
case (by assumption p
sell
= p
buy
in this case). This irreversibility is much bigger
than the one found by Cooper and Haltiwanger (2005) for the U.S. This degree of
irreversibility is consistent with the asymmetric distribution for the gross investment
observed in the Colombian census. The high costs of adjusting both factors at the
same time are somewhat surprising. However, the functional form for the congestion
e?ects case does not allow for a direct comparison between the individual costs and
the congestion cost. The adjustment costs are not large, but ignoring them does
not allow a good match of the moments in the data.
With respect to the statistical signi?cance of the estimates, the procedure
allows to accept statistically the disruption costs for capital and labor, the convex
73
costs for capital but not for labor and the congestion e?ect present in the convex
cost joint parameter and the disruption cost joint parameter. The low statistical
signi?cance of the ?xed costs may be due to the fact that the disruption cost takes
all its e?ects. Also, according to the procedure, I can not reject the possibility that
the convex costs are present in the Colombian ?rms when they adjust capital or
when they adjust capital and labor at the same time.
1.5.3 Non-formal Tests of Goodness of Fit
After getting the parameters, the following exercises look to determine how
well the model can, using the estimated parameters, ?t the distributions of adjust-
ment and other moments not considered in the estimation procedure.
Figure 1.13. replicates the distributions of adjustments generated using the
model and the estimated parameters. The simulated distributions are more lumpy,
but the main characteristics observed in the data are present here. In particular,
the continuous adjustment in materials and energy contrast with the lumpy pattern
observed in the distributions of adjustments of capital and labor. It is interesting
to notice the asymmetry in the capital adjustment distribution and the symmetry
in the labor adjustment distribution.
Table 1.18. tries to replicate the logit estimates for the probability of spikes
in adjustment or inaction given spikes of adjustment or inaction in the other fac-
tor. In order to do so, I generated a panel with 1000 ?rms and 500 periods using
the estimated parameters, dropping the ?rst twenty observations in each simulated
74
Figure 1.14: Distributions of Factor Adjustments for the Simulated Series. Percent-
age of observations (y-axis) in a range of adjustments (x-axis).
Gross Investment Rate
0
5
10
15
20
25
30
-
0
.
5
-
0
.
4
-
0
.
3
-
0
.
3
-
0
.
2
-
0
.
1
-
0
0
.
0
6
0
.
1
4
0
.
2
2
0
.
3
0
.
3
8
0
.
4
6
I/K
%
o
f
o
b
s
e
r
v
a
t
i
o
n
s
Wks growth
0
5
10
15
20
25
30
-
0
.
5
-
0
.
4
-
0
.
3
-
0
.
3
-
0
.
2
-
0
.
1
-
0
0
.
0
6
0
.
1
4
0
.
2
2
0
.
3
0
.
3
8
0
.
4
6
Workers growth
%
o
f
O
b
s
e
r
v
a
t
i
o
n
s
Energy Growth
0
5
10
15
20
25
30
-
0
.
5
-
0
.
4
-
0
.
3
-
0
.
3
-
0
.
2
-
0
.
1
-
0
0
.
0
6
0
.
1
4
0
.
2
2
0
.
3
0
.
3
8
0
.
4
6
Energy growth (log difference)
%
o
f
o
b
s
e
r
v
a
t
i
o
n
s
Materials Growth
0
5
10
15
20
25
30
-
0
.
5
-
0
.
4
-
0
.
3
-
0
.
3
-
0
.
2
-
0
.
1
-
0
0
.
0
6
0
.
1
4
0
.
2
2
0
.
3
0
.
3
8
0
.
4
6
Materials Growth (log difference)
%
o
f
O
b
s
e
r
v
a
t
i
o
n
s
75
Table 1.18: Probability of inaction/adjustment conditional on Inaction/adjustment
of the other factor: Simulated data
Investment Employment growth
Variable x P(inaction/x) P(Spike/x) P(inaction/x) P(Spike/x)
0.026 ** -0.021**
Inaction
(0.007) (0.007)
Investment
-0.017* -0.001
Spike
(-0.008) (-0.008)
0.031** -0.035**
Employment
Inaction
(0.008) (0.008)
Growth -0.003 -0.008
Spike
(-0.008) (0.008)
Observations 49000 49000 49000 49000
†/*/** signi?cant at 10%, 5% and 1%. Shocks in regression
Dummies for inaction are de?ned as 1 if abs(x) < 0.01 and dummies for spikes are de?ned as 1 if
x > 0.2
series. The logit estimated using the simulated panel does a mix job matching the
empirical coe?cients, but it is worth to notice that the de?nition of small or large
adjustment is arbitrary and given the lumpier nature of the simulated panel, these
de?nitions can a?ect the results. In particular, there is a signi?cant and negative
probability of adjusting capital and labor when there is inaction in the other factor,
which is not observe in the data. Even if it will be worth to incorporate this set
of moments in the estimation, the problem would come from the de?nition of large
and small adjustments. This is left for future work.
1.6 Conclusions
In this paper I have used the Census of Manufacturing Firms in Colombia to
analyze if labor and capital adjustments are interrelated, whether there are conges-
76
tion e?ects in the adjustment process, and what is the nature of the adjustment
costs.
Empirically, ?rms adjust employment and capital in an interrelated way, using
several margins of adjustment in the process. As is the case for U.S. ?rms, there is a
distribution of adjustment that is at the same time lumpy and infrequent for capital
and labor, being more frequent in the case of materials and energy. These patterns
suggest that to understand the e?ect of policies such as tax investment incentives or
reductions in the ?ring/hiring costs, a model of joint capital and labor adjustment
is needed.
I argue that these patterns can be explained with a dynamic model in which
labor and capital are costly to adjust. The adjustment cost structure is chosen to
match some facts observed in the data, such as the decrease in output after the
adjustment, the cost of hiring and ?ring workers, the cost of installing capital and
a convex component to capture the mix of smooth and lumpy adjustment.
The proposed model is ?rst calibrated taken the adjustment costs parame-
ters in an arbitrary way to serve as example and then estimated with a minimum
distance procedure. The analysis of the decision rules for ?rms’ capital and labor
adjustment shows that the adjustment patterns are highly nonlinear and they can
be characterized as a bidimensional (S,s) policy where adjustment depends not just
of the states of the system but also on the choices. The calibrated model is able to
replicate some features from Colombian ?rms’ adjustment patterns, but none of the
di?erent adjustment cost types ?t the data when considered alone. We also observe
that a model with adjustment costs only in capital or in labor predicts di?erent
77
behavior. Importantly, models with high congestion e?ects more closely resemble
the data.
Finally, I estimate the deep parameters of the model using a structural ap-
proach with a minimum distance algorithm. This method reveals that a model that
incorporates congestion e?ects ?ts the data best and the structural methodology al-
lows me to reject statistically the existence of ?xed costs and to accept the existence
of disruption costs for capital and labor, the existence of convex costs for capital
but not for labor and the existence of congestion e?ects.
The main conclusion is that labor and capital adjustment should be analyzed
together. This is supported both by theory and by facts. The data show an inter-
related adjustment pattern. Moreover, a model that incorporates adjustments for
both capital and labor, generates sharply di?erent predictions if adjustment costs
are assumed for one factor alone.
The main advantage of the type of methodology proposed in this paper is that
several policy experiments can be analyzed. The e?ects of taxes on capital and
employment and the aggregate e?ects of these policies are among the main ones.
Also, Colombia undertook several market liberalization reforms at the beginning of
the 1990s, so it would be interesting to use this structural framework to explore
how the reforms a?ected ?rm behavior in terms of factor adjustment. And ?nally,
it may be worth exploring sectoral di?erences in ?rm behavior, especially since the
parameters and functional forms may not be the same for all types of industries. This
paper took an aggregate approach to this problem, but a more micro-level analysis
may prove useful, particulary if micro level behavior is the key to understanding
78
aggregate responses.
79
Chapter 2
Costs of Adjusting Production Factors: The Case of a Glass Mould
Company
2.1 Introduction
In chapter 1, I proposed and estimated a model to explain the main empiri-
cal ?ndings observed in the distributions of factor adjustments for the Colombian
Census of Manufacturing Firms. This explanation relied on the existence of a wide
range of adjustment costs for capital and labor and in the interrelation of such ad-
justments. The present chapter presents direct evidence for the adjustment costs
proposed in chapter one, in order to relate these rather abstract concepts about
adjustment costs and interrelation to a concrete ?rm. The approach of this chapter
is simply to observe the internal records of a ?rm and determine directly how much
this ?rm has to pay for adjusting production factors
1
. Using these observed adjust-
ment costs, the chapter also evaluates how well the generic model presented in the
previous chapter can ?t a speci?c ?rm.
Ever since the work of Holt, Modigliani, Muth and Simon (1960), economists,
under the pro?t maximizing agent paradigm, have tried to derive optimal production
decision rules and to test these rules with actual data from operating plants. Despite
their e?ort, the number of di?erent production factors, the heterogeneity in di?erent
1
In some cases, the adjustment costs analyzed in the previous chapter are not directly observed,
but the numbers presented in this section are either directly observed or part of a reduced form
data analysis; in the former case, the reduced form analysis does not pretend to uncover the
structural parameters because of endogeneity problems, and are simply aimed to illustrate the
concepts developed in chapter one.
80
production processes and the mathematical complexities of the problem, in addition
to the di?culty in accessing the data, have been and still are a big challenge for
economists.
Production decisions are taken in an uncertain and dynamic environment
where decisions today a?ect the decision tomorrow. At the ?rm level, the usual
approach to the problem of deriving optimal decision rules for production factors
was to specify a quadratic cost function and derive the optimal decision rules. The
choice of a quadratic function was to simplify the mathematical problem. At the
aggregate level, this quadratic function was implemented to ?t the smooth series
observed in the data capturing the fact that it takes time to adjust production
factors.
Despite its simplicity, the quadratic adjustment cost implies continuous adjust-
ment, a feature that is not observed in the adjustment of many production factors at
the ?rm level, and in particular, not observed in the adjustment of employment and
capital. Instead, at the micro level, we observe infrequent and lumpy adjustments.
The main explanation for this ?rm behavior is that there are non-convex costs of
adjusting production factors, which translate into discrete payments or costs, like
the cost that a ?rm has to pay to hire or ?re a worker, or the resources in time and
money that a ?rm has to allocate to adjust capital.
Adding to the debate, this chapter presents direct and detailed evidence of
the type of costs a ?rm has to pay when hiring/?ring a worker or when adjusting
capital, using detailed monthly data from a glass container mould ?rm in Colombia.
At this frequency, we observe a ?xed cost when the ?rm hires or ?res workers
81
and an adjustment cost that comes from the disruption in the production process
during periods of adjustment, which increases when the adjustment is simultaneous
in capital and employment. These adjustment costs are directly related to the ones
proposed in chapter one’s model and are speci?c examples of such adjustment costs.
It is important to emphasize that the adjustment costs present here are not estimated
as in the previous chapter uncovering the structural parameters, but instead they
are directly observed and analyzed using reduced form equations.
The observed magnitudes of the adjustment costs are important. Hiring a
new worker costs $1, 320 US dollars and ?ring an existing worker costs $53, 000 US
dollars, a striking asymmetry. The existence of a powerful union increases the cost
of adjusting the number of workers through contractually established fees for ?ring
in addition to high legal costs. With respect to the disruption costs, hiring a worker
increases the production time by 1.02% a month and installing new units of capital
requires on average 1,417 hours a month, which correspond respectively to 0.073%
and 1.6% of total monthly sales. The disruption cost of installing capital is increased
by 0.86%, to 1.614% of total sales, when there is simultaneous adjustment of capital
and employment.
Besides presenting direct evidence on the di?erent types of adjustment costs,
this paper examines the pertinence of using the model developed in the previous
chapter that ?ts the average factor adjustment behavior of ?rms in Colombia, to
describe and predict the actual decision rules for this particular ?rm. In order to
do so, I use the available data on production and adjustment costs for this ?rm to
calibrate the model.
82
The model matches many of the qualitative features of the data and pro-
vides a good ?t quantitatively in other dimensions. Speci?cally, it is able to closely
match the correlation between capital and employment adjustment and productiv-
ity shocks. However, it falls short in explaining the e?ects of employment growth
in investment. There are some conceptual issues described later with respect to the
type of production process the model in the previous section describes compared to
the production process in this speci?c ?rm, but in any case it is useful to link the
direct evidence of adjustment costs obtained in this ?rm with a generic model that
?ts the macro level. Overall, the level of detail and the quality of the data, together
with the particularities of the ?rm, help us understand, on the one hand, the nature
of the adjustment costs observed at the ?rm level, and on the other hand, the the
ability of a model estimated at the macro level to ?t the data for a micro level ?rm
The paper has 5 sections. Section 2 describes the ?rm and the production
process. Section 3 presents the data and calculates adjustment costs, while section
4 describes the model, estimates the remaining parameters needed for the simulation
and presents the results, discussing the validity of simulating the model from the
previous chapter without any modifycation. Section 5 concludes and gives directions
for future research.
83
2.2 Description of the ?rm and the production process
2.2.1 History of Moldes Medellin
The ?rm used in this study is a glass mould company called Moldes Medellin.
This ?rm is a subsidiary of Ross Mould International and it is located in Medellin,
Colombia. Ross Mould International is the largest glass bottle mould company in
the world, owning plants in Colombia, England, Hungary, South Africa and U.S.
2
Moldes Medellin started operations in 1999. Before that, it was called Met-
alicas Peldar and it was a division of Peldar, a subsidiary of Owens Illinois located
in Medellin and Bogota. Peldar (Owens Illinois) sold Metalicas in 1999 to Ross
Mould International, a long term US Owens Illinois’ supplier.
3
Ross Mould made a
big initial investment, represented not only by machinery and land but also in the
form of knowledge of the production process (embodied in local labor with years of
experience); since then, no other big investments have been made.
The main customers for Moldes Medellin and for Ross International are the
two worldwide leading companies in the glass industry: Owens Illinois and Saint
Govain. Owens Latin America (Colombia, Peru, Venezuela, Ecuador, Dominican
Republic and Puerto Rico) has an special agreement with Moldes Medellin to supply
90% of their needs for the next 10 years
4
. As a consequence, the ?rm’s investment in
2
Ross Mould International has four US subsidiaries: Ross Mould, Penn Mould, OMCO mould
and Brockway Mould. Together, these operations design and built moulds for virtually every
glass bottled product on the U.S. market, including those for leading food, beverage, cosmetics
manufacturers such as Kraft, Gerber, General Foods, Coca Cola, Avon, and many others.
3
The Glass industry requires high levels of capital. These industries used to be vertically
integrated with their supply chains, and it was common to ?nd units within the ?rms in charge of
supplying the moulds required for glass production.
4
Ross International has similar agreements with Owens all around the world.
84
publicity and marketing is almost zero, allowing the company to focus on production
and service.
It is important to point out that Ross Mould does not have competitors in
Colombia and there are very few companies in Europe and America able to manu-
facture this kind of product
5
. As a result, it is very di?cult to ?nd quali?ed labor
and the company needs to provide most of the speci?c training for new workers.
2.2.2 The Production Process
Moldes Medellin produces moulds primarily for glass container companies.
A glass mould consists of several parts, each creating a stage in glass container
manufacturing process, giving the shape to the containers in a progressive way.
Glass moulds require high precision in the dimensions and high technology both in
design and manufacturing.
This company uses machine tools directed by computer programs which are
adapted for each batch. The operator of the machine tools has to do a special
mounting for each job, then charges and proofs the programs and measures the ?nal
result. Maintenance also plays a very important role since a production disruption
caused by a machine breakdown can have a considerable impact on service costs
and time.
Manufacturing the moulds has two phases: planning and production. The
planning phase starts with the designing of the mould using CAD (Computer As-
5
PEREGO and CISPER are perhaps the most signi?cant competitors that Ross Mould has to
face in Europe and America.
85
sisted Design). Once the design is done, the engineers program the production
process and write codes to program the machines for each step in the process, using
special engineering programming software (CNC- Computer Numerical Control and
CAM -Computer Assisted Machining). The next step is to assign the tools and
cutting conditions.
The production phase starts with an initial machining to the raw cast iron
material, and then a special welding process is applied to a part of the mould.
Depending of the shape of the mould, di?erent machining processes are applied
afterwards. In order to guarantee the precision of the product, a Coordinate Measure
Machine is used during the process to measure results. Each piece is analyzed by
this machine and the dimensional report is sent directly to the customer.
For each batch, the machine tools have to be set using di?erent tools depending
on the job. These tools last between 6 to 12 months and are very expensive. Also,
there are special additional elements added to the machine tools in order to execute
special processes which are called ?xtures.
In the next subsection I will describe the type of adjustment costs the company
faces when adjusting machines for new jobs and when hiring new workers. Later,
these costs are quanti?ed with ?rst-hand data on costs from the internal records of
the ?rm.
86
2.3 Data: Production process, Factor Adjustment Dynamics and Ad-
justment Costs
2.3.1 Data
I have three years of monthly data from Moldes Medellin, from January 2003
until December 2005. The data set has information on production (sales in US
dollars and quantities by item), investment (book values in Colombian pesos, cal-
culated as in Eslava et al (2004)), energy (quantities and prices), materials (prices
and quantities by job), labor hours and number of workers (production and non
production), and total labor costs in US dollars
6
. There is also data on setup times
in man-hours. I consider setup times are to be an adjustment cost for reasons I will
discuss later. All prices are converted to December 2005 US dollars using the o?cial
exchange rate and the US CPI series from the BLS.
My measure of capital consists of two parts. The ?rst part is the book values
of capital excluding land and vehicles. The second component consists of the tools
that the company uses to produce the moulds which have an approximate lifetime
of 6 months in Moldes Medellin and are not including in the book value measure of
capital
7
.
6
The calculation of labor costs is done by the plant manager day by day, converting payments
in colombian pesos to dollars using the daily o?cial exchange rate
7
These two types of capital have di?erent depreciation rates. The depreciation rate for the ?rst
type, following Oliner (1996), was set equal to the 9.5% annual depreciation rate for numerically
controlled machine tools In the second type, the depreciation taken was 35% monthly, implying a
scrap value of 12% in 6 months and a zero value in 12 months. The average selling price Moldes
Medellin gets is 12%.
87
2.3.2 A First look at the Production and Factor Adjustment Dynam-
ics
This section explores how Moldes Medellin adjusts its input factor choices
when production changes. Speci?cally it looks at the behavior of production in
sales and units, the number of production and non production workers, production
labor hours and the costs and units of materials and energy.
I start by describing basic statistics and graphing time series, then discuss
volatility and comovement among the variables in levels and in percentage terms.
Although the sample size is very small (36 observations), it is still useful to look at
these numbers to get an idea of the behavior of the ?rm.
8
Table 2.1 shows the mean
and standard deviation of the levels and growth rates of these variables. We can see
from this table that Moldes Medellin is not a very big ?rm. Monthly sales are less
than a million dollars on average and there are only 82 workers with a capital stock of
7.5 million dollars. Almost all the capital consists of machine tools, 23% of the total
workers are engineers and 89% of the production workers are high skilled workers.
The ?rm does not hold inventories because all jobs made made to order. It is also
worth noticing that the plant was underutilized during the entire sample period
which indicates no shortage of capacity. Finally, the company had an interesting
downsizing process in December 2003 in output and labor, since the management
started to build another plant to get rid of the ?nancial burden imposed by the
union; this can be seen in ?gure 2.1. This regime change plays an important role
8
A small sample size can a?ect the standard deviation of the variables and the statistical
signi?cance of the correlations.
88
Table 2.1: Basic Statistics. Monthly values
Levels Growth
Mean Std Mean (%) Std
Sales 906 229 1.84 0.21
Production Workers 53 2 0.02 0.02
Nonproduction Workers 29 2 -0.34 0.03
Total Workers 82 3 -0.12 0.02
Energy 8.4 2.0 7.23 0.34
Materials 306 115 3.96 0.30
Units produced 7.8 1.9 4.18 0.30
Hours 7.2 1.8 2.79 0.22
Energy (thousand Kw) 125 9 1.19 0.08
Capital 7571 420
Capital Tools 65 26
Investment 59 80
Investment Tools 23 19
Investment Rate (I/K) 0.80 0.01
Inv. Tools/ Capital 0.30 0.00
Inv.Tools/Capital Tools 33.88 0.11
Sales, Capital, Investment, Energy and Materials in thousand of 2005 US$ dollars.
Hours and Units produced in thousands
and it is considered later in the estimations.
Figure 2.1 shows the series for employment and labor hours, investment and
capital, energy in units (Kw) and monetary values, materials, total costs, total
sales and total units produces. Figure 2.2 shows the factor adjustment graphs at a
monthly frequency. The peaks observed in production and non production workers
adjustment and the lumpiness in their adjustment suggest the presence of non-
convex adjustment costs to change the number of workers. Hours, energy and mate-
rials, move much more often than employment. Total investment has some inaction
months mixed with some peaks. In the case of the long term tools, which depreciate
quickly, investment is always positive, with a peak that represents a special ?xture
the company bought to produce a special mould part.
89
Figure 2.1: Production Factors Series
Capital (thousand US$)
6000
6500
7000
7500
8000
8500
J
a
n
-
0
3
A
p
r
-
0
3
J
u
l
-
0
3
O
c
t
-
0
3
J
a
n
-
0
4
A
p
r
-
0
4
J
u
l
-
0
4
O
c
t
-
0
4
J
a
n
-
0
5
A
p
r
-
0
5
J
u
l
-
0
5
O
c
t
-
0
5
Labor cost (pdn) thousand US$
0
10
20
30
40
50
60
J
a
n
-
0
3
A
p
r
-
0
3
J
u
l
-
0
3
O
c
t
-
0
3
J
a
n
-
0
4
A
p
r
-
0
4
J
u
l
-
0
4
O
c
t
-
0
4
J
a
n
-
0
5
A
p
r
-
0
5
J
u
l
-
0
5
O
c
t
-
0
5
Labor (pdn) thousand hours
0
2
4
6
8
10
12
14
J
a
n
-
0
3
A
p
r
-
0
3
J
u
l
-
0
3
O
c
t
-
0
3
J
a
n
-
0
4
A
p
r
-
0
4
J
u
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-
0
4
O
c
t
-
0
4
J
a
n
-
0
5
A
p
r
-
0
5
J
u
l
-
0
5
O
c
t
-
0
5
Energy (thousand US$)
0
2
4
6
8
10
12
14
J
a
n
-
0
3
A
p
r
-
0
3
J
u
l
-
0
3
O
c
t
-
0
3
J
a
n
-
0
4
A
p
r
-
0
4
J
u
l
-
0
4
O
c
t
-
0
4
J
a
n
-
0
5
A
p
r
-
0
5
J
u
l
-
0
5
O
c
t
-
0
5
Energy units (thousand KW)
100
110
120
130
140
150
160
170
J
a
n
-
0
3
A
p
r
-
0
3
J
u
l
-
0
3
O
c
t
-
0
3
J
a
n
-
0
4
A
p
r
-
0
4
J
u
l
-
0
4
O
c
t
-
0
4
J
a
n
-
0
5
A
p
r
-
0
5
J
u
l
-
0
5
O
c
t
-
0
5
Materials (thousand US$)
0
100
200
300
400
500
600
700
J
a
n
-
0
3
A
p
r
-
0
3
J
u
l
-
0
3
O
c
t
-
0
3
J
a
n
-
0
4
A
p
r
-
0
4
J
u
l
-
0
4
O
c
t
-
0
4
J
a
n
-
0
5
A
p
r
-
0
5
J
u
l
-
0
5
O
c
t
-
0
5
Production (Sales thousand US$)
0
200
400
600
800
1000
1200
1400
1600
J
a
n
-
0
3
A
p
r
-
0
3
J
u
l
-
0
3
O
c
t
-
0
3
J
a
n
-
0
4
A
p
r
-
0
4
J
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-
0
4
O
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t
-
0
4
J
a
n
-
0
5
A
p
r
-
0
5
J
u
l
-
0
5
O
c
t
-
0
5
Production units (thousand)
0
2
4
6
8
10
12
14
J
a
n
-
0
3
A
p
r
-
0
3
J
u
l
-
0
3
O
c
t
-
0
3
J
a
n
-
0
4
A
p
r
-
0
4
J
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l
-
0
4
O
c
t
-
0
4
J
a
n
-
0
5
A
p
r
-
0
5
J
u
l
-
0
5
O
c
t
-
0
5
Production jobs
0
50
100
150
200
250
J
a
n
-
0
3
A
p
r
-
0
3
J
u
l
-
0
3
O
c
t
-
0
3
J
a
n
-
0
4
A
p
r
-
0
4
J
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l
-
0
4
O
c
t
-
0
4
J
a
n
-
0
5
A
p
r
-
0
5
J
u
l
-
0
5
O
c
t
-
0
5
Investment (thousand US$)
-200
-100
0
100
200
300
400
500
J
a
n
-
0
3
A
p
r
-
0
3
J
u
l
-
0
3
O
c
t
-
0
3
J
a
n
-
0
4
A
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r
-
0
4
J
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-
0
4
O
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-
0
4
J
a
n
-
0
5
A
p
r
-
0
5
J
u
l
-
0
5
O
c
t
-
0
5
Capital Tools (thousand US$)
0
40
80
120
160
200
J
a
n
-
0
3
A
p
r
-
0
3
J
u
l
-
0
3
O
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0
3
J
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4
A
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4
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4
O
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4
J
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5
A
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-
0
5
J
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-
0
5
O
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-
0
5
90
Figure 2.2: Production Factors Adjustment
Production growth (Sales)
-60%
-40%
-20%
0%
20%
40%
60%
80%
J
a
n
-
0
3
A
p
r
-
0
3
J
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0
3
O
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3
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4
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5
A
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-
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5
J
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-
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5
O
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-
0
5
Production Units Growth
-80%
-40%
0%
40%
80%
120%
J
a
n
-
0
3
A
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r
-
0
3
J
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3
O
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0
5
A
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-
0
5
J
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-
0
5
O
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-
0
5
Materials Growth
-80%
-40%
0%
40%
80%
120%
J
a
n
-
0
3
A
p
r
-
0
3
J
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-
0
3
O
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-
0
3
J
a
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-
0
4
A
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-
0
4
J
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-
0
4
O
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-
0
4
J
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-
0
5
A
p
r
-
0
5
J
u
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-
0
5
O
c
t
-
0
5
Workers growth
-6%
-4%
-2%
0%
2%
4%
6%
8%
10%
J
a
n
-
0
3
A
p
r
-
0
3
J
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l
-
0
3
O
c
t
-
0
3
J
a
n
-
0
4
A
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0
4
J
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0
4
O
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-
0
4
J
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-
0
5
A
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r
-
0
5
J
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l
-
0
5
O
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t
-
0
5
Production Workers growth
-6%
-4%
-2%
0%
2%
4%
6%
8%
10%
12%
J
a
n
-
0
3
A
p
r
-
0
3
J
u
l
-
0
3
O
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t
-
0
3
J
a
n
-
0
4
A
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-
0
4
J
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0
4
O
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-
0
4
J
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-
0
5
A
p
r
-
0
5
J
u
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-
0
5
O
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t
-
0
5
Non Production Workers growth
-12%
-8%
-4%
0%
4%
8%
12%
J
a
n
-
0
3
A
p
r
-
0
3
J
u
l
-
0
3
O
c
t
-
0
3
J
a
n
-
0
4
A
p
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-
0
4
J
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-
0
4
O
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t
-
0
4
J
a
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-
0
5
A
p
r
-
0
5
J
u
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-
0
5
O
c
t
-
0
5
Hours Growth
-80%
-40%
0%
40%
80%
J
a
n
-
0
3
A
p
r
-
0
3
J
u
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-
0
3
O
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t
-
0
3
J
a
n
-
0
4
A
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-
0
4
J
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-
0
4
O
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-
0
4
J
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-
0
5
A
p
r
-
0
5
J
u
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-
0
5
O
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t
-
0
5
Energy Kw Growth
-30%
-20%
-10%
0%
10%
20%
30%
J
a
n
-
0
3
A
p
r
-
0
3
J
u
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-
0
3
O
c
t
-
0
3
J
a
n
-
0
4
A
p
r
-
0
4
J
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-
0
4
O
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t
-
0
4
J
a
n
-
0
5
A
p
r
-
0
5
J
u
l
-
0
5
O
c
t
-
0
5
Energy Cost Growth
-80%
-40%
0%
40%
80%
120%
160%
J
a
n
-
0
3
A
p
r
-
0
3
J
u
l
-
0
3
O
c
t
-
0
3
J
a
n
-
0
4
A
p
r
-
0
4
J
u
l
-
0
4
O
c
t
-
0
4
J
a
n
-
0
5
A
p
r
-
0
5
J
u
l
-
0
5
O
c
t
-
0
5
Investment Rate (I/K)
-2%
-1%
0%
1%
2%
3%
4%
5%
6%
J
a
n
-
0
3
A
p
r
-
0
3
J
u
l
-
0
3
O
c
t
-
0
3
J
a
n
-
0
4
A
p
r
-
0
4
J
u
l
-
0
4
O
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t
-
0
4
J
a
n
-
0
5
A
p
r
-
0
5
J
u
l
-
0
5
O
c
t
-
0
5
Investment rate (Tools / K)
0.0%
0.2%
0.4%
0.6%
0.8%
1.0%
1.2%
1.4%
1.6%
1.8%
J
a
n
-
0
3
A
p
r
-
0
3
J
u
l
-
0
3
O
c
t
-
0
3
J
a
n
-
0
4
A
p
r
-
0
4
J
u
l
-
0
4
O
c
t
-
0
4
J
a
n
-
0
5
A
p
r
-
0
5
J
u
l
-
0
5
O
c
t
-
0
5
Investment rate (Tools / Ktools)
0%
10%
20%
30%
40%
50%
60%
70%
80%
J
a
n
-
0
3
A
p
r
-
0
3
J
u
l
-
0
3
O
c
t
-
0
3
J
a
n
-
0
4
A
p
r
-
0
4
J
u
l
-
0
4
O
c
t
-
0
4
J
a
n
-
0
5
A
p
r
-
0
5
J
u
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-
0
5
O
c
t
-
0
5
91
Table 2.2: Correlation among the levels of the variables
Pdn Nonpdn Total K Units
Sales Wks Wks Wks K Tools Energy Materials pdn
Sales 1.00
Pdn Workers 0.26 1.00
Nonpdn Wks 0.36 0.32 1.00
Total Wks 0.37 0.87 0.75 1.00
K -0.46 0.01 -0.71 -0.36 1.00
K Tools 0.06 -0.41 0.38 -0.09 -0.32 1.00
Energy -0.47 -0.18 -0.69 -0.49 0.83 -0.19 1.00
Materials 0.95 0.37 0.29 0.41 -0.37 -0.07 -0.48 1.00
Units pdn 0.82 0.32 0.04 0.25 -0.10 -0.14 -0.21 0.87 1.00
Hours 0.86 0.18 0.30 0.28 -0.38 0.05 -0.34 0.76 0.61
Table 2.3: Correlation among the Growth of the variables
Pdn Nonpdn Total
I
K
Itools
K
Itools
Ktools
Units
Sales Wks Wks Wks Energy Mat. pdn
Sales 1.00
Pdn Wks -0.07 1.00
Nonpdn Wks 0.17 0.30 1.00
Total wks 0.05 0.82 0.79 1.00
I
K
-0.21 -0.08 -0.05 -0.08 1.00
Itools
K
0.13 -0.26 -0.01 -0.17 -0.03 1.00
Itools
Ktools
0.26 -0.19 0.00 -0.13 -0.01 0.75 1.00
Energy -0.11 -0.01 0.00 0.00 0.08 -0.01 0.01 1.00
Materials 0.94 -0.09 0.11 0.00 -0.16 0.01 0.17 -0.18 1.00
Units pdn 0.87 -0.04 0.03 -0.01 -0.19 -0.05 0.07 -0.08 0.91 1.00
Hours 0.78 -0.10 0.09 -0.01 -0.09 0.19 0.38 0.16 0.63 0.64
Table 2.2 shows the correlation among variables and Table 2.3 shows the cor-
relation among adjustments. It is interesting to notice the positive and strong
correlation between hours growth and investment in long lived tools and between
hours and energy and materials. This ?rm chooses to adjusts hours rather than
workers since workers adjustment is very costly.
The dynamic correlations between adjustments are presented in Table 2.4,
which shows a VAR of factor adjustments. Having in mind the small sample size
and the fact that this is just an empirical exercise, the only statistically signi?cant
correlations are between lagged hours growth and investment in long lived tools, and
between hours growth and lagged energy growth. The same interrelation between
capital and labor is observed at the aggregate level in other studies using the number
92
Table 2.4: VAR for Growth of the variables
Itools
Ktools
?M
M
?e
e
?h
h
-0.192 0.009 -0.186 0.001
(
Itools
Ktools
)
?1
-0.169 -0.238 -0.176 -0.165
0.228 -0.288 -0.138 0.181
(
?Materials
Materials
)
?1
-0.173 -0.244 -0.18 -0.169
0.096 0.082 -0.505 0.017
(
?Energy
Energy
)
?1
-0.149 -0.21 (0.156)** -0.146
0.632 0.402 0.239 0.016
(
?Hours
Hours
)
?1
(0.276)* -0.389 -0.288 -0.27
-2.34 -0.541 -0.36 -0.98
(
?TFP
TFP
)
?1
(0.767)** -1.08 -0.8 -0.75
Constant 0.395 -0.009 0.074 -0.007
(0.059)** -0.083 -0.061 -0.058
Observations 34 34 34 34
R-squared 0.4 0.09 0.29 0.1
of workers. It is possible that at this frequency and with the high adjustment costs
in employment this ?rm faces, the utilization of labor, re?ected in the production
hours, is more closely related to investment than the number of workers.
This descriptive evidence suggests that given the constraints this ?rm faces on
adjusting workers or the capital stock, it instead uses intensively other margins of
adjustment such as hours, materials and energy. The low capacity utilization gives
the ?rm larger cushion to adjust these factors both upwards and downwards. With
respect to investment, even if Moldes Medellin faces high costs of capital adjustment
due to setup costs for its tools, it still invests almost continuously, but in a lumpy
way as seen in ?gure 2.2. The next section presents direct evidence on the costs
that this ?rm has to pay when adjusting capital and labor.
93
2.3.3 A Description and Calculation of the Adjustment Costs faced
by the Company
This section discusses the type of adjustment costs that Moldes Medellin faces,
at a monthly frequency, when it decides to change its production factors, speci?cally
capital and employment in response to changes in demand. The methodology used
in this section is descriptive, meaning that the adjustment costs are directly observed
as payments or increases in costs that the ?rm incurs when adjusting. I use some
reduced form regressions to isolate individual e?ects of the adjustment costs.
Adjustment Costs in Capital
When Moldes Medellin has to manufacture a batch of moulds, it must set up
the machine tools for that speci?c job. Setting the machines involves three stages:
the ?rst stage is to charge the programs into the machine’s computer; the second
stage consists of adding elements and structures to the machine in order to position
the pieces (known as “?xtures”) and the tools in the process; and the third stage is
to set up the speci?c tools for the job.
These ?xtures and tools should be considered as investments because they are
used in several jobs to produce several pieces, and are literally interchangeable parts
of the machine. They have a lifetime of around six months. They are not materials
and are not counted as materials.
This setup process takes a considerable amount of time and disrupts the pro-
duction process. In Moldes Medellin all these steps are timed and they represent
between 10% to 35% of the total time in man-hours depending on the month and
94
on the past and current job, and between 1% to 3% of the total sales in a month
(1.6% on average). Figure 2.3 shows the total setup time in hours and the average
setup time per job, the setup time as a percentage of the total time, and the setup
time as a percentage of the total sales and the total costs. Around 20% of the total
time it takes to produce a mould in the plant is devoted to installing the new capital
required for the production; it is clearly observed in this ?gure that the ?uctuations
are not generated only by ?uctuations in sales or total costs.
Figure 2.3: Setup Costs
cost man hour cost setup total cost sales Setup cost / Total cost Setup cost / Sales
12 16 548 906 3.0% 1.8%
12 22 830 1170 2.7% 1.9%
12 22 805 1040 2.7% 2.1%
11 21 1077 1372 2.0% 1.6%
11 17 747 929 2.4% 1.9%
11 13 784 972 1.7% 1.4%
11 16 943 1245 1.8% 1.4%
11 13 913 1308 1.5% 1.1%
11 17 934 1397 1.9% 1.2%
11 15 758 1107 2.0% 1.4%
11 10 606 900 1.8% 1.2%
11 12 293 459 4.3% 2.7%
10 11 273 476 4.1% 2.4%
8 9 500 784 1.9% 1.2%
7 7 504 847 1.5% 0.9%
7 13 469 781 3.1% 1.8%
7 14 412 688 3.6% 2.2%
7 14 396 669 3.9% 2.3%
7 14 495 777 3.1% 2.0%
7 12 502 767 2.7% 1.8%
7 12 494 751 2.7% 1.8%
7 10 527 821 2.2% 1.4%
7 11 499 705 2.4% 1.7%
7 8 438 646 2.0% 1.3%
7 10 416 637 2.7% 1.8%
7 10 429 644 2.7% 1.8%
5 7 363 513 2.1% 1.5% 0.203704
7 12 444 628 3.1% 2.2%
7 12 559 806 2.4% 1.7%
7 7 487 681 1.8% 1.3%
7 7 587 841 1.5% 1.0%
7 7 565 816 1.4% 0.9%
7 8 600 854 1.5% 1.0%
7 6 549 749 1.4% 1.0%
7 6 498 704 1.5% 1.1%
7 13 501 700 2.9% 2.1%
308 435 20744 30089 1 1
Setup cost as percentage of Total Cost and as
percentage of Total Sales
0.5%
1.0%
1.5%
2.0%
2.5%
3.0%
3.5%
4.0%
4.5%
J
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Setup cost / Total cost Setup cost / Sales
Setup Costs
(Dec 2005 prices, thousand of dollars)
7
9
11
13
15
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21
23
25
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Setup time
(Thousand of hours)
0.5
0.7
0.9
1.1
1.3
1.5
1.7
1.9
2.1
2.3
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Total time and setup time per job
(hours)
1
11
21
31
41
51
61
71
81
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setup hours per job time per job
95
The fact that the disruption in the production process due to the machine
setup is quanti?ed, and that it can be translated into forgone pro?ts due to the
adjustment, gives ?rst hand support for the modeling mechanism adopted in the
literature of adjustment costs in which a decrease in productivity is observed during
the adjustment of capital or labor, which translates into longer production times.
It is important to notice that the setup costs in capital presented here are an
upper limit for the disruption costs caused by adjustment in capital, since some jobs
require only to re-align a set of tools without buying any new tools. However, the
short life of the tools and the speci?city of the jobs make this disruption costs to be
associated very often with investment episodes. In a related matter, sometimes it is
enough for the ?rm to change the computer programs but not necessarily the tools
it operates when a new job arrives, and in other cases it is necessary to change the
programs and the tools. This relates to the ideas of ?xed costs of adjustment and
”disruption costs”, but these are more like job speci?c investments, or ?xed costs.
This is an important di?erence with the model in chapter one, since that model
really does treat investment as an addition to long term capital stock, and not as a
job speci?c investment or short run ?xed cost of production.
Adjustment Costs in Employment
There are 3 types of observable adjustment costs in employment: (i) the direct
costs that ?rms have to pay to hire and to ?re a worker and (ii) the costs of shifting
resources from other workers to train the new ones, and (iii) the lower productivity
96
Table 2.5: Legal Firing Costs in the Colombian Legislation
Contract Type Firing Fee
Fixed term contract Time left to expiration
Contracts for the duration of the job Maximum between the time left to expiration or 15 days
Workers with less than 45 days
1 year of continuous service
Workers with more than 1 year 45 days and 15 more for every year after
and less than 5 years of continuous service the ?rst year and proportional for each fraction of year
Workers with more than 5 years 45 days and 20 more for every year after
and less than 10 years of continuous service the ?rst year and proportional for each fraction of year
Workers with more than 10 years 45 days and 40 more for every year after
of continuous service the ?rst year and proportional for each fraction of year
of the new workers compared with the old ones
9
.
The ?rst type of costs have received the most attention in the literature since
they are more directly observable. They are typically modeled as ?xed costs. The
second type of costs are known in the literature as disruption costs.
The average payment to ?re a worker in Moldes Medellin is around US$ 53,000,
which includes legally mandated ?ring costs and the union agreement cost. Because
of the strength of the union, the ?ring cost is more than four times the legally
mandated payment for laying o? a worker. Table 2.5 shows these legal fees. In
the case of Moldes Medellin this translates into 71 dollars per day of legal payment
(assuming an average hourly wage of US$8.9) which means that, accounting for
the average tenure time of 6 years, the average legally mandated ?ring cost is about
US$10,300. The rest of the ?ring cost (US$42,700) comes from the union agreements.
In order to hire a worker, the ?rm pays around US$1,320. This money is
spent on medical and psychological examinations, training costs and increases in
production times (reduction in productivity) while the new worker learns the job.
The training costs are a form of disruption costs since the ?rm shifts resources to
9
The main hiring costs are psychological, medical and ability tests, and the ?ring costs are the
legal ?ring costs and the union agreement fees.
97
train new workers using old workers; in total, this training takes 6 shifts of 8 hours
each. Given the average hourly rate (US$8.9), the total training cost has been
quanti?ed to be US$427
10
. The increase in the production time is calculated to be
2% during the ?rst month after a new worker is hired according to the manager
of the ?rm; to test this number, I ran a regression in logs of the production hours
on the number of workers and controlling for the number of units produced, which
con?rmed the manager’s estimate: an increase of 1% in the labor force increases the
total production time by 1.02%
11
. Given the average production hours per month
(7,240), this represents a cost of US$657 assuming that the worker is fully productive
after the ?rst month. Finally, the medical and psychological examinations cost
US$240 according to the company records.
Summarizing, there are two important points with respect to employment ad-
justment in this ?rm. The ?rst one is that the disruption cost is the most important
adjustment cost that ?rms face when hiring. The ?xed cost of hiring is per-se rela-
tively very low. The second point is that there exists a big asymmetry between the
hiring and the ?ring cost. In the case of Moldes Medellin this asymmetry is even
bigger because of the existence of the union, but in any case, the legally mandated
?ring cost is much higher than the hiring cost
12
.
10
This number is just an approximation, since during some periods the worker’s marginal pro-
ductivity may be higher (or lower) than the wage, causing a higher (or lower) disruption cost.
11
This regression controls for tfp (the solow residual, which is calculated and explained later in
the paper) and the level of capital. It also controls for the change in regime observed in December
2003 using a dummy variable. The standard deviation of the coe?cient is 0.27, meaning a statistical
signi?cance of 1%
12
The hiring cost is about 2.5% of the ?ring cost or 12.9% if we consider only the legal payments.
98
Interaction E?ects in the Adjustment Costs
Besides the individual adjustment costs that Moldes Medellin has to pay when
adjusting capital or employment, it is worth investigating whether the cost of ad-
justing capital increases or decreases when the ?rm adjusts employment simultane-
ously. As it was analyzed in chapter one, I call this interaction e?ects, which could
be positive (complementarities) or negative (congestion e?ects). In chapter one,
the parameters governing this interaction e?ect were uncovered with a simulation
procedure. In this section, the approach is di?erent and a reduced form regression
is ran in order to illustrate the e?ects. This reduced form analysis does not pretend
to uncover the structural parameters governing the interaction e?ects, since there
are some endogeneity problems; instead, the empirical analysis of the interaction
e?ects is aimed to clarify the concepts presented in chapter one and give ?rst-hand
empirical support for the existence of interaction e?ects. Although I do not have a
series of the employment adjustment costs, I have the series for the setup costs paid
by the ?rm every month when adjusting capital, which, as was mentioned above,
gives an upper limit for the disruption adjustment costs.
In order to ?nd out if employment growth a?ects the disruption adjustment
costs for capital (i.e. if the disruption adjustment costs are higher or lower than
average during periods of worker adjustment), I ran regressions of the logs of capital
set-up costs and capital set-up hours on the change in employment level. The
coe?cient should be interpreted as the e?ect of employment growth on disruption
cost growth (set-up cost or set-up time growth). If it is cheaper to adjust both
99
Table 2.6: E?ect of a Change in the Number of Workers on the Capital Disruption
Adjustment Cost
Dependent Variable
log Set-up costs log Set-up time
1.17 0.255
? Workers
(2.04) (2.174)
1.128 0.579
? Non Pdn Workers
(1.323) (1.412)
-0.173 -2.226
? Pdn Workers
(2.123) 9.661
R-squared 0.51 0.52 0.31 0.31
Other Controls: tfp, lagged tfp, dummy at Dec 2003 (regime change)
and log of units produced. Standard errors in parenthesis
capital and employment at the same time, this coe?cient will have a negative sign
and it will be positive otherwise.
Table 2.6 shows the results of this regression. With respect to the sign of the
e?ect, we can see from this table that an increase in the number of workers increases
the adjustment costs for capital, suggesting the existence of congestion e?ects in the
adjustment costs (an extra cost of adjusting both factors together). Moreover, we
can see that it is the increase in the number of non production workers that increases
the setup costs. The same happens in the case of the set-up time. However, the
the coe?cients are not statistical signi?cant. Overall, this result may be due to the
small variation on the number of nonproduction workers or due to the nature of the
production process. In this particular production process the set-up of the machine
tools depends on the planning made by the non production workers: the engineers
have to plan the times and the speci?c ways the tools and ?xtures are placed.
I have shown the factor adjustment behavior of Moldes medellin and the cost
that it has to pay when adjusting. The next section explores to what extent a
100
model that closely matches the factor adjustment moments of the whole Census of
Manufacturing ?rms in Colombia is able to reproduce the adjustment of production
factors in Moldes Medellin.
2.4 How Well the Model from Chapter One Can ?t this Particular
Firm?
The objective of the previous section was to illustrate with a concrete example
the adjustment costs de?nitions proposed in chapter one. In particular, we could
observe in the data the costs that Moldes Medellin has to pay when hiring or ?ring
a worker (?xed costs), the increases in production time and the reallocation of re-
sources that the ?rm has to make when adjusting capital and labor(disruption costs),
and the increase in capital setup time when the ?rm adjust at the same time the
number of workers (congestion e?ects). This section looks to link the generic model
?tted for the Colombian ?rms to the particular production process that Moldes
Medellin has. As in chapter one, the objective of this model is to understand the
existence of infrequent and lumpy adjustment across input factors and especially in
labor and capital. The explanation given for this behavior lies in the di?erent ad-
justment costs a company faces when adjusting production factors. The model also
captures the observed interrelation between capital and labor adjustment. The pa-
rameters for the adjustment costs are taken directly from the evidence collected from
Moldes Medellin. The other parameters needed to simulate the model, such as the
production function elasticities and the productivity shocks, are directly estimated
from the data using the same methodology I applied in chapter one.
101
2.4.1 Model
The model is a dynamic ?rm problem with adjustment costs in employment
and capital, where ?rms decide how much input factors to use in response to changes
in demand and productivity. The main di?erence with previous adjustment cost
models in the literature is the existence of a complementarity e?ect which makes the
joint adjustment of capital and labor more expensive (or cheaper, since no restriction
is imposed) than the individual adjustments. What motivates the ?rm to adjust
capital and employment together is the gain of the joint adjustment compared with
the opportunity cost of adjusting only one or no factors.
Equation (2.1) describes the general problem. In this equation I
t
= k
t+1
?
(1 ??) k
t
represents investment and ? represents depreciation. C(•) is the cost of
adjustment, which takes di?erent parameter values depending on whether the ?rm
adjusts employment, capital or both. ? is the discount factor and the integral term
represents the expected value of the ?rm subject to shocks z. This shock distribution
f(z
/z) is parameterized as an AR(1) process estimated using the Solow residual
from the production function estimation. For notation reasons, this shock includes
materials and energy, which are chosen optimally every period in a static fashion
13
.
V (z, k, l
?1
) = max
k
,l
_
?(z, l
?1
, l, k, k
) +?
_
V (z
, (1 ? ?)k + I, l)f(z
/z)dz
_
= max
k
,l
{zk
?
l
µ
? w(l) ?C(z, l
?1
, l, k, k
)
+?
_
V (z
, (1 ? ?)k + I, l)f(z
/z)dz
} (2.1)
13
For more details on the model, see chapter one.
102
The cost of adjustment C(•) potentially includes disruption costs, ?xed costs
and convex costs. The following is the functional form assumed for the adjustment
costs when ?rms adjust l (labor), k (capital) or kl (capital and labor):
C (z, k, I, l, l
?1
) =
_
¸
¸
¸
¸
¸
¸
¸
¸
¸
¸
¸
¸
¸
_
¸
¸
¸
¸
¸
¸
¸
¸
¸
¸
¸
¸
¸
_
C
l
= ?
l
R(•) +F
l
l
?1
+
?
l
2
_
?l
l
?1
_
2
l
?1
if ?l = 0
C
k
= ?
k
R(•) +F
k
k +
?
k
2
_
I
k
_
2
k + p
I
? I if I = 0
C
lk
= C
l
+ C
k
+ ?
lk
R(•) + F
lk
?
l
?1
k
+
?
lk
2
_
I
k
_ _
?l
l
?1
_
?
l
?1
k if ?l ? I = 0
(2.2)
In the case of labor or capital adjustment, (C
l
and C
k
respectively) the ?rst term
?
j
R(•) represents the disruption cost, the second term involving F
j
represents
the ?xed cost and the third term involving ?
j
represents the convex cost, with
j=k(capital) and l(labor). In the case of capital adjustment, there is an extra cost
which represents the investment price, which can take values of p
I
= {p
buy
, p
sell
}
depending on if the ?rm buys or sells capital, having the selling price a negative
value. The asymmetry in the price for buying and selling capital implies that capital
is not fully reversible.
The convex cost term is the benchmark used in the cost function estimation
literature and it also appears also in this general model. In this paper, however, I
do not ?t with a quadratic function the observed adjustment costs. In fact, the data
does not show a quadratic shape. Neither do I use a ?xed capital adjustment cost,
since I do not have data on it.
In the model, if the ?rm adjusts capital and employment at the same time,
the adjustment cost is the sum of the cost of adjusting capital (C
k
), plus the cost of
adjusting employment independently (C
l
), plus a collection of terms that represent
103
the extra cost of the joint adjustment. The parameters to be inserted in the model
are the observed ones: {?
k
, ?
l
, ?
kl
} for the disruption cost, F
l
for the ?xed cost, and
p
I
for the investment price.
There are important di?erences between the production process represented
in the generic model in chapter one and the production process in Moldes medellin.
For example, Moldes Medellin “produces to order” and stochastic arrivals of orders
or ”jobs” seems like the appropriate way to model the glass mould factory. However,
the production function chosen for the generic model can be interpreted this way
if the shock processes are taken as demand shocks, or demand ?uctuations that
trigger the production factor adjustment every time they arrive. Also, many of the
adjustment costs that the glass mould company incurs are related to retooling from
one job to another, as it was said above. In this sense, the adjustment costs should
be seen as an upper limit.
2.4.2 Calibration/Estimation of the Parameters
The existence of a disruption cost takes the form of lower productivity and
can be also thought as the shift of resources in order to adjust the other factor. In
the previous section, this cost was observed to ?uctuate between 1% and 3% of the
total sales, with an average of 1.6% in the case of capital and of 1.02% increase in
the production time in the case of labor, or 0.073% of the total sales.
The ?xed adjustment cost represents the installation costs (in both time and
resources) in the case of capital and ?ring and hiring costs in the case of labor. I
104
only observe the ?xed labor adjustment cost, which is calculated to be $53,000 US
for ?ring and $240 US for hiring (out of the total of $1320 of hiring costs). This
translates into 5.8% of total monthly sales in the case of ?ring costs and 0.026% in the
case of hiring costs. Since my benchmark model assumes a symmetric adjustment
cost in employment, I use the average between the hiring and ?ring costs to be the
?xed cost parameter in the model. This cost (US$26,620) is scaled in the model by
the employment level. To get the parameter value, I consider the average number
of employees (80) as the scale value, getting a adjustment cost parameter of 333 or
0.333 in thousand dollars.
14
With respect to the selling price, this ?rm sells the used tools after a couple of
months for a recovery price which ?uctuates approximately between 10% and 20%
of the original price with an average of 12%.
Congestion e?ects in the adjustment costs are also observed in Moldes Medellin,
speci?cally in the capital disruption cost when the ?rm increases the number of work-
ers. The estimations above suggest that a 1% increase in the number of workers
increases the cost of adjusting capital by 1.17%. Table 2.7 summarizes the adjust-
ment cost parameters to be introduced in the model.
15
The values for the adjustment cost parameters calculated for Moldes Medellin
are consistent with the ones found in Chapter one using the generic model for the
Colombian ?rms. For example, the disruption cost parameter was 0.046 compared
to 0.01693 for Moldes Medellin. The ?xed cost parameter is much higher for Moldes
14
In future work, I intend to incorporate the asymmetry of these costs into the model and change
the scale value for the increment.
15
In order to make the parameters comparable with the ones in the previous chapter, I consider
capital and sales to be thousands of dollars.
105
Table 2.7: Adjustment Cost Parameters
Capital Employment
Disruption 0.016 0.00073
Fixed 0.332
Complementarity (disruption) 0.016 + 0.00073 + 0.0002 = 0.01693
Medellin than for the average ?rm in Colombia according to the estimates in chapter
one (0.332 vs. 0.007), but this may be due to several causes like the very high
cost imposed by the contractual obligations with the union, to the long tenure of
the workers in Moldes Medellin (the longer the tenure, the higher the ?ring cost),
and the failure of the model in capturing the asymmetry between hiring and ?ring
costs. On the other hand, the capital in this glass mould ?rm is very irreversible
compared with the typical Colombian ?rm (0.12 vs 0.42 times the buying price);
this is reasonable since we are dealing here with a form of capital that depreciates
very fast and is speci?c for the process.
The next step is to estimate the other parameters needed to simulate the
model in the case of Moldes Medellin. These parameters are the production function
elasticities, the wage equation parameters and the productivity shocks that will drive
the adjustment of the production factors.
What Function Can Describe the Production Process?
There may be many functional forms that can describe the production process
in Moldes Medellin. Since the objective of this section is to compare the perfor-
mance of the model proposed in the previous chapter, the natural choice is to ?t
a Cobb-Douglas production function. However, a closer look at the production
process suggests that such a choice is not a bad one. The main characteristic of
106
the Cobb-Douglas production function is that the cost shares remain constant. Fig-
ure 2.4 shows this value for Moldes Medellin. We can see that the cost shares do
not ?uctuate much, giving some support for the assumption of the Cobb-Douglas
production function. Table 2.8 shows the OLS estimates of the Cobb-Douglas pro-
Figure 2.4: Cost Shares
Cost Shares
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
J
a
n
-
0
3
A
p
r
-
0
3
J
u
l
-
0
3
O
c
t
-
0
3
J
a
n
-
0
4
A
p
r
-
0
4
J
u
l
-
0
4
O
c
t
-
0
4
J
a
n
-
0
5
A
p
r
-
0
5
J
u
l
-
0
5
O
c
t
-
0
5
labor pdn energy materials
duction function relating sales to capital, labor costs, energy cost and materials cost.
Even if the OLS coe?cients may be biased, the fact that the observed cost shares
are similar to the coe?cients estimated with the OLS suggest that this functional
form and these coe?cients are reasonable. The cost shares are on average 0.15 for
labor (total hours), 0.48 for materials, 0.02 for energy and 0.04 in the case of the
capital (long lived tools). The cost shares for labor and materials are very close
to the OLS estimates but the energy and the capital costs are not. This may be
because variation in capacity utilization occurs through capital (energy) more than
other factor and the existence of other type of capital. Figure 2.5 shows the
107
Table 2.8: Production Function Estimates
Coe?cient. Stdandard Error
Capital 0.116 0.034
Energy 0.085 0.046
Materials 0.560 0.061
Labor 0.175 0.061
F(4,31)=126.14
Adj R-squared=0.9346
Number of obs=36
residual from the previous production function estimation. The big jump between
January and April 2004 is associated with the change in the plant management and
the downsizing of the plant in order to control the union. From this residual, I esti-
Figure 2.5: Residual Production Function
Residual production function
-0.1
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
J
a
n
-
0
3
A
p
r
-
0
3
J
u
l
-
0
3
O
c
t
-
0
3
J
a
n
-
0
4
A
p
r
-
0
4
J
u
l
-
0
4
O
c
t
-
0
4
J
a
n
-
0
5
A
p
r
-
0
5
J
u
l
-
0
5
O
c
t
-
0
5
mate an AR(1) process tfp
t
= ?
tfp
tfp
t?1
+?
t
getting an autocorrelation coe?cient
of 0.487 (std=0.134) and a ?
?
= 0.021 which in turn implies that ?
tfp
= 0.024.
The wage function is taken as wage = w
0
? e + w
1
? e ? h
(
?) and estimated
directly from the data on wages and hours.
16
The elasticity of wages with respect to
16
The numbers are given in thousands of December 2005 dollars.
108
hours is taken as 1.1, as in the previous chapter. The results from an OLS estimation
of this equation are w
0
= 1.11(std = 0.58) and w
1
= 0.12(std = 0.000).
The energy price is calculated as the average kilowatt price paid by the ?rm
across all sample months and is equal to 0.067US$. The materials price is the
average across months of the ratio of total cost to quantities (measured in pounds
of casting per unit produced) and equal to 1.4 US$. The buying price of capital is
normalized to 1. The selling price of capital is calculated as follows: The lifetime
of the tools is one year. However, they are sold when they are 6 months old by
around 12% of their value. This implies a monthly depreciation of 35%. Finally,
the discount rate is taken as 0.95 per year which implies a discount rate of 0.996 per
month.
Benchmark Moments
At this frequency, some of the variables are not as relevant to this particular
company as they are to the average Colombian ?rm observed in the annual Cen-
sus of Manufacturing ?rms. These variables are the employment growth and the
investment rate. On the other hand, some variables that are not observed in the
census play a key role describing the behavior of Moldes Medellin, like labor hours
and the investment rate in long lived tools. That is the reason why the benchmark
moments taken from the census can be compared with the moments for Moldes
Medellin for energy and materials, but not in capital and labor. Table 2.9 summa-
rizes the moments that are taken as benchmarks to compare with the simulations
of the model.
109
Table 2.9: Benchmark Moments (Monthly Values From the Data)
Wks Growth Hours Growth
T
KTools
90
th
percentile 0.013 0.229 0.444
10
th
percentile -0.013 -0.153 0.200
?(
T
KTools
, x) -0.1277 0.38372
?(x, tfp) -0.0133 0.42224 -0.0711
VAR Coe?cients
I
K
?Wks
Wks
?Hours
Hours
(
I
K
)
?1
-0.191 0.021 0.002
(
?Wks
Wks
)
?1
0.038 -0.075 0.019
(
?Hours
Hours
)
?1
0.631 -0.068 0.016
2.4.3 Simulations Results
Table 2.10 shows the simulation results using the model and the calibrated
parameters. A quick view of the results reveals that the model does not get a perfect
?t, but is able to reproduce some qualitative features of the data. In particular,
although it does not match exactly any moment exactly, it does yield the correct
sign in most cases. In particular, the model predicts the correct signs in the case of
the percentiles of workers growth, hours growth and the capital growth.
The model matches the qualitative behavior for the correlation between work-
ers, hours and investment with productivity shocks. With respect to the VAR, the
model is not able to explain the e?ect of lagged employment and hours growth on
capital, but it does a better job in explaining the e?ect of investment on employment
growth and hours growth. The best match is the correlation between the investment
rate and the productivity shock.
The lack of a good match between the simulated moments and the moments
from the data may come from di?erent explanations. First, it is possible that the
110
model does not re?ect all the variables management considers when adjusting fac-
tors. With respect to this ?rst argument, it is true that the existence of the union
imposes intangible restrictions, such as political ?ghts inside the ?rm, that the man-
agement tries to avoid, or long processes which retard the response of the ?rm to
shocks in demand or productivity. It is also hard to consider in one single model
all the factors that the management weighs when making decisions. Second, it is
possible that the ?rm does not act completely as pro?t maximizing agent. With
respect to the second argument, if it is true that the ?rm is not acting as a pro?t
maximizing agent, it must be true that it is in its best interest to modify its be-
havior. For example, the model suggests that the ?rm should respond much more
adjusting workers, hours and investment despite the high adjustment costs; it also
suggests substitution between hours and capital instead of substituting workers and
capital.
I do not view the results of the simulations as a failure. Instead I regard them
as very promising, considering this model is taken directly from a model ?t to the
average behavior of all ?rms in Colombia
17
.
Some modi?cations to the model regarding the observed asymmetry in the
?xed costs of adjusting labor, or the modeling of di?erent types of workers (i.e.
production and non production), or di?erent types of production functions, could
signi?cantly improve the ?t of the model to the data. The ?nal goal is to deliver
a model that can assist the managers of Moldes Medellin in their decision making
process.
17
The only modi?cation made was a di?erent calibration/estimation of the parameters.
111
Table 2.10: Simulations Results
Wks Growth Hours Growth
T
KTools
90
th
percentile 0.037 0.49 0.710
10
th
percentile -0.037 -0.31 0.000
?(
T
KTools
, x) -0.017 -0.059
?(x, tfp) 0.384 0.115 -0.027
VAR Coe?cients
I
K
?Wks
Wks
?Hours
Hours
(
I
K
)
?1
-0.1632 0.029 0.081
(
?Wks
Wks
)
?1
-0.033 -0.0048 0.089
(
?Hours
Hours
)
?1
-0.039 -0.006 0.103
2.5 Conclusions and Future work
In this paper, I have presented direct evidence of the costs that a glass mould
?rm has to pay when adjusting input factors using detailed production monthly
data. The observed adjustment costs come on the one hand from the disruption
in production when adjusting capital and employment, resulting from the resources
diverted to adjust these factors, and on the other hand from the ?xed costs that
the ?rm has to pay when hiring or ?ring a worker. I presented also direct evidence
of the existence of an additional cost for the ?rm when adjusting both factors at
the same time, since the disruption cost is higher during these periods. The most
salient features of the adjustment costs are the high asymmetry between the ?ring
and the hiring cost and the high disruption cost in both capital and employment
adjustment.
These observed adjustment costs were introduced in a model that ?t the aver-
age behavior of the manufacturing sector in Colombia. In that case, the parameters
were estimated and not observed, in contrast with this paper, where the costs are
112
observed and not estimated.
With this direct calibration, the model is able to reproduce many qualitative
features from the Glass Mould ?rm behavior, and in some cases, the qualitative re-
sults match the data, as in the response of investment and labor hours to shocks in
productivity, or in the case of the extreme percentiles (10
th
and 90
th
) of labor hours
growth. However, the overall quantitative ?t, and some qualitative features like the
dynamic relationship between capital and employment, are not good. The expla-
nations for this could come from misspeci?cation of the model or from suboptimal
behavior of the ?rm.
The model can be improved by incorporating features like the asymmetry of
the ?xed employment adjustment costs or other constrains that the management
faces because of the union. But if the model is a good approximation of the produc-
tion process in Moldes Medellin, it suggests that despite the high adjustment costs,
the ?rm should adjust employment, hours and investment more frequently and use
more the substitution margin between capital and workers.
In the future, I plan to carefully consider a speci?c model that can ?t the
operation of Moldes Medellin, introducing elements like those mentioned above.
The ?nal goal is to show to the management and the owner how they can improve
their pro?ts with modi?cations to the production choices suggested by an economic
model.
113
Chapter 3
Conclusions and Final Thoughts
In analyzing input factor decisions using the unique data sets presented in
chapters two and three, this dissertation makes three main contributions. First, it
reveals the fact that it is more costly for ?rms to adjust capital and employment at
the same time, an e?ect called congestion. This e?ect is important in explaining the
observed interrelation between capital and employment growth. Second, it provides
direct evidence of the existence of adjustment costs using data from a particular ?rm;
these adjustment costs take the form of disruption in the production process and
reallocation of internal resources to adjust the input factors, ?xed costs of adjusting
factors and complementarities in the adjustment costs as de?ned before. And third,
it proposes a model that is able to explain the empirical evidence about capital and
employment adjustment, namely the mix of smooth and lumpy adjustments, the
mix of inaction, small and large adjustments and the interrelation in capital and
employment adjustment. The key for the success of the explanation lies in the joint
analysis of dynamic capital and employment decisions with a very complete and
realistic structure of adjustment costs.
In the ?rst chapter I have used the Census of Manufacturing Firms in Colom-
bia to analyze if labor and capital adjustment are interrelated, whether there are
interrelations in this process, and what the nature of this adjustment is. The data
114
shows the same patterns observed in other data sets: mix of smooth and lumpy ad-
justments in capital and employment, mix of inaction, small and large adjustments,
continuous adjustment in energy and materials and interrelation between capital
and employment adjustment.
I argue that these patterns can be explained with a dynamic model in which
labor and capital are costly to adjust. The adjustment cost represents some facts
from the data, such as the decrease in output after the adjustment, the cost of hiring
and ?ring workers, the cost of installing capital and a convex component to capture
the mix of smooth and lumpy adjustment. The model also incorporate the fact that
the adjustment is more costly when done simultaneously in capital and employment.
The decision rules for ?rms’ capital and labor adjustment show that the adjustment
patterns are highly nonlinear and they can be characterized as a bidimensional (S,s)
policy where adjustment depends not just of the states of the system but also on the
choices. Importantly, the model with high complementarities more close resemble
the data statistics.
The main conclusion from the ?rst chapter is that labor and capital adjust-
ment should be analyzed together when considering a dynamic model of adjustment
dynamics with convex and non-convex costs. This is supported by an empirical rea-
son as well as a theoretical one. The data show an interrelated adjustment pattern.
Moreover, in a model that incorporates adjustments for both capital and labor, the
conclusions about factor movements are di?erent if adjustment costs are presented
in one factor alone. The structural methodology allows me to reject statistically the
existence of ?xed costs and to accept the existence of disruption costs for capital and
115
labor, the existence of convex costs for capital but not for labor and the existence
of congestion e?ects.
The main advantage of the type of methodology proposed in this paper is that
several policy experiments can be analyzed. The e?ects of taxes on capital and
employment and the aggregate e?ects of these policies are among the main ones.
Also, Colombia undertook several market liberalization reforms at the beginning
of the 1990s, so it would be interesting to explore with this structural framework,
how the reforms a?ected the ?rm behavior in terms of factor adjustment. And
?nally, it may be worth exploring sectoral di?erences in ?rm behavior, especially
since the parameters and functional forms may not be the same for all types of
industries. This paper took an aggregate approach to this problem, but a more
micro-level analysis may prove useful, particulary if micro level behavior is the key
to understanding aggregate responses.
In the second chapter I have presented direct evidence of the costs that a
glass mould ?rm has to pay when adjusting production input factors using detailed
production monthly data. The evidence presented con?rms part of the adjustment
cost structure proposed in chapter one. The observed adjustment costs come on the
one hand from the disruption in production when adjusting capital and employment
and from the resources used to adjust these factors, and in the other hand from the
?xed costs that the ?rm has to pay when hiring or ?ring a worker. I presented also
direct evidence of the existence of an additional cost for the ?rm when adjusting
both factors at the same time since the disruption cost is higher during these periods.
The most salient features of the adjustment costs are the high asymmetry between
116
the ?ring and the hiring cost and the high disruption cost in both capital and
employment adjustment.
The observed adjustment costs where introduced in the model from chapter
one. In chapter one, the parameters were estimated and not observed, in contrast
with chapter two, where the costs are observed and not estimated.
With this direct calibration, the model is able to reproduce many qualitative
features from the Glass Mould ?rm behavior, and in some cases the qualitative
results get close to the data as in the response of investment and labor hours to
shocks in productivity, or in the case of the labor hours growth extreme percentiles
(10
th
and 90
th
). However, the overall quantitative ?tting and some quantitative
features like the dynamic relationship between capital and employment are not good.
The explanations for this can come from the misspeci?cation of the model or from
the suboptimal behavior of the ?rm.
The model can be improved in features like the asymmetry of the ?xed em-
ployment adjustment costs or the production function or incorporating some other
constrains that the management faces because of the union. But if the model is a
good approximation of the production process in Moldes Medellin, it suggests that
despite the high adjustment costs, the ?rm should adjust more employment, hours
and investment and use more the substitution margin between capital and workers.
In the future, I plan to carefully consider a speci?c model that can ?t the
operation of Moldes Medellin, introducing elements like the mentioned above. The
?nal goal is to show to the management and the owner how they can improve
their pro?ts with modi?cations to the production choices suggested by an economic
117
model.
118
Appendix 1
Appendix Chapter 1: Complementary Analysis of the Variables
Around Spikes in Capital and Employment
This appendix has three main goals. The ?rst one is to analyze how the
adjustments of capital and employment and the levels of energy, materials, output
and productivity are interrelated before, during and after a spike in investment or
employment. The second goal is to show that the patterns of adjustment have a mix
of lumpy and smooth elements as argued in previous sections. And the third goal is
to show that TFP and output decrease after episodes of large adjustments specially
in capital, suggesting the presence of adjustment costs in the form of forgone pro?ts.
Following a similar methodology to Sakellaris (2004) and Letterie et al. (2004),
I analyze the conditional expected values of the variables of interest around the
spikes in investment and employment adjustment. Speci?cally, I create a dummy
variable for the investment spikes if the investment rate is greater than 20% and was
lower than 20% in the previous period; that is
I
t
K
t
> 0.2 and
I
t?1
K
t?1
< 0.2. In order
to make a comparison with the existing literature, and given the arbitrary nature
of the de?nition of thresholds for “large” adjustments, I also construct a dummy
variable signalling the job creation bursts if the adjustment is bigger than 10% in t
but less than 10% in absolute value in t ?1. Job destruction bursts are determined
by the same rule on the negative side (less than -10% labor adjustment in t and
more than 10% in t ?1). An important assumption is that two years of consecutive
large adjustment correspond to the same episode. Consequently, I analyze 5 years
119
around the investment episode.
The analysis is based on the following regression:
X
is
= µ
i
+ v
s
+
j=2
j=?2
?
j
? EV ENTD
t+j
is
+
st
(1.1)
X
is
is the variable of interest for ?rm i in period s. µ
i
stands for plant e?ects
to control for unobserved heterogeneity and ?
s
stands for year e?ects to control for
aggregate e?ects in the variable; EV ENTD = 1 if the event D happens in time s,
where D can be an investment spike, job creation burst or job destruction burst.
The reported coe?cients in tables A1, A2 and A3 are the ?
j
’s of equation (1.1).
They account for the conditional expected values of the adjustments in capital and
employment and the levels of energy, materials, output and productivity in the time
window composed by the two periods before and two periods after the episode of
large adjustment in capital and employment.
We should expect a statistically signi?cant coe?cient on capital and employ-
ment growth around the spikes of the opposite factor if there is an interrelation
between capital and labor adjustment. Also, if there is smooth adjustment, we
should observe a constant increase or decrease in the coe?cients before or after the
episodes; in contrast, lumpy adjustment would be seen as jumps in these coe?-
cients. If there is evidence of a disruption cost, we expect productivity and output
to decrease after the spikes.
In fact, as expected, the most relevant facts drawn from the tables A1, A2
and A3 are that there is interrelation in the adjustment, that there is evidence of
disruption costs, especially after capital adjustments and that ?rms adjust with mix
120
Table A1. Conditional Expected Values during Investment spikes episodes
I/K ?L/L log log(k) log(L) log(E) log(M) log(TFP)
t+2 0.092 0.003 0.043 0.384 0.044 0.033 0.045 -0.107
(0.013)** 0.005 (0.009)** (0.014)** (0.007)** (0.010)** (0.009)** (0.008)**
t+1 0.195 0.008 0.052 0.401 0.052 0.026 0.05 -0.107
(0.014)** 0.005 (0.010)** (0.015)** (0.008)** (0.011)* (0.010)** (0.009)**
I/K spike 0.615 0.026 0.052 -0.262 0.052 0.014 0.061 0.088
t (0.014)** (0.005)** (0.010)** (0.015)** (0.007)** 0.011 (0.010)** (0.009)**
t-1 -0.071 0.008 0.036 -0.204 0.025 -0.001 0.05 0.071
(0.014)** 0.005 (0.009)** (0.015)** (0.007)** -0.011 (0.010)** (0.009)**
t-2 -0.021 0.003 0.013 -0.167 0.013 -0.02 0.026 0.052
-0.013 0.005 0.009 (0.015)** 0.007 -0.011 (0.010)** (0.009)**
Obs. 20093 27835 26578 27946 28068 28132 26060 24410
R
2
0.13 0.01 0.18 0.25 0.03 0.08 0.23 0.1
Standard errors in parentheses* signi?cant at 5%; ** signi?cant at 1%
of smooth and lumpy adjustment. These coe?cients are particular for the episodes
of capital and employment spikes, but the analysis in the main text supports the
results found here
Table A2. Conditional Expected Values during Employment growth spikes
I/K ?L/L log log(k) log(L) log(E) log(M) log(TFP)
t+2 0.006 -0.012 -0.054 -0.068 -0.123 -0.06 -0.05 0.017
0.005 (0.003)** (0.007)** (0.012)** (0.005)** (0.008)** (0.008)** (0.007)**
t+1 0.01 -0.024 -0.037 -0.066 -0.166 -0.05 -0.024 0.034
0.005 (0.003)** (0.007)** (0.011)** (0.005)** (0.008)** (0.007)** (0.007)**
L spike=t 0.042 0.34 0.058 -0.045 0.175 0.019 0.058 0.014
(0.005)** (0.003)** (0.007)** (0.011)** (0.005)** (0.008)* (0.007)** (0.007)*
t-1 0.035 -0.023 0.075 0.035 0.13 0.041 0.076 0.008
(0.005)** (0.003)** (0.007)** (0.011)** (0.005)** (0.008)** (0.007)** -0.007
t-2 0.016 -0.008 0.074 0.093 0.11 0.037 0.07 -0.002
(0.005)** (0.003)** (0.007)** (0.012)** (0.005)** (0.008)** (0.008)** -0.007
Obs. 19770 27800 26578 27946 28068 28132 26060 24410
R
2
0.03 0.43 0.19 0.19 0.16 0.09 0.24 0.09
Standard errors in parentheses* signi?cant at 5%; ** signi?cant at 1%
121
Table A3. Conditional Expected Values during Negative Employment growth
spikes
I/K ?L/L log log(k) log(L) log(E) log(M) log(TFP)
t+2 0.002 0.005 0 0.005 0.086 0.019 0.013 -0.028
0.005 0.003 0.007 0.012 (0.005)** (0.008)* 0.008 (0.007)**
t+1 0 0.016 -0.02 0.027 0.124 0.009 -0.01 -0.053
0.006 (0.003)** (0.007)** (0.012)* (0.005)** 0.008 -0.008 (0.007)**
-L spike -0.017 -0.36 -0.11 0.036 -0.243 -0.07 -0.103 -0.026
t (0.006)** (0.003)** (0.007)** (0.012)** (0.005)** (0.009)** (0.008)** (0.007)**
t-1 -0.02 0.033 -0.101 0.005 -0.176 -0.078 -0.107 -0.019
(0.006)** (0.003)** (0.007)** -0.012 (0.005)** (0.009)** (0.008)** (0.007)**
t-2 -0.006 0.015 -0.087 -0.034 -0.139 -0.071 -0.084 -0.011
-0.006 (0.003)** (0.008)** (0.013)** (0.006)** (0.009)** (0.008)** -0.007
Obs. 19770 27800 26578 27946 28068 28132 26060 24410
R
2
0.02 0.42 0.19 0.18 0.17 0.09 0.24 0.09
Standard errors in parentheses* signi?cant at 5%; ** signi?cant at 1%
122
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doc_388616868.pdf
Factor Adjustment Dynamics
ABSTRACT
Title of dissertation: ESSAYS ON FACTOR ADJUSTMENT
DYNAMICS
Juan M. Contreras, Doctor of Philosophy, 2006
Dissertation directed by: Professor John P. Rust
Professor John C. Haltiwanger
Department of Economics
This study analyzes dynamic production input factor decisions using the an-
nual Census of Manufacturing ?rms from Colombia and monthly production data
from a glass mould ?rm. It proposes a model that is able to explain the empiri-
cal evidence about capital and employment adjustment observed in these data-sets,
namely the mix of smooth and lumpy adjustment, and both the static and dy-
namic interrelation in capital and employment adjustment. The key points of the
explanation are the joint analysis of capital and employment adjustment and the
existence of adjustment costs for capital and labor. These adjustment costs take the
form of disruption in the production process and reallocation of internal resources
to adjust the input factors, ?xed costs of adjusting factors and congestion e?ects
in the adjustment costs, meaning that it is more costly for ?rms to adjust capital
and employment at the same time. The study uses a structural approach and a
simulated minimum distance algorithm to estimate the adjustment cost parameters
in the case of the Census of Manufacturing Firms and a calibration procedure to
explore the ?t of the model in the speci?c case of the glass mould ?rm
ESSAYS ON FACTOR ADJUSTMENT DYNAMICS
by
Juan M. Contreras
Dissertation submitted to the Faculty of the Graduate School of the
University of Maryland, College Park in partial ful?llment
of the requirements for the degree of
Doctor of Philosophy
2006
Advisory Committee:
Professor John P. Rust, Co-Chair/Advisor
Professor John C. Haltiwanger, Co-Chair/Advisor
Professor John Shea, Advisor
Professor Michael J. Pries, Advisor
Professor Vojislav Maksimovic
c Copyright by
Juan M. Contreras
2006
DEDICATION
To my father, mother, brother and wife
ii
ACKNOWLEDGMENTS
I want to thank ?rst and foremost John Rust, who took the time and had the
patience to teach me how to think and work as an economist. It has been a pleasure
and an honor to have learned from such a ?ne person and professional.
I also want to give special thanks to John Haltiwanger, who helped me enor-
mously with the data and guided me through all the dissertation process giving me
constant and good advice. It has been a privilege having him as advisor.
I am thankful to John Shea, who gave extensive comments for all my drafts
and helped me to improve greatly this paper, to Mike Pries and Alex Whalley who
also helped me with his comments and to Marcela Eslava, who very kindly made
possible for me to access the Colombian Census of Manufacturing Firms. I also
acknowledge the ?nancial support from the Central Bank of Colombia.
Special mention deserves the owner of the glass mould ?rm, who allow me to
get access to the production records of his company. My brother and manager of
the plant, Luis Fernando Contreras, also deserves my deepest gratitude for helping
me to collect and organize the data from this ?rm. I thank also Bandy S. who gave
access to excellent computer resources and support.
Finally, I can not thank enough the help and care of my wife and colleague,
Ignez Tristao, whose many ideas and discussions are re?ected in this dissertation.
iii
INTRODUCTION
Along the years, managers, economists and engineers have shared a common
question: how to maximize the gains from an industry operation. This simple
question has stimulated a broad range of research, ranging from the development
of mathematical tools and computer algorithms for the solutions of the problem, to
applications in speci?c industries and the analysis of the aggregate implications for
the overall economy.
Maximizing the pro?ts is equivalent to choosing optimally production input
factors, a problem that has received a lot of attention in the economic literature.
This research has lead to remarkable developments in production theory, in indus-
trial organization and in business cycles analysis. At the ?rm level, starting with
the work of Holt et al. (1960), the standard approach has been to ?t quadratic
cost functions to the production problem in order to obtain linear decision rules for
the amount of inputs to use. More recently, in order to get closer to the discrete
decisions observed at the micro level, other line of research has considered di?erent
types of non quadratic adjustment costs functions and di?erent types of non-linear
(i.e. discrete) decision rules as the key to determine optimal operation decisions, as
in Rust (1987) and Hall (2000).
At the aggregate level, the neoclassical model of investment and labor demand
had also used quadratic adjustment costs functions in order to match the smooth
iv
adjustment observed at the aggregate level. Hall and Jorgenson (1967), Abel (1979)
and Hamermesh and Pfann (1996) are examples of this approach. Nadiri and Rosen
(1969) also uses convex adjustment costs to explain the aggregate interrelation be-
tween capital and labor adjustment. These explanations for the investment and
labor demand rely on the representative agent paradigm according to which the
aggregate economy can be described by a single representative agent and the het-
erogeneity across agents comes from pure luck, because they receive di?erent shocks
in productivity and demand.
The problem with this approach is that recent studies using ?rm level data
such as Caballero et al. (1995), Caballero et al. (1997),Narazani (2004) and Sakel-
laris (2004) have shown that the representative agent does not act according to the
convex cost model. In particular, three key facts about investment and dynamic
employment demand emerge from this evidence: ?rst, there are a lot of inaction pe-
riods when ?rms do nothing and some periods when the ?rms adjust continuously;
second, when ?rms adjust there is a mix of very large and small adjustments; and
third, there is an interrelation between capital and labor adjustment, which means
signi?cant dynamic correlations and a higher probability of investing when the ?rm
is hiring more workers and viceversa.
Building in part over this empirical evidence and over single-agent decision
studies
1
, Caballero and Engel (1999), Cooper et al. (1999), Cooper and Haltiwanger
(2005) and Cooper et al. (2004), to mention a few, have proposed models which
do not rely only on quadratic adjustment costs and are able to generate discrete
1
Like the Bus replacement problem in Rust (1987)
v
and non smooth adjustment. They are dynamic in nature and match both the
micro evidence and the macro facts. However, these models do not explain the
interrelation between employment and capital adjustment since they analyze each
factor by separate. Also, they have been subject to criticism because of the lack of
direct empirical support for the existence of adjustment costs.
This dissertation addresses directly those two criticisms and continues this line
of research exploring ?rm’s behavior with a focus on the real rigidities that ?rms face
when they desire to optimally adjust the combination of production input factors.
Speci?cally, it analyzes from an empirical and theoretical point of view the costs
that ?rms have to pay when adjusting capital and the number or workers, together
with the patterns of energy and materials adjustment. The ?rst chapter uses an
annual census of manufacturing ?rms while the second one focuses in a single ?rm
with monthly data on production. The implications of a model that explain their
behavior are compared when applied to both cases.
In the ?rst chapter, I analyze the empirical evidence about factor adjustment
dynamics using the Colombian Annual Manufacturing Census from 1982 to 1998,
and propose a model able to account for the three facts mentioned above and ob-
served in this data set (i.e. mix of smooth and lumpy adjustments, mix of small
and large adjustments and interrelation in capital and employment adjustment).
The main feature of this chapter’s dynamic model of ?rms’ factor demand
decisions is the existence of adjustment costs for capital and employment. The
adjustment cost structure captures key features of the data such as reductions in
output during adjustment (disruption cost), the costs of installing capital and cre-
vi
ating or destroying a job vacancy (?xed costs), a convex cost component introduced
to capture the observed mix of smooth and lumpy adjustment, and an extra cost of
adjusting capital and labor simultaneously (congestion e?ects).
The adjustment cost structural parameters of the model are estimated by ap-
plying a minimum distance algorithm. The structural methodology allows me to
reject statistically the existence of ?xed costs and to accept the existence of disrup-
tion costs for capital and labor, the convex costs for capital and the existence of
congestion e?ects. The conclusions of the analysis are that (i) there exist signi?-
cant dynamic interrelations between factor adjustments; (ii) both interaction e?ects
in the adjustment cost parameters and the convex and non convex nature of the
adjustment costs appear to be important in explaining ?rms’ mix of smooth and
lumpy adjustments on the one hand and small and large adjustments on the other
hand, in capital and employment; and (iii)depending on their capital to labor ratio,
?rms either do not adjust or adjust only capital, only labor or both capital and
labor simultaneously.
The second chapter presents direct evidence of the adjustment costs that a
glass mould ?rm has to pay when adjusting capital and employment in response
to the arrival of new orders using detailed monthly data on production. At this
frequency, it is observed a disruption in the production process due to the installation
of small units of capital represented by speci?c tools with limited life (usually less
than one year). This cost is measured in man hours and quanti?ed as an average of
1.6% of the total sales. Hiring a worker also increases the average production time
(decreases productivity) by 1.02%
vii
The existence of a powerful union also creates a high cost of adjusting the
number of workers through established fees for ?ring and hiring in addition to the
high legal ?ring costs. These costs are asymmetric and quanti?ed in US$53,000 and
US$1,320 dollars respectively. Given the high technology involved in the process,
hiring a new worker implies an extra cost of training for the speci?c process and
a cost in the lower productivity this new worker has while learning quanti?ed in
US$1,534 dollars. Moreover, the adjustment of one worker increases the disruption
cost in the adjustment of capital by 1.17%, the same congestion e?ect observed in
the case of the colombian data.
I describe these adjustment costs and the production process using the model
from the previous chapter to understand the e?ect on the factor adjustment dy-
namics, comparing the results with the ones in the previous chapter. Overall, the
higher frequency of the data and the particularities of the ?rm help to understand
the nature of the adjustment costs observed at the ?rm level.
viii
TABLE OF CONTENTS
List of Figures xi
List of Tables xii
1 An Empirical Model of Factor Adjustment Dynamics 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Factor Adjustment: An Exploration of the Facts from the Micro-data 8
1.2.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.2.2 Basics About Factor Adjustment: Distributions and Correla-
tions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.2.3 Factor Adjustment Interrelation: Dynamic Dependence . . . . 22
1.2.4 The Role of Heterogeneity . . . . . . . . . . . . . . . . . . . . 25
1.3 A Dynamic Model of Firms’ Factor Adjustment . . . . . . . . . . . . 32
1.3.1 Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
1.3.2 Analysis of the Model . . . . . . . . . . . . . . . . . . . . . . 38
1.4 Capital and Labor Adjustment: A Numerical Analysis of the Pro-
posed Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
1.4.1 Numerical Methods . . . . . . . . . . . . . . . . . . . . . . . . 45
1.4.2 About the Parameters: Estimation and Calibration . . . . . . 47
1.4.3 Decision Rules for Capital and Employment Adjustment . . . 50
1.4.4 Congestion E?ects and Adjustment Costs: A Simulation ex-
ploration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
1.5 Structural Estimation of the Adjustment Cost Parameters . . . . . . 69
1.5.1 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
1.5.2 Adjustment Costs Parameters: Fitting the Data . . . . . . . . 71
1.5.3 Non-formal Tests of Goodness of Fit . . . . . . . . . . . . . . 74
1.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
2 Costs of Adjusting Production Factors: The Case of a Glass Mould Company 80
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
2.2 Description of the ?rm and the production process . . . . . . . . . . . 83
2.2.1 History of Moldes Medellin . . . . . . . . . . . . . . . . . . . . 83
2.2.2 The Production Process . . . . . . . . . . . . . . . . . . . . . 85
2.3 Data: Production process, Factor Adjustment Dynamics and Adjust-
ment Costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
2.3.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
2.3.2 A First look at the Production and Factor Adjustment Dynamics 87
2.3.3 A Description and Calculation of the Adjustment Costs faced
by the Company . . . . . . . . . . . . . . . . . . . . . . . . . 93
2.4 How Well the Model from Chapter One Can ?t this Particular Firm? 100
2.4.1 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
2.4.2 Calibration/Estimation of the Parameters . . . . . . . . . . . 104
2.4.3 Simulations Results . . . . . . . . . . . . . . . . . . . . . . . . 109
ix
2.5 Conclusions and Future work . . . . . . . . . . . . . . . . . . . . . . 111
3 Conclusions and Final Thoughts 114
1 Appendix Chapter 1: Complementary Analysis of the Variables Around
Spikes in Capital and Employment 119
x
LIST OF FIGURES
1.1 Factor Adjustment for a Particular Firm from the Colombian Census
of Manufacturing Firms. . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.2 Distributions of Factor Adjustment. Percentage of observations (y-
axis) in a range of adjustment (x-axis) . . . . . . . . . . . . . . . . . 14
1.3 Distribution of Factor Adjustment in High and Low Capital Intensive
Firms. % of observations (y-axis) in a range of adjustment (x-axis) . . 27
1.4 Value functions: lateral view, labor. . . . . . . . . . . . . . . . . . . . 52
1.5 Decision rules. All costs in K,L. . . . . . . . . . . . . . . . . . . . . . 54
1.6 Decision rules. Comparison among Adjustment costs. Low shock. . . 54
1.7 Decision rules. Comparison among Adjustment costs. Intermediate
shock. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
1.8 Decision rules. Comparison among Adjustment costs. High shock. . . 55
1.9 Time Series: All Costs Present. . . . . . . . . . . . . . . . . . . . . . 58
1.10 Time Series: Investment Rate, Adjustment Costs Comparison . . . . 58
1.11 Time Series: Labor Growth, Adjustment Costs Comparison . . . . . . 59
1.12 Labor and Capital Adjustment Levels. Intermediate Shock, High and
Low values for Capital and Labor . . . . . . . . . . . . . . . . . . . . 60
1.13 Labor and Capital Adjustment Levels. Intermediate Shock, Mix of
High and Low values for Capital and Labor . . . . . . . . . . . . . . 61
1.14 Distributions of Factor Adjustments for the Simulated Series. Per-
centage of observations (y-axis) in a range of adjustments (x-axis). . . 75
2.1 Production Factors Series . . . . . . . . . . . . . . . . . . . . . . . . 89
2.2 Production Factors Adjustment . . . . . . . . . . . . . . . . . . . . . 90
2.3 Setup Costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
2.4 Cost Shares . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
2.5 Residual Production Function . . . . . . . . . . . . . . . . . . . . . . 108
xi
LIST OF TABLES
1.1 Distribution of factor adjustment(%) . . . . . . . . . . . . . . . . . . 16
1.2 Factor adjustment contemporaneous correlation . . . . . . . . . . . . 18
1.3 Correlations among incidence of episodes (dummies for inaction/spikes) 19
1.4 Probability of inaction/adjustment conditional on Inaction/adjustment
of the other factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
1.5 Dynamic relations in factor adjustment . . . . . . . . . . . . . . . . . 23
1.6 Factor adjustment contemporaneous correlation: Low Capital Inten-
sive Firms (Lower quartile in
K
L
ratio) . . . . . . . . . . . . . . . . . . 26
1.7 Factor adjustment contemporaneous correlation: High Capital Inten-
sive Firms (Upper quartile in
K
L
ratio) . . . . . . . . . . . . . . . . . 26
1.8 Probability of inaction/adjustment conditional on Inaction/adjustment
of the other factor: Low Capital Intensive Firms . . . . . . . . . . . . 28
1.9 Probability of inaction/adjustment conditional on Inaction/adjustment
of the other factor: High Capital Intensive Firms . . . . . . . . . . . 29
1.10 Dynamic relations in factor adjustment: Low Capital Intensive Firms 30
1.11 Dynamic relations in factor adjustment:High Capital Intensive Firms 31
1.12 Parameters Adjustment Costs . . . . . . . . . . . . . . . . . . . . . . 50
1.13 Basic simulated statistics . . . . . . . . . . . . . . . . . . . . . . . . . 66
1.14 Correlation(
I
K
, ?L) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
1.15 Simulated V AR(1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
1.16 Simulated Moments . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
1.17 Calculated Adjustment Cost Parameters . . . . . . . . . . . . . . . . 73
1.18 Probability of inaction/adjustment conditional on Inaction/adjustment
of the other factor: Simulated data . . . . . . . . . . . . . . . . . . . 76
2.1 Basic Statistics. Monthly values . . . . . . . . . . . . . . . . . . . . . 91
2.2 Correlation among the levels of the variables . . . . . . . . . . . . . . 92
xii
2.3 Correlation among the Growth of the variables . . . . . . . . . . . . . 92
2.4 VAR for Growth of the variables . . . . . . . . . . . . . . . . . . . . . 93
2.5 Legal Firing Costs in the Colombian Legislation . . . . . . . . . . . . 97
2.6 E?ect of a Change in the Number of Workers on the Capital Disrup-
tion Adjustment Cost . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
2.7 Adjustment Cost Parameters . . . . . . . . . . . . . . . . . . . . . . . 105
2.8 Production Function Estimates . . . . . . . . . . . . . . . . . . . . . 107
2.9 Benchmark Moments (Monthly Values From the Data) . . . . . . . . 109
2.10 Simulations Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
xiii
Chapter 1
An Empirical Model of Factor Adjustment Dynamics
1.1 Introduction
It was not until a decade ago, with the availability of new ?rm-level datasets,
that lumpiness and infrequent adjustment in capital and labor
1
could be observed
in ?rms’ behavior; this was in stark contrast to the smooth adjustment shown in
aggregate data for those factors
2
. At the same time, models attempting to explain
the aggregate behavior of these variables had to be revised to account for the mi-
croeconomic facts if models with micro foundations were to be useful in terms of
policy and predictions at the ?rm and aggregate levels. However, previous studies of
adjustment have tended to analyze one factor at a time, which has made it di?cult
to understand the joint adjustment of capital and labor at the micro level and its
macroeconomic implications.
Looking for a better understanding of ?rms’ factor adjustment behavior, this
paper analyzes to what extent it is important to consider joint capital and labor de-
cisions at the ?rm level from an empirical and theoretical point of view. Speci?cally,
1
The term labor is used in this paper to indicate the number of workers which can also be
referred to as employment.
2
In order to clarify terms, lumpiness refers to coexistence of inaction and large adjustments with
little in between; this is the opposite of a smooth adjustment that occurs when the adjustment
is done in a continuous way. The main distinctive feature between them is the existence of long
inaction periods and large adjustments in the case of lumpy adjustments and the non existence of
inaction periods in the case of smooth adjustments; note, however, that one could observe large
and smooth adjustments at the same time.
1
it asks whether ?rms adjust labor independently of capital, if there exist interaction
in this adjustment and what the nature of this interrelation is. Although capital
and labor movements are the main focus, I also incorporate materials and energy
adjustments into the analysis.
The implicit view in the early investment
3
and labor demand literature was
that pro?t-maximizing ?rms would adjust factor demand constantly in response to
shocks in demand and productivity. It was natural to think that way since the
aggregate series were smooth, and the literature instead focused on issues such as
the role of the cost of capital, the serial correlation in investment and the aggregate
dynamics of labor demand. Recent ?rm-level empirical studies have shown, however,
that ?rms do not adjust as often as they should under convex costs, and when they
do adjust, this response comes often simultaneously from adjustment in several
margins. Moreover, new emerging evidence, such as that presented in this paper,
shows that capital and labor adjustment distributions have fat tails, a mix of small
and large adjustments and a mass point around the inaction region, which has been
taken as evidence of lumpy adjustment
4
; the recent evidence also shows that their
adjustments are interrelated
5
.
Subsequent models of investment and labor demand made e?orts to incor-
porate this emerging empirical evidence and specially the lumpy and infrequent
3
See Hall and Jorgenson (1967), Tobin (1969), Abel (1979) and Hayashi (1982) among others.
4
Davis and Haltiwanger (1992), Davis et al. (1996), Caballero et al. (1995, 1997) and Cooper
and Haltiwanger (2005), have shown the mentioned patterns in the separate analysis of labor and
capital adjustment distributions using micro-level data. Rust (1987) shows the lumpy nature of
the adjustment for a single agent in the case of machine replacement.
5
Nadiri and Rosen (1969) using aggregate data and Sakellaris (2004), Eslava et al. (2004) and
Narazani (2004), using micro data, ?nd that the adjustment processes for capital and labor are
interrelated.
2
adjustment
6
. An important point they neglect, however, is that ?rms adjust not
just along one but along several margins, particulary for capital and labor. The few
studies that consider capital and labor together do so at a very aggregate level, which
does not exploit the rich and heterogeneous adjustment observed at the micro level
and does not account for the correlation among adjustments
7
. As a consequence,
estimated parameters governing the adjustment of capital and labor in response to
shocks may be biased
8
.
The lack of understanding of factor adjustment at the ?rm level has important
implications. For example, increasing ?ring costs may a?ect capital formation. Or
a policy aiming to increase investment may not be as e?ective as expected if labor
hiring/?ring costs are una?ected or if the elasticity of factor use with respect to its
relative price is not properly estimated. Non-convexities arising from adjustment
costs, understood as infrequent and lumpy movements, may lead to very di?erent in-
dustry responses to public policies aimed at job creation, destruction or investment.
There is a need to estimate those responses in a consistent and realistic way, not
6
These facts were incorporated in the early theoretical literature as models of infrequent ad-
justment, while later models also attempted to reproduce the lumpiness in such adjustments. See
for example Dixit and Pindyck (1994), Abel and Eberly (1994, 1998) in the case of investment
and Hamermesh (1989), Hamermesh and Pfann (1996) in the case of labor. More recent work
includes Cooper and Haltiwanger (2005) and Cooper et al. (2004), who consider also the small
and smooth adjustments present in such distributions in conjunction with episodes of large and
infrequent adjustments.
7
At the macro level, see Shapiro (1986), Hall (2004) for analysis of capital and labor adjustment
assuming convex costs . Caballero et al. (1995, 1997), Cooper and Haltiwanger (2005), Cooper et al.
(2004) analyze capital and labor adjustment in a separate way. Rust (1987) analyzes investment
for a single ?rm. Abel and Eberly (1998) model capital and labor adjustment but do not take into
account the interactions between them. Rendon (2005) features a model with a simpler adjustment
cost structure, to answer if liquidity constraints restrict job creation.
8
The biases arise because the models analyze the response of either capital or labor to shocks,
incorporating all the other factor decisions into the shocks. For example, movements in one factor,
such as, capital would a?ect the shock in a labor adjustment model, and the real response of labor
to shocks would be overstated.
3
only for the sake of predicting the e?ects of public policies, but also because the be-
havior of aggregate investment and job creation and destruction is directly a?ected
by the microeconomic response of ?rms to shocks in demand and technology.
In exploring these issues, this paper uses ?rm level data from the Colombian
Annual Manufacturing Census, covering the period 1982 to 1998. This is a unique
data set because it contains ?rm level data on the value of production, energy and
materials, prices for each product and each material used, the number of workers
and payroll and book values of equipment and structures. The existence of ?rm level
prices opens a wide range of empirical possibilities
9
; in this paper they are useful
because they allow the precise identi?cation of technology and demand shocks and
of input factor elasticities and considerably reduce the measurement error in factor
demand due to confusion between prices and quantities
10
.
In line with recent studies, the empirical analysis reveals the mix of small
and large adjustments in the capital and labor adjustment distributions, which
also present fat tails and large inaction periods; the analysis also uncovers their
interrelated nature. In addition to these studies, the analysis reveals the adjustment
patterns in energy and materials and their relation to capital and labor adjustment.
The picture that emerges is that in response to shocks, ?rms adjust capital and labor
in a non-trivial, interrelated way. Firms also adjust energy and materials when they
9
With the existence of ?rm level prices for the whole Census of manufacturing ?rms, issues that
before could not be clearly analyzed because of identi?cation problems or simply because of lack of
data, can be analyzed better. Among them we could mention the comprehensive analysis of price
stickiness or the e?ects of technology shocks in the business cycle.
10
Note that while other studies, dealing with di?erent issues, have used a similar Colombian
dataset, all but Eslava et al. (2004) and Eslava et al. (2005) use a shorter period (up to 1991) and
they do not have price information. I follow Eslava et al. (2004) in the Total Factor Productivity
(TFP) and demand shocks estimation.
4
are hit by demand and technology shocks. This is not surprising if we think that
?rms face a pro?t maximization problem over all inputs. What is interesting is the
observed dynamics of the adjustment.
The data analysis motivates the main contribution of this paper, which is to
propose, analyze and estimate a theoretical model of ?rm behavior that combines
a labor decision problem with a machine replacement problem along with a rich
speci?cation of adjustment costs. None of the previous models in the literature
have been able to explain the interrelation between capital and labor adjustment,
in part because the existence of this type of empirical evidence is very recent and
not complete for all the production factors, and in part because of the di?culty in
the analysis and estimation of such a model (analytically or numerically).
The proposed adjustment cost structure captures key features of the data such
as reductions in output during adjustment (disruption costs), the cost of installing
capital and creating or destroying a job vacancy (?xed costs) and a convex cost com-
ponent introduced to capture the observed mix of smooth and lumpy adjustment
11
.
One of the key features in the model is the presence of interaction e?ects in
the adjustment of capital and labor. Interaction e?ects are precisely de?ned as the
11
An important point not addressed here relates to the current debate about the production fac-
tors’ response to technology shocks. Besides the serious identi?cation issues faced in the literature
trying to estimate technology shocks (where IV methods or other identifying assumptions attempt
to di?erentiate technology shocks from other shocks given the lack of rich enough ?rm level data
and especially of ?rm level prices), previous work has not considered the possibility that, while
adjusting, ?rms decrease production (as it is shown later in this paper), suggesting the presence of
an adjustment cost in productivity shock estimates that may lead to misleading conclusions about
the e?ects of pure technology shocks on factor adjustment. This is an important insight that may
be worth exploring in future work. See for example Shea (1998), Gali (1999), Basu et al. (2004),
Christiano et al. (2003), and Alexopoulus (2004). I thank Martin Eichenbaum for highlighting this
point.
5
extra cost or bene?t
12
of jointly adjusting capital and labor. If the interaction e?ect
is a cost I call it congestion e?ect, and if it is a bene?t I call it complementarity
e?ect. For example, the interaction e?ect may be present as congestion if ?rms
have to train new workers to operate new machines, incurring in this way in an
extra cost; or in the opposite way, the interaction may be present in the form of
a complementarity e?ect, for example, if the incorporation of a new process in a
production plant requires a new physical space for the machines or the workers, and
this space can be shared by them; another example of the congestion e?ect would
be if disruption in the production process occurs while incorporating new workers
and machines simultaneously, incurring production losses that may be greater or
less than if hiring new workers or making new investments independently.
Once the key parameters such as factor elasticities, productivity shocks and
demand shocks are estimated, the theoretical model is compared with the data in
two ways. First, the adjustment cost parameters from the model are arbitrarily cho-
sen in order to give an example of the implications for ?rm behavior. In a second
stage, these adjustment cost parameters are estimated with a minimum distance
algorithm in order to match key moments that comprehensively describe ?rms’ ad-
justment patterns in capital and employment. The decision rules and the time series
implications that emerge from the model are also analyzed. This part of the paper
is the core analytical contribution because it gives an idea of how labor and capital
adjustments are potentially interrelated and how they interact (or not) at the ?rm
12
It is important to note that the model does not restrict this e?ect to be a cost but it also can
be a bene?t. It is the empirical analysis which determines it as a cost.
6
level, depending on the capital to labor ratio a particular ?rm has.
The model is indeed a good representation of ?rm behavior: it is able to
reproduce the mix of smooth and lumpy adjustments in the one hand, and the mix
of large and small adjustments in the other hand observed empirically for capital and
labor. Moreover, the dynamic relationships observed in the data are also reproduced.
The model that best ?ts the data includes the interaction term in the adjustment
costs for capital and labor and it is present as a congestion e?ect, which suggests
that investment in?uences hiring decisions in an important way (and viceversa)
because the extra cost that this joint decision implies. The congestion e?ects are
key, especially to match the contemporaneous correlation between capital and labor
adjustment. It turns out that, according to the model, the type of real rigidity
(represented by the type of adjustment cost the ?rms face) is as important as the
interaction between capital and labor adjustment, which appears as an extra cost
(congestion e?ect). The structural methodology allows me to reject statistically the
existence of ?xed costs and to accept the existence of disruption costs for capital and
labor, the existence of convex costs for capital but not for labor and the existence
of congestion e?ects. Finally, the benchmark model of convex costs, widely used in
the macroeconomic literature, is not able to explain by itself the type of behavior
observed in ?rm investment and dynamic employment demand decisions.
The paper proceeds as follows. Section 2 presents the empirical evidence,
which is descriptive and with minimal structure imposed on the data. Section 3
presents the model used to explain the empirical patterns and discusses the adjust-
ment cost assumptions. Section 4 discusses some important numerical issues dealing
7
with the model and analyzes the decision rules that emerge from an illustrative pa-
rameterization of the model. Section 5 recovers the parameters governing the joint
adjustment of capital and labor from the model and carries on some experiments in
order to give an idea of the goodness of ?t in the estimated parameters. Section 6
concludes and gives directions for further research.
1.2 Factor Adjustment: An Exploration of the Facts from the Micro-
data
The ?rst task is to analyze empirically whether capital and labor adjustments
are interrelated. Because the variables of interest are adjustments, I look at the gross
investment rate and at the growth in demand for labor, energy and materials. I start
by showing the distribution of factor adjustments, then presenting basic correlations
among them. Given the low (but statistically di?erent from zero) correlation among
factor adjustments, I analyze the behavior of the variables during large adjustment
and inaction episodes.
13
I use again basic correlations of the incidence of adjustment,
also analyzing the conditional probability of inaction or adjustment.
14
I also run a
VAR(1) for factor adjustments to get a sense of the magnitude of the dynamic
interactions between factor adjustments at the ?rm level for the whole range inputs.
Finally, I explore if di?erent types of ?rms exhibit di?erent patterns in the capital
and labor adjustments. Speci?cally, I divide Census of Manufacturing ?rms in
high and low capital intensive ?rms. The analysis reveals that the adjustment
13
The criteria used to de?ne inaction and large episodes is discussed later in the paper.
14
To give continuity to the argument in the main text, I present in the appendix an additional
analysis of the interrelations between labor and capital during periods of large adjustments. In
particular, I use a variation of the methodology of Sakellaris (2004) and Letterie et al. (2004) to
analyze the interrelated adjustment between capital, labor, energy and materials.
8
distributions present very similar patterns across ?rms and the contemporaneous
correlations keep the signi?cance and low variation in all types of ?rms; the dynamics
of adjustments, however, is heterogenous depending on the ?rms characteristics, at
least in the dimension considered here. Even if this analysis is beyond the scope
of the present paper, it suggests that it is worth to explore more the di?erences by
sector in capital and employment adjustments.
These empirical exercises are built around the issue of interest, which is the
interrelation in capital and employment adjustment. The distributions show a mix
of small and large adjustments of capital and labor with large inaction periods at
the ?rm level; this has been interpreted in the literature as lumpy adjustment, but
it misses the point that infrequent adjustment periods can be followed by smooth
and small adjustment periods. In the case of materials and energy, the adjustment
is more continuous, but they show also a mix of small and large adjustments; in
this sense, their adjustment can not be called lumpy as the capital and labor ad-
justment; these distributions also show di?erences in the frequency of adjustment
across factors. This micro evidence is in contrast to the smooth aggregate series that
have been extensively analyzed in the literature. The contemporaneous correlations,
and the analysis of the episodes of large adjustments and inaction, show that these
adjustments indeed have a statistically signi?cant degree of interrelation.
15
The
VAR(1) aims to show that the dynamic interrelation between factor adjustment
holds during all episodes of adjustment, not just spikes, which are important and
15
The analysis of these episodes, found in the appendix, reinforces the view that adjustments are
interrelated, that there is a mix of small and large adjustments and a mix of smooth and lumpy
factor adjustments, and that there exists evidence of adjustment costs based on the observation of
the decrease in productivity and output after the adjustment, especially in the case of capital.
9
also statistically signi?cant.
While the main focus of this paper is the adjustment of capital and labor, I
also consider energy and materials adjustment in order to motivate the assumption
below that these factors are adjusted at no cost. The distributions of adjustment
presented later on justify this claim, as will become clear.
This section is in the same spirit as other recent work showing evidence on
the interrelation between capital and labor adjustment using micro data. Narazani
(2004) focuses on a small subset of large Italian ?rms to study capital and labor ad-
justment. Sakellaris (2004) shows evidence on the interrelation in factor adjustment
in episodes of considerable adjustment in capital and labor. Letterie et al. (2004) an-
alyze this adjustment for Denmark ?rms and Polder and Verick (2004) compare the
adjustment dynamics in Denmark and Germany. Eslava et al. (2004) use the same
dataset used in this paper and employ Caballero, Engel and Haltiwanger’s (1995,
1997) methodology to analyze the nonlinear interrelation between capital and labor
adjustment. None of these studies, however, contain the structural approach and
comprehensive analysis that this paper presents.
One of the most important points to note is that the analysis is carried over
the whole Census of manufacturing ?rms, and not just for a subset as most previous
studies have done. It is also important to note the high quality of the capital
measure, something not common in this type of panel, and the fact that the existence
of prices at the ?rm level reduces measurement error in factor adjustment, a unique
characteristic of this dataset. This initial exploration of the facts is the basis for the
factor adjustment model presented later.
10
1.2.1 Data
The data come from the Colombian Annual Manufacturing Census (AMS)
during the period 1982 -1998. The AMS is an annual unbalanced panel of around
13,000 ?rms per year containing ?rms with more than 10 employees or sales above
a certain limit. It contains the values of production, materials and energy con-
sumption; physical quantities of energy; prices for each product and material used;
production and non-production workers and payroll; and book values of equipment
and structures. I use the panel of pairwise continuing ?rms constructed by Eslava
et al. (2004), which accounts for a total of 2,167 ?rms in the period 1982-1998. I
choose to work with a balanced panel because I do not analyze the e?ects of ?rm
entry or exit. In this section I describe how the variables were constructed. For
more information about the construction of the variables, see Eslava et al. (2004).
Price level indices are constructed for output and materials using Tornqvist
indices. Tornqvist indices are the weighted average of the growth in prices for all
individual products (or materials) generated (used) by the plant. The weights are
the average of the shares in the total value of production (or materials used). More
formally, the index for each plant j producing outputs (or using materials) h in year
t is:
ln P
jt
= ln P
jt?1
+ ?P
jt
with P
j1982
= 100 as the base year, ?P
jt
=
H
h=1
¯ s
hjt
?ln(P
hjt
) representing the
weighted average of growth in prices for all products h, and ¯ s
hjt
=
s
hjt
+s
hjt?1
2
as
the simple average of the share of product (material) h in plant j’s total value of
11
production (materials usage).
Quantities of materials and output are constructed by dividing the reported
value by the prices. Energy quantities and number of workers are reported by the
plants. Investment represents gross investment and is generated from the informa-
tion on ?xed assets reported by the plants. More speci?cally, gross investment is
calculated recursively with the formula
I
jt
= K
NF
jt
? K
NI
jt
+d
jt
??
A
jt
where K
NF
jt
?K
NI
jt
is the di?erence in the value of the ?xed assets reported by plant
j at the end and beginning of year t and d
jt
? ?
A
jt
is the depreciation minus the
in?ation adjustment reported by plant j at the end of year t. In the rest of the
paper, all the variables are in logs unless indicated. The reported growth is the log
di?erence, and the observations are considered outliers if they are greater than 10
(adjustment of 1000%) or lower than -1 (adjustment of -100%).
1.2.2 Basics About Factor Adjustment: Distributions and Correla-
tions
Distributions of Factor Adjustments
Before showing the complete distributions of factor adjustment for the whole Census
of Colombian Firms during the period from 1982 to 1998, it is useful to introduce
the behavior of one particular ?rm during this period. The selected ?rm is from
the food sector and satis?es no particular criteria other than illustrating of how
12
Figure 1.1: Factor Adjustment for a Particular Firm from the Colombian Census of
Manufacturing Firms.
individual ?rms adjust input factors . Figure 1.1 shows the time series behavior
for this ?rm in the case of capital, employment, energy and materials adjustments.
This ?gure illustrate the basic patterns observed in the panel. In particular, for this
?rm there is no negative investment; there exist some periods of inaction in capital
and labor; the ?rm continuously adjusts energy and materials; and there are periods
of large adjustment in all the factors mixed with periods of small adjustment.
Figure 1.2 shows the distribution of factor adjustments for all plants in my
sample. The factors are capital, employment (number of workers), energy and ma-
terials. Table 1.1 summarizes ?gure 1.2. In Table 1.1, the inaction zone is de?ned
as an adjustment lower than 1% in absolute value, while the spikes are de?ned as
13
Figure 1.2: Distributions of Factor Adjustment. Percentage of observations (y-axis)
in a range of adjustment (x-axis)
Gross Investment Rate
0
5
10
15
20
25
-
0
.
5
-
0
.
4
-
0
.
3
-
0
.
3
-
0
.
2
-
0
.
1
-
0
0
.
0
6
0
.
1
4
0
.
2
2
0
.
3
0
.
3
8
0
.
4
6
I/K
%
o
f
o
b
s
e
r
v
a
t
i
o
n
s
Wks growth
0
5
10
15
20
25
-
0
.
5
-
0
.
4
-
0
.
3
-
0
.
3
-
0
.
2
-
0
.
1
-
0
0
.
0
6
0
.
1
4
0
.
2
2
0
.
3
0
.
3
8
0
.
4
6
Workers growth (log difference)
%
o
f
O
b
s
e
r
v
a
t
i
o
n
s
Energy Growth
0
5
10
15
20
25
-
0
.
5
-
0
.
4
-
0
.
3
-
0
.
3
-
0
.
2
-
0
.
1
-
0
0
.
0
6
0
.
1
4
0
.
2
2
0
.
3
0
.
3
8
0
.
4
6
Energy growth (log difference)
%
o
f
o
b
s
e
r
v
a
t
i
o
n
s
Materials Growth
0
5
10
15
20
25
-
0
.
5
-
0
.
4
-
0
.
3
-
0
.
3
-
0
.
2
-
0
.
1
-
0
0
.
0
6
0
.
1
4
0
.
2
2
0
.
3
0
.
3
8
0
.
4
6
Materials Growth (log difference)
%
o
f
O
b
s
e
r
v
a
t
i
o
n
s
adjustments above 20% in either direction.
16
An observation is de?ned as the adjust-
ment of ?rm j in year t. I will analyze these distributions in terms of the frequency,
symmetry and size of the adjustments.
With respect to the size of adjustments, there is no standard de?nition for
large or small adjustments, but a visual inspection of the capital and labor adjust-
ment distributions shows a combination of small and large values with a mass point
16
The inaction and spike zones are de?ned with this arbitrary criteria to give a sense of “small”
and “large” adjustment and to be consistent with previous literature on factor adjustment.
14
around the inaction region(i.e. zero adjustment). The existence of these mass points
around zero adjustment and the fat tails of the distributions can be interpreted as
lumpy adjustment; for example, in table 1.1, the lumpy pattern can be observed in
the proportion of the adjustments above 20%, considering this number as a large
adjustment indicator, compared to the proportion of the adjustments lower than
1% in absolute value, considering this as the inaction region; in the other hand, the
smooth adjustment can be observed in the proportion of adjustments below 20%
and above the inaction region. The materials and energy adjustment distributions
fail to be considered lumpy under this criteria since the percentage of observations
in the inaction region is not very high; what these distributions show is more a
continuous adjustment with jumps in the size of the adjustments.
Perhaps a more standard measure of how many extreme observations are ob-
served in a distribution is the excess kurtosis. In the case of input factor adjustments,
all distributions have large excess kurtosis, indicating that many observations are
far away from the mean.
17
Speci?cally, excluding outliers greater than 10 in each
distribution (which is an adjustment of 1000%) the excess kurtosis measures are 59,
35, 11 and 92 for capital, employment, materials and energy adjustment respectively.
Excluding the outliers greater than 2 (adjustment of 200%) the excess kurtosis mea-
sures remain large and equal to 7.65, 7.96, 2.2 and 3.85, respectively. These numbers
indicate fat tails in the distributions of adjustment and a clear lumpy adjustment
pattern for capital and labor because of the existence of a mass point around the
17
The normal distribution has an excess kurtosis of zero. The fatter the tails of a distribution,
the bigger the excess kurtosis.
15
Table 1.1: Distribution of factor adjustment(%)
I
K
?L
L
?m
m
?e
e
Inaction (abs
< 1%) 18.9 13.4 3.2 5.6Positive Spike (y > 20%) 29.8 11.6 28.4 23.7
Negative Spike (y < 20%) 1.8 11.1 18.8 15.8
?(y, y
?1
) 0.025 -0.057 0.0 -0.298
Number of Obs 24467 34243 31977 34597
inaction region; in the case of materials and energy, as it was said before, it indicates
the existence of large adjustments but not of a lumpy pattern since there is no mass
point around the inaction region.
With respect to the symmetry of the adjustments, ?gure 1.1 suggests that the
investment distribution is very asymmetric: there is very little negative investment.
This suggests irreversibility of capital in Colombia. The labor adjustment distrib-
ution is much more symmetric. Putting together those two distributions, we can
conclude that it is easy for ?rms to adjust employment negatively but not capital,
perhaps because of di?erences in the adjustment costs involved for each input fac-
tor (the selling price of capital is lower than the buying price) due in turn to the
physical nature of the factors re?ecting the irreversibility of capital. Materials and
energy distributions are also symmetric, though not as much so as the employment
adjustment distribution.
With respect to the frequency of adjustments, we observe that ?rms often leave
capital and employment essentially ?xed, but adjust materials and energy more fre-
quently. This is the justi?cation for the assumption later in the model that materials
and energy are not subject to adjustment costs. Firms adjust them in an almost
16
continuous fashion. The evidence for Colombia is in line with the evidence for the
U.S. using the LRD (Longitudinal Research Database), where lumpiness in capital
and employment is also present together with signi?cant periods of smooth adjust-
ment. This evidence alone suggests the presence of adjustment costs and, as many
others have pointed out, may indicate (S,s) behavior in capital and employment
adjustment.
Summarizing the information observed in the distributions, we can conclude
that: (i) the distributions of input factor adjustment have fat tails; (ii) the invest-
ment distribution is asymmetric, showing a large degree of irreversibility, while the
labor adjustment distribution is highly symmetric; (iii) Capital and employment ad-
justments are infrequent (large mass point around zero adjustment) but materials
and labor adjustment are much more frequent (no mass points around zero). Points
(i) and (iii) signal the existence of lumpiness in the adjustment of capital and labor
due to non-convex costs in capital and labor adjustment; and (iv) small and large
values coexist in the distributions of adjustment for all the factors.
Correlations of Factor Adjustments
Table 1.2 shows the contemporaneous correlations among factor adjustments
18
The
highest correlation coe?cients are for employment and materials growth, followed
by the correlations between materials and energy growth and employment and en-
ergy growth. The correlation between the investment rate and employment growth
18
The correlations are calculated regressing adjustment on time dummies to take out business
cycle e?ects, and I consider only the residuals which re?ect ?rm-level shocks. Another interesting
possibility would be to consider the business cycle e?ects as well, but this is left for future work.
17
Table 1.2: Factor adjustment contemporaneous correlation
I
K
?L
L
?m
m
?e
e
I
K
1
?L
L
0.057 1
?m
m
0.026 0.175 1
?e
e
0.041 0.107 0.147 1
All correlations are statistically
di?erent from zero at 1% signi?cance
is small but nonzero. All the correlations are statistically di?erent from zero. More-
over, even if the correlation coe?cient for capital and employment growth hides a
considerable amount of sectoral heterogeneity, many sectors
19
share a similar coe?-
cient, which is near the one reported in Table 1.2.
The contemporaneous correlations give a sense that capital and employment
adjustment periods are interrelated. However, given the low correlation between
capital and employment, it is worth analyzing the correlation of adjustment during
inaction periods, during spike episodes and during a combination of both.
20
The
questions here are whether inaction or spikes in employment are correlated with
inaction or spikes in capital, and whether inaction or spikes in one factor increase
the probability that ?rms adjust the other factor. Equivalently, we could ask if ?rms
stagger capital and labor adjustments. If ?rms stagger, we would observe a negative
correlation between the incidence of adjustments in investment and employment
and an increase in the probability of adjustment conditional on inaction in the
19
The sectors present in the data are Food, Drinks and Beverages, Tobacco, Textiles, Wood,
Paper, Chemicals and Rubber, Oil, Glass and Non-metallic, Metals and Metal products, Machinery
and others. Of these, just the Oil sector, the Drinks and Beverages sector and the Tobacco sector
have a negative correlation coe?cient.
20
The inaction and spike episodes are de?ned as above: less than 1% in absolute value for
inaction and more than 20% in absolute value for the spikes.
18
Table 1.3: Correlations among incidence of episodes (dummies for inaction/spikes)
Investment Rate:
I
K
Employment Growth:
?e
e
Dummies for: Inaction Spike Pos Spike Inaction Spike Pos spike
Inaction 1
I
K
Spikes -0.335* 1
Pos. Spike -0.241* 0.719* 1
Inaction 0.081* -0.035* -0.030* 1
?e
e
Spike 0.006 0.030* 0.006 -0.229* 1
Pos spike -0.041* 0.055* 0.024* -0.231* 0.361* 1
Neg spike 0.040* 0.01 0.026* -0.216* 0.364* -0.325*
The correlations are among 0/1 dummies during large adjustment episodes
*: statistically di?erent form zero at 1% of signi?cance. Dummies for inaction
are de?ned as 1 if abs(x) < 0.01 and dummies for spikes are de?ned as 1 if x > 0.2
other factor.
To further explore these issues, and to characterize ?rms’ adjustments dur-
ing inaction and spike episodes, the rest of the subsection explores the correlation
between the incidence of zeros and spikes in capital and employment and the prob-
abilities of inaction/spike in one factor conditional on inaction/spike in the other
factor.
21
Even though the de?nition of inaction and spikes given above may be some-
what arbitrary and may be capturing adjustments that are not small or large for
certain types of capital,
22
it is useful to characterize the behavior of capital and em-
ployment around “small” and “large” episodes of adjustment. Table 1.3 shows the
correlation of the incidence of inaction and spikes in investment and employment
adjustment.
21
The appendix has a more extensive analysis of the behavior of several variables around inactions
and spikes in capital and employment adjustment.
22
For example, many ?rms need small tools important for production which signal a positive
investment but lower than 1% of their capital stock.
19
After a closer look at table 1.3, several facts emerge
23
.First, the correlation
between investment and employment adjustment is positive and higher during inac-
tion times than during spike times for both factors. Moreover, the only statistically
signi?cant correlation during spikes in employment is with spikes in investment, due
to positive employment spikes and not negative ones. Also, the negative correlation
between the incidence of positive spikes in employment and inaction in capital sug-
gests that after a positive spike in employment, there is inaction in capital. All this
would suggest that during some periods, ?rms increase capital and employment in
large amounts at the same time, and have inaction periods for the two factors after
the adjustment.
There is also a positive correlation between negative spikes in employment and
both inaction and positive spikes in investment. This suggests that sometimes ?rms
substitute one factor for another (increasing capital and decreasing employment)
and at other times ?rms choose to adjust only employment down given the high
irreversibility of capital. Table 1.3 suggests that capital and labor tend to move
together during inaction and spike episodes.
Table 1.4 shows the results of estimating four di?erent logit models, each one
for investment and employment and inaction and spikes respectively, where the
dependent variable is the probability of adjustment or inaction in one factor and
the independent variables include the adjustment and inaction
24
status in the other
23
Two clarifying points: ?rst, observe that the correlation between Inaction and spikes episodes
is not -1 because these episodes are not consecutive and instead there exist adjustments larger than
1% and smaller than 20% in between; second, the “spikes” are di?erent from “positive spikes” in
the sense that they include negative spikes.
24
both dummies are included at the same time
20
factor. The logit estimation includes controls for ?rm-speci?c variables such as Total
Factor Productivity (TFP) and demand shocks
25
and the adjustment of energy and
materials. It is important to control for the shocks in this context since they lessen
the chances that the comovement between employment and investment is merely
due to an omitted third factor. Moreover, controlling for the TFP and demand
shocks identify the movements in employment and capital as dependent not only
from shocks but from other sources, in this case interpreted later as adjustment
costs.
From table 1.4, it can be observed that the probability of inaction in invest-
ment increases if there is inaction in employment. The same is true in the case of
employment, but the e?ect is not statistically signi?cant. At the same time, the
probability of an investment spike increases if there is an employment spike, and
the probability of an employment spike increases when there is an investment spike.
These numbers con?rm the conclusions drawn from table 1.3: capital and labor tend
to move together. The probability of inaction in employment decreases when there
is an investment spike. The other e?ects are not statistically signi?cant. All these
numbers suggest that, on the one hand, when there is a large adjustment in either
capital or employment, it is more likely that ?rms are having large adjustments in
both factors; on the other hand, when ?rms do not adjust employment, it is more
likely that they do not adjust capital, but when ?rms do not adjust capital, it does
not mean necessarily that they do not adjust labor.
As further evidence of the interrelation of capital and labor adjustment, other
25
The estimation of these shocks is explained later in the paper in the calibration section.
21
Table 1.4: Probability of inaction/adjustment conditional on Inaction/adjustment
of the other factor
Investment Employment growth
Variable x P(inaction/x) P(Spike/x) P(inaction/x) P(Spike/x)
0.057 0.012
Inaction
(0.071) (0.061)
Investment
-0.11† 0.205**
Spike
(-0.06) (0.048)
0.143* -0.033
Employment
Inaction
(0.067) (-0.058)
Growth -0.033 0.208**
Spike
(-0.059) (0.046)
Observations 12864 17055 12410 14459
†/*/** signi?cant at 10%, 5% and 1%. TFP, demand shocks and year e?ects in regression
Dummies for inaction are de?ned as 1 if abs(x) < 0.01 and dummies for spikes are de?ned as 1 if
x > 0.2
interesting results on the dynamic behavior of the input factors around episodes of
spikes and inaction in capital and labor are reported in the appendix. In particular,
there is evidence that TFP and output fall after periods of adjustment, especially
in the case of capital, suggesting a cost in terms of foregone pro?ts.
The analysis in tables 1.3 and 1.4 examines the case of large changes in capital
and labor. A natural question that follows is whether this analysis extends to all
adjustments in a dynamic context. I discuss the basic empirical approach for this
problem next.
1.2.3 Factor Adjustment Interrelation: Dynamic Dependence
In this subsection, I present the coe?cients of a simple VAR with one lag,
intended to describe how ?rms’ factor adjustments are dynamically interrelated.
22
The VAR variables of interest are gross investment and growth in employment,
energy and materials. The coe?cients and their statistical signi?cance are quite
robust to several controls. The reported VAR is estimated controlling for shocks in
demand and productivity
26
and for year e?ects. Table 1.5 shows the results for this
estimation procedure.
Table 1.5: Dynamic relations in factor adjustment
I
K
?L/L ?m/m ?e/e
-0.008 -0.008 0.023 -0.038
(
I
K
)
?1
0.006 (0.003)** (0.004)** (0.006)**
0.037 -0.147 0.049 0.091
(
?L
L
)
?1
(0.017)* (0.007)** (0.012)** (0.017)**
-0.007 0.024 -0.247 0.036
(
?m
m
)
?1
0.01 (0.004)** (0.007)** (0.010)**
0.013 0.009 0.006 -0.345
(
?e
e
)
?1
-0.007 (0.003)** (0.005)* (0.007)**
Observations 17653 17653 17653 17653
R-squared 0.03 0.07 0.26 0.23
Standard errors in parentheses; **/* signi?cant at 1% and 5%;
year e?ects and shocks in regression
Table 1.5 shows that an increase in labor demand signals a posterior investment
episode (the coe?cient of the e?ect of lagged labor growth on investment is positive
and statistically signi?cant). Moreover, the coe?cient of lagged investment in the
labor equation is negative and signi?cant. F-tests for the cross coe?cients of labor
and capital in this VAR with 4 variables and in a simpler version with just capital
and employment were run to verify Granger causality. Both coe?cients are di?erent
from zero, which does not give much more information since it is not conclusive about
which one causes the other.
26
Later in the paper I explain how these shocks are estimated using the price information
23
It is important to note that the other factors exhibit large coe?cients and
small standard errors, indicating that the ?rms use several margins of adjustment
in capital, labor, materials and energy. Moreover, the diagonal elements (the auto-
correlation) for all factors are negative, suggesting that if ?rms adjust in one period
it is very likely that either they will not do so the next period or that they will adjust
in the opposite direction. The negative autocorrelation in the VAR is a re?ection
of the patterns from the distribution of adjustments. Capital is the factor with
smaller negative autocorrelation in adjustment, which may signal inaction in the
following periods since the distributions show a mass around zero and the negative
coe?cient signals inaction or adjustment in the opposite direction, as mentioned
above. Materials and energy are the factors with higher negative autocorrelation in
adjustment, which may signal instead free adjustment in the opposite direction the
following period.
An interesting point with respect to the autocorrelation coe?cient in the in-
vestment rate is that it changes sign when controlling for individual ?rm charac-
teristics through ?xed e?ects (being positive when ?xed e?ects are not present,
showing a similar coe?cient to that of the simple contemporaneous correlations).
This suggests that unobservable characteristics are important and that the simple
autocorrelation observed before in table 1.2 may be a result of aggregation e?ects
more than ?rm-level e?ects
27
.
27
Exploring this issue even further, this autocorrelation coe?cient for the investment rate main-
tains a consistently positive sign in 2 sectors (Wood and Paper), and maintains the negative sign
in the Chemicals sector for both cases. Moreover, the size of the coe?cient and the statistical sig-
ni?cance is important in 8 out of 12 sectors when controlling for ?xed e?ects, and it is statistically
signi?cant in just 2 sectors when ?xed e?ects are not present, the two with a consistently positive
sign.
24
1.2.4 The Role of Heterogeneity
One question that emerges after the empirical exercises above is if the same
adjustment patterns repeat for all types of ?rms. In particular, this subsection
asks if the interrelation between capital and labor adjustment, if the fat tails and
the mix of small and large adjustments present in the distributions of adjustments,
and if the dynamic correlations among adjustments, are present for all types ?rms.
The characteristic chosen to answer this question is the capital intensity a ?rm has,
dividing the data in high and low capital intensive ?rms. The following empirical
exercises take the high capital intensive ?rms as the ones in the upper quartile of
the capital to labor ratio; the low capital intensive ?rms are in the lower quartile in
that ratio.
Figure 1.3 shows the distributions of adjustments for capital, labor, energy
and materials in the case of low and high intensive capital ?rms. Even if the pat-
terns are the same in both groups, the main di?erence is present in the investment
rate distributions, since low capital intensive ?rms adjust in a more lumpy way: the
percentage of observations with zero adjustment in capital is more than 30%, while
in the case of the high capital intensive ?rms is 15%; in the other hand, the per-
centage of observations with an investment rate of 50% or more is 15% for the low
capital intensive ?rms, while it is less than 10% in the case of high capital intensive
?rms. In the case of labor, materials and energy adjustment, they are very similar.
Based on these distributions of adjustments, we can conclude that there is not much
heterogeneity and that the patterns of interest observed in the previous sections are
25
Table 1.6: Factor adjustment contemporaneous correlation: Low Capital Intensive
Firms (Lower quartile in
K
L
ratio)
I
K
?L
L
?m
m
?e
e
I
K
1
?L
L
0.063* 1
?m
m
0.031 0.170* 1
?e
e
0.019 0.078* 0.093* 1
*signi?cant at 1%
Table 1.7: Factor adjustment contemporaneous correlation: High Capital Intensive
Firms (Upper quartile in
K
L
ratio)
I
K
?L
L
?m
m
?e
e
I
K
1
?L
L
0.039 1
?m
m
0.032 0.143 1
?e
e
0.079 0.103 0.139 1
All correlations are statistically
di?erent from zero at 1% signi?cance
very similar across ?rms, suggesting adjustment costs in capital and labor adjust-
ment for all types of ?rms, perhaps with a higher in?uence of non-convexities(i.e.
disruption and ?xed costs in the sense explained later as opposite to convex costs)
in the case of ?rms with a low capital to labor ratio.
Tables 1.6 and 1.7 show the contemporaneous correlations among factors for
low and high capital intensive ?rms respectively. The most important point these
tables show is that the correlation in capital and labor adjustment is statistically
signi?cant for both groups and not very di?erent; in this case, we also observe that
both groups are not very di?erent and that heterogeneity is not very important.
This heterogeneity in the contemporaneous correlations is more important
26
Figure 1.3: Distribution of Factor Adjustment in High and Low Capital Intensive
Firms. % of observations (y-axis) in a range of adjustment (x-axis) .
HIGH CAPITAL INTENSITY FIRMS (Upper quartile in K/L ratio)
LOW CAPITAL INTENSITY FIRMS (Lower quartile in K/L ratio)
Gross Investment Rate
0
5
10
15
20
25
30
-
0
.
5
-
0
.
4
-
0
.
3
-
0
.
3
-
0
.
2
-
0
.
1
-
0
0
.
0
6
0
.
1
4
0
.
2
2
0
.
3
0
.
3
8
0
.
4
6
I/K
%
o
f
o
b
s
e
r
v
a
t
i
o
n
s
Wks growth
0
5
10
15
20
25
30
-
0
.
5
-
0
.
4
-
0
.
3
-
0
.
3
-
0
.
2
-
0
.
1
-
0
0
.
0
6
0
.
1
4
0
.
2
2
0
.
3
0
.
3
8
0
.
4
6
Workers growth (log difference)
%
o
f
O
b
s
e
r
v
a
t
i
o
n
s
Energy Growth
0
5
10
15
20
25
30
-
0
.
5
-
0
.
4
-
0
.
3
-
0
.
3
-
0
.
2
-
0
.
1
-
0
0
.
0
6
0
.
1
4
0
.
2
2
0
.
3
0
.
3
8
0
.
4
6
Energy growth (log difference)
%
o
f
o
b
s
e
r
v
a
t
i
o
n
s
Materials Growth
0
5
10
15
20
25
30
-
0
.
5
-
0
.
4
-
0
.
3
-
0
.
3
-
0
.
2
-
0
.
1
-
0
0
.
0
6
0
.
1
4
0
.
2
2
0
.
3
0
.
3
8
0
.
4
6
Materials Growth (log difference)
%
o
f
O
b
s
e
r
v
a
t
i
o
n
s
Gross Investment Rate
0
5
10
15
20
25
30
-
0
.
5
-
0
.
4
-
0
.
3
-
0
.
3
-
0
.
2
-
0
.
1
-
0
0
.
0
6
0
.
1
4
0
.
2
2
0
.
3
0
.
3
8
0
.
4
6
I/K
%
o
f
o
b
s
e
r
v
a
t
i
o
n
s
Wks growth
0
5
10
15
20
25
30
-
0
.
5
-
0
.
4
-
0
.
3
-
0
.
3
-
0
.
2
-
0
.
1
-
0
0
.
0
6
0
.
1
4
0
.
2
2
0
.
3
0
.
3
8
0
.
4
6
Workers growth (log difference)
%
o
f
O
b
s
e
r
v
a
t
i
o
n
s
Energy Growth
0
5
10
15
20
25
30
-
0
.
5
-
0
.
4
-
0
.
3
-
0
.
3
-
0
.
2
-
0
.
1
-
0
0
.
0
6
0
.
1
4
0
.
2
2
0
.
3
0
.
3
8
0
.
4
6
Energy growth (log difference)
%
o
f
o
b
s
e
r
v
a
t
i
o
n
s
Materials Growth
0
5
10
15
20
25
30
-
0
.
5
-
0
.
4
-
0
.
3
-
0
.
3
-
0
.
2
-
0
.
1
-
0
0
.
0
6
0
.
1
4
0
.
2
2
0
.
3
0
.
3
8
0
.
4
6
Materials Growth (log difference)
%
o
f
O
b
s
e
r
v
a
t
i
o
n
s
27
Table 1.8: Probability of inaction/adjustment conditional on Inaction/adjustment
of the other factor: Low Capital Intensive Firms
Investment Employment growth
Variable x P(inaction/x) P(Spike/x) P(inaction/x) P(Spike/x)
0.35 -0.08
Inaction
(0.13)** (0.11)
Investment
0.17 0.06
Spike
(0.13) (0.10)
0.41 -0.06
Employment
Inaction
(0.13)** (0.13)
Growth -0.06 0.16
Spike
(0.11) (0.10)
Observations 3269 3839 2800 3372
†/*/** signi?cant at 10%, 5% and 1%. TFP, demand shocks and year e?ects in regression
Dummies for inaction are de?ned as 1 if abs(x) < 0.01 and dummies for spikes are de?ned as 1 if
x > 0.2
when considering the probability of adjustment given inaction/adjustment in the
other factor. Table 1.8 and 1.9 illustrate this point. None of the coe?cients esti-
mated for the high capital intensive ?rms is statistically signi?cant and many signs
are di?erent to the estimated considering all types of ?rms; for example, for the
high capital intensive ?rms, the probability of inaction in investment decreases with
inaction in employment growth, while it increases in the estimation with all the
?rms; in the same way, the probability of a spike in employment growth increases
with inaction in investment, which is the opposite when. considering all types ?rms
in the estimation. The coe?cients are closer to the obtained for all types of ?rms
in the case of the low capital intensive ?rms and some are statistically signi?cant as
well. We can say from these tables that the low capital intensive ?rms tend to move
more together than in the case of the high capital intensive ?rms.
28
Table 1.9: Probability of inaction/adjustment conditional on Inaction/adjustment
of the other factor: High Capital Intensive Firms
Investment Employment growth
Variable x P(inaction/x) P(Spike/x) P(inaction/x) P(Spike/x)
0.02 -0.20
Inaction
(0.18) (0.15)
Investment
-0.13 0.08
Spike
(0.12) (0.10)
-0.1 -0.12
Employment
Inaction
(0.19) (0.12)
Growth -0.24 0.04
Spike
(0.17) (0.11)
Observations 1898 3520 2612 3034
†/*/** signi?cant at 10%, 5% and 1%. TFP, demand shocks and year e?ects in regression
Dummies for inaction are de?ned as 1 if abs(x) < 0.01 and dummies for spikes are de?ned as 1 if
x > 0.2
In the case of the dynamic correlations, heterogeneity seems to play a more
important role and ?rms seem to show a di?erent behavior. Tables 1.10 and 1.11
show a VAR(1) estimated for low and high capital intensive ?rms respectively. With
respect to the dynamic interrelation between capital and labor adjustment, the only
sign consistent in all the estimations is the e?ect of the lagged investment rate in
the labor adjustment, even if not signi?cant for each subgroup but signi?cant for
all the Census of Manufacturing ?rms. In the case of the e?ect of lagged labor
growth in the investment rate, the high capital intensive ?rms have a slightly higher
coe?cient than that estimated for all the ?rms and it has the same sign, which does
not happen in the case of the low capital intensive ?rms The low capital intensive
?rms present. The other coe?cient look similar in general, but the autocorrelation of
investment rates is positive in contrast to the coe?cient obtained when all the ?rms
29
Table 1.10: Dynamic relations in factor adjustment: Low Capital Intensive Firms
I
K
?L/L ?m/m ?e/e
0.023 -0.002 0.038 -0.135
(
I
K
)
?1
0.037 0.011 0.021 (0.030)**
-0.055 -0.167 0.071 0.083
(
?L
L
)
?1
0.044 (0.013)** (0.025)** (0.035)*
0.002 0.019 -0.281 0.055
(
?m
m
)
?1
0.025 (0.008)* (0.014)** (0.020)**
0.009 0.006 -0.013 -0.412
(
?e
e
)
?1
0.016 0.005 0.009 (0.013)**
Observations 4540 4540 4540 4540
R-squared 0.04 0.1 0.29 0.31
Standard errors in parentheses; **/* signi?cant at 1% and 5%;
year e?ects and shocks in regression
are considered. In general, we can say that the dynamic correlation coe?cients
estimated for the high capital intensive ?rms look more similar to the estimates
considering all the ?rms; this suggests some room to explore with respect to the
dynamic behavior across heterogeneous ?rms.
The empirical evidence presented above indicating the infrequent nature and
the mix of smooth and lumpy adjustment in capital and labor, indicates a dynamic
dependence in these adjustments. There is some heterogeneity in the dynamic rela-
tions and in the case of inaction and large adjustment episodes, but the interrelation
pattern is present across all types of ?rms. In the following section, I set up a model
that aims to explain the patterns observed in the data, in particular, the infrequent
and lumpy adjustments, and the interrelation among factor adjustment. The main
features of the model are the presence of convex and non-convex adjustment costs
in capital and labor (but not in the other factors) and the possibility of mutual
interaction e?ects in the form of congestion (if more costly) or complementarities (if
30
Table 1.11: Dynamic relations in factor adjustment:High Capital Intensive Firms
I
K
?L/L ?m/m ?e/e
0.023 -0.002 0.006 -0.026
(
I
K
)
?1
(0.007)** 0.004 0.007 (0.009)**
0.042 -0.182 0.011 0.044
(
?L
L
)
?1
0.029 (0.015)** 0.028 0.038
0.019 0.032 -0.249 0.06
(
?e
e
)
?1
0.016 (0.008)** (0.015)** (0.021)**
0.01 0.007 0.034 -0.357
(
?m
m
)
?1
0.011 0.006 (0.011)** (0.015)**
Observations 4231 4231 4231 4231
R-squared 0.06 0.08 0.25 0.22
Standard errors in parentheses; **/* signi?cant at 1% and 5%;
year e?ects and shocks in regression
cheaper) in the adjustment process through di?erent adjustment costs if the ?rms
adjust capital and labor independently or at the same time. As stated previously,
non-convexities in the decision problem coming from the adjustment costs cause
jumps or infrequent movements in ?rms’ factors and interaction e?ects are de?ned
as changes in cost due to joint adjustment.
The driving forces of factor adjustment in the model are technology and de-
mand shocks, but not factor price shocks; this is assumed for simplicity. Simplicity
also leads me to assume symmetry in the adjustment costs, an assumption that
can be tested in the data. This assumption seems very plausible in the case of
labor adjustment, as the analysis in the appendix reveals a marked symmetry in
the behavior of all variables around bursts of job creation and destruction. Another
important assumption is the lack of inventories as an adjustment variable. This
could be an argument for using only sectors without signi?cant inventories in the
estimation procedure. Factor price e?ects, inventory adjustments and asymmetry
31
of the adjustment costs are interesting and are left for future work.
1.3 A Dynamic Model of Firms’ Factor Adjustment
This model must capture the existence of small and large adjustments and
the mix of smooth and lumpy adjustments and allow for several margins of factor
adjustment as described in section 2. At the same time, the model must also cap-
ture the observed interrelation between capital and labor adjustment. This section
describes the model and analyzes its main implications. For notation purposes, the
subscript it is dropped, but is implicitly applied to all the variables.
1.3.1 Basics
Demand and Production Function
There is imperfect competition and ?rms face a downward sloping demand
curve
Q
d
=
_
P
X
_
??
(1.1)
where X is a stochastic shock to demand, ? is the price elasticity of demand and P
is the price level.
The production function incorporates capital, labor, materials and energy.
Capital and labor are costly to adjust, while materials, energy and hours
28
per
worker can be adjusted at no cost. In this context, hours can be thought of as a
28
In some range, ?rms adjust employment instead of hours because they pay wage premia for
overtime.
32
form of labor utilization, and while this is not explored in the model, energy is likely
to be correlated with capital utilization. The assumption here is that all ?rms have
the same Cobb-Douglas production function and that elasticities and factor shares
vary by sector
29
. This function does not represent an aggregate production function
but instead the production function of each ?rm. If we were to assume heterogeneity
in the production function, it would introduce too much complexity in the problem
and a separate analysis would have to be done for each ?rm or industry. Since I am
interested here in the average behavior of ?rms, this functional form seems to be
the one that can characterize the greatest number of ?rms. Formally,
Q
s
= Bk
?
(lh)
?
e
?
m
?
= Ak
?
l
?
(1.2)
where ?, ?, ? and ? are the input factor elasticities for capital, labor, energy and
materials, A = Be
?
m
?
h
?
, B is a productivity shock, k is the capital level, l is the
stock of workers, h represents hours per worker, e is energy consumption and m
is the materials level. It is convenient for notation to cluster the terms for hours,
energy, materials and productivity in the term A, since they are optimally chosen
period by period in a static maximization problem and there are no intertemporal
links in their case.
Revenue Function and pro?t
Putting together (1.1) and (1.2) we get the revenue function:
R(¯ z, k, l) = ¯ zk
ˆ
?
l
ˆ µ
(1.3)
29
In future work I plan to explore the role of heterogeneity in the elasticities.
33
where: ¯ z = XA
(
1?
1
?
)
,
ˆ
? = ?
_
1 ?
1
?
_
, ˆ µ = ?
_
1 ?
1
?
_
. This type of revenue func-
tion is used by most of the literature because of the lack of ?rm-level information
on prices. It has a demand component that is hard to identify separate from the
technology shock, even if estimated at the ?rm-level. For the Colombian Census
of Manufacturing, however, ?rm-level prices are observed. In equation(1.3), ?rms
implicitly account for the e?ects of their input choices on output prices when maxi-
mizing pro?t. The existence of ?rm-level prices allowed Eslava et al. (2004) to obtain
arguably unbiased estimates of the input elasticities and the elasticity of demand,
which I utilize in this paper.
Before de?ning the ?rm’s intertemporal decision problem, it is useful to de?ne
the pro?t level. Pro?t incorporates the cost of all the inputs, including the adjust-
ment cost which will be de?ned more formally later in this section. For now, pro?t
is given by ?(z, l
?1
, l, k, k
) = zk
?
l
µ
?w(l) ?C(z, l
?1
, l, k, k
) where w(l) is the pay-
ment to employment, C(•) is the adjustment cost, z is a term that incorporates the
technology and demand shocks, together with materials and energy price shocks.
Note that the input factor elasticities are given by ? =
ˆ
? ? M and µ = ˆ µ ? N, where
M and N are terms that incorporate the elasticities of materials and energy coming
from the static optimal ?rm choice for hours, materials and energy.
30
30
Without this simplifying notation, the complete expression including materials and energy
would be ?(•) = ¯ zk
ˆ
?
l
ˆ µ
?l(w
0
+ w
1
h
?
) ?C (z, l
?1
, l, k, k
) ?p
e
e ?p
m
m. Note the functional form
assumed in the wage equation representing a base payment plus a payment for the hours, where
? is the hours wage elasticity. The main di?erence in both equations is the term for the shocks,
¯ z, and the explicitness of the energy and material prices, p
e
e ? p
m
m.. In the text, the term z
captures all of them since the ?rm solves a static optimization problem in energy and materials
every period that can be characterized in the term z.
34
Firms’ Decision Problem
I start by discussing the timing of the decisions and the outcomes.
31
Firms
choose employment taking into account the employment level in the previous period.
Newly hired workers become productive in the same period. However, new invest-
ment becomes productive only in the next period. In this sense there is a “time to
build” for capital but not a “time to hire” for employment. Firms also chose hours,
energy and materials and can adjust them at no cost. Formally, the ?rm’s problem
is given by:
32
V (z, k, l
?1
) = max
k
,l
_
?(z, l
?1
, l, k, k
) + ?
_
V (z
, k
, l)f(z
/z)dz
_
= max
k
,l
{zk
?
l
µ
?w(l) ?C(z, l
?1
, l, k, k
)
+?
_
V (z
, k
, l)f(z
/z)dz
} (1.4)
where I = k
? (1 ??) k represents investment and ? represents depreciation. C(•)
is the cost of adjustment, which takes di?erent parameter values depending on
whether the ?rm adjusts employment, capital or both. ? is the discount factor
and the integral term represents the expected value of the ?rm subject to shocks z.
This shock distribution f(z
/z) includes the joint distribution of the demand and
productivity shocks h(x
/x) and g(A
/A) respectively. I assume these shocks are
independent.
33
31
The model proposed is similar in several dimensions to the ones used by Abel and Eberly
(1998), Cooper et al. (1999), Cooper and Haltiwanger (2005) and Cooper et al. (2004).
32
The notation implicitly states that ?rms optimally choose energy, materials and hours in a
static maximization problem. These values are embedded in the term z.
33
This assumption would not hold if the productivity shocks were not idiosyncratic but instead
common, since in this case TFP would be correlated with demand. Since the estimations of the
shocks in this paper take out the aggregate e?ects, this e?ect is mitigated. This assumption
has been used before by Syverson (2005) to estimate production functions using demand shift
35
The cost of adjustment C(•) potentially includes disruption costs, ?xed costs
and convex costs. The existence of a disruption cost taking the form of lower pro-
ductivity in adjustment periods is justi?ed by the ?ndings of Power (1998) and
Sakellaris (2004). In the appendix, I show that production and TFP decrease when
adjustment takes place, especially after investment spikes. In an additional em-
pirical exercise not shown here, I regressed TFP against a dummy of adjustment
(separately for capital and employment), obtaining a negative and signi?cant co-
e?cient for both factors, giving more support for the inclusion of this disruption
cost. The disruption cost can also be associated with the stochastic adjustment cost
present in Caballero and Engel (1999).
The convex cost term does not have a clear micro-foundation but has been
assumed to exist in previous literature because of the smooth adjustment observed at
the macro level. The distributions shown in section 2 also present regions of smooth
and lumpy adjustments as discussed previously. In the analysis in the appendix,
some ?rm-level adjustments look smooth
34
and the convex cost is incorporated into
the model to capture this fact. This mix of smooth and lumpy adjustment is more
pronounced in the evidence for the U.S. in Sakellaris (2004) than in the evidence
shown in the appendix of this paper. One of the main advantages of the modeling
mechanism taken in this paper is the ability to identify the importance of such a
cost at the ?rm level.
The ?xed adjustment cost can be seen as representing installation costs (in
instruments to calculate productivity and in the recent discussion about the relevance of VAR to
business cycles analysis.
34
Lumpy adjustment is observed in the peaks for the growth variables and smooth adjustment
is observed in the smooth slope of the coe?cients for these adjustments.
36
both time and resources) in the case of capital and ?ring and hiring costs in the
case of labor.
35
Speci?cally, the functional form assumed for the adjustment costs when ?rms
adjust l (labor), k (capital) or kl (capital and labor), is the following:
C (z, k, I, l, l
?1
) =
_
¸
¸
¸
¸
¸
¸
¸
¸
¸
¸
¸
¸
¸
_
¸
¸
¸
¸
¸
¸
¸
¸
¸
¸
¸
¸
¸
_
C
l
= ?
l
R(•) +F
l
l
?1
+
?
l
2
_
?l
l
?1
_
2
l
?1
if ?l = 0
C
k
= ?
k
R(•) +F
k
k +
?
k
2
_
I
k
_
2
k + p
I
? I if I = 0
C
lk
= C
l
+ C
k
+ ?
lk
R(•) + F
lk
?
l
?1
k
+
?
lk
2
_
I
k
_ _
?l
l
?1
_
?
l
?1
k if ?l ? I = 0
(1.5)
In the case of labor or capital adjustment, (C
l
and C
k
respectively) the ?rst term
?
j
R(•) represents the disruption cost, the second term involving F
j
represents
the ?xed cost and the third term involving ?
j
represents the convex cost, with
j=k(capital) and l(labor). In the case of capital adjustment, there is an extra cost
which represents the investment price and it can take values of p
I
= {p
buy
, p
sell
} de-
pending on if the ?rm buys or sells capital. The asymmetry in the price for buying
and selling capital implies that capital is not fully reversible, which is easily observed
in the distribution for capital adjustment shown at the beginning of the paper.
If the ?rm adjusts capital and employment at the same time, the adjustment
cost is the sum of the cost of adjusting capital (C
k
), plus the cost of adjusting
employment independently (C
l
), plus a collection of terms that represent the extra
cost of the joint adjustment. The parameters are then {?
k
, ?
l
, ?
kl
} for the disruption
cost, {F
k
, F
l
, F
kl
} for the ?xed cost, {?
k
, ?
l
, ?
kl
} for the convex cost and p
I
for the
35
The set up of the model and, speci?cally, the setup of the adjustment cost model, will allow
the estimation procedure below to distinguish which component is more important in the factor
adjustment process.
37
investment price.
To check for the existence of interaction e?ects in the adjustment of capital and
employment, the cost function for joint capital and employment adjustment is as-
sumed to be a linear function of the adjustment cost for employment, the adjustment
cost for capital and an interaction term. That is, C
kl
= C
k
+ C
l
+ C
joint adjustment
.
To be more precise, if interaction e?ects exist, the terms re?ecting joint adjustment,
(?
lk
,?
lk
and F
lk
), will be di?erent from zero. This interaction will be in the form of
a congestion e?ect if the cost is positive or in the form of a complementarity if the
cost is negative (i.e. it is a bene?t). Intuitively, interaction e?ects in the disruption
cost mean that forgone pro?ts due to interruption in the production process, or de-
creases in productivity while adjusting capital and labor, may be higher (congestion)
or lower (complementarities) than when adjusting just one factor. For example, the
learning process for new workers operating new machines maybe more expensive
than the cost of training new workers and of buying new machines separately, in-
ducing a congestion e?ect. Congestion e?ects in the ?xed cost may be due to higher
installation costs for workers speci?c to certain machines, and congestion e?ects in
the convex costs may be due to a longer adjustment period in the plants.
1.3.2 Analysis of the Model
The approach in this paper di?ers from previous analysis in the modeling
of the adjustment cost for capital and labor together and in the possibility for
interaction e?ects in this adjustment. These features may lead to behavior di?erent
38
from traditional models, where ?rms have just one factor that is costly to adjust.
In particular, even with convex costs, in our model ?rms may have inaction regions
because of corner solutions in the optimization problem. The economics of joint
adjustment can be summarized as “adjust if the marginal bene?t is bigger than the
marginal cost of adjustment.” In this sense, the relative values of the adjustment
costs play a key role, since they determine which factor to adjust.
The subsections that follow will highlight the main di?erences between this
model and the conventional models, and the new implications of considering joint
adjustment of capital and labor when they are costly to adjust. As a ?nal point,
the ?rm’s optimization problem assumes that ?rms have already optimally chosen
hours, energy and materials as a function of the state space composed of the shocks
in demand and technology, the capital stock and number of workers.
Case 1. No Adjustment Costs
I will start with the case where no adjustment costs are present. In this case, the ?rm
faces a static optimization problem for capital and labor, in addition to the static
optimization problem faced for energy and materials and captured in the term z.
39
The FOCs are:
36
k
: ?
_
V
k
(z
, k
, l) f (z
/z) dz
= p
I
(1.10)
l : µzk
?
l
µ?1
= w
l
(l) (1.11)
It can be seen that labor and capital are very sensitive to shocks. Without adjust-
ment costs, the correlation between investment and demand and technology shocks
is very high, and the same is true for employment adjustment. It is clear that
in order to reproduce the main features of the data some nominal or real rigidity
is needed. The initial candidate in the literature was the convex cost component,
later adding non convex costs to account for inaction and lumpiness. This topic is
analyzed next.
Case 2. Adjustment Costs for Capital and Employment
If ?rms face any type of adjustment costs, the analysis changes. The FOCs and
envelope conditions of the problem in the general case are:
k
: C
k
(z, l
?1
, l, k, k
) + ?
_
V
k
_
z
, k
, l
_
f
_
z
/z
_
dz
? 0 (1.12)
l : µzk
?
l
µ?1
?w
l
(l) ?C
l
(z, l
?1
, l, k, k
) + ?
_
V
l
_
z
, k
, l
_
f
_
z
/z
_
dz
? 0 (1.13)
C
l
?1
(z, l
?1
, l, k, k
) ?V
l
?1
(z, k, l
?1
) ? 0 (1.14)
?zk
??1
l
µ
+ (1 ??) ? C
k
(z, l
?1
, l, k, k
) ?C
k
(z, l
?1
, l, k, k
) ?V
k
(z, k, l
?1
) ? 0 (1.15)
36
The FOCs for labor, energy, materials and hours under the full speci?cation of the model using
the pro?t function in footnote (30) are:
l : µ¯ zk
ˆ
?
l
ˆ µ?1
e
?
m
?
= w
0
+ w
1
h
?
(1.6)
h : ˆ µ¯ zk
ˆ
?
(lh)
ˆ µ
h
?1
e
?
m
?
= ?w
1
lh
??1
(1.7)
e : ? ¯ zk
ˆ
?
(lh)
ˆ µ
e
??1
m
?
= p
e
(1.8)
m : ?¯ zk
ˆ
?
?(lh)
ˆ µ
e
?
m
??1
= p
m
(1.9)
In this case, hours are independent of shocks, as can be seen from (1.7) and (1.6): h =
_
w
0
w
1
(??1)
_1
?
.
40
These FOCs and envelope conditions reveal that the functional form of the adjust-
ment costs is crucial to understanding ?rm’s factor adjustment. These expressions
are inequality conditions because of the possibility of corner solutions. Equations
(1.12), (1.13), (1.14) and (1.15) will hold with equality only when the adjustment in
both factors is nonzero. The ?rm will adjust one factor if the net gain of adjustment
is higher than if the ?rm adjusts the other factor or both employment and capital
together. This opens the possibility of staggered adjustment, even if the adjustment
cost is convex, which di?ers from previous models where convex adjustment costs
imply continuous adjustment.
Another point to notice is that the discounted marginal value of labor ad-
justment depends on investment, and the discounted marginal value of investment
depends on labor adjustment, whenever ?rms decide to adjust both factors or when-
ever the adjustment cost re?ects interaction e?ects.
Convex Adjustment Costs
With convex costs, hours depend on shocks and are negatively related to employ-
ment.
37
As mentioned above, if ?rms face convex costs in both factors, there is a
possibility of inaction if adjusting one factor gives a higher net marginal bene?t
than adjusting both factors at the same time. It has been thought that convex costs
guarantee continuous adjustment, but that is not the case in the setting presented
37
To show this, take the full speci?ed model and assume a convex cost model where the inter-
action term in the adjustment cost for capital and labor is not present. In that case, the FOCs
for labor and hours imply h =
_
µzk
?
e
?
m
?
?w
1
l
1?µ
_ 1
??µ
. Since ? > 1 > µ, hours are negatively related to
employment. However, this feature of the convex cost model with the functional forms assumed
would not be supported by the data, since the correlation between hours growth and labor growth
with ?rm-level data is positive, in contrast to the U.S.
41
in this model.
If both equations hold with equality(i.e., when adjustment is nonzero in both
factors), an interesting result can be seen, assuming a convex cost only for the
interrelation term: ?
kl
(l ? l
?1
)
_
I
k
_
. Updating (1.14) and plugging the result into
(1.13), we ?nd:
E
_
I
k
_
=
1
??
kl
_
w
0
+ ?
kl
_
I
k
_
?µzk
?
l
µ?1
_
(1.16)
From (1.16) we can see that investment rates are positively correlated in time, which
is a common feature of convex cost models of investment. Moreover, since µ < 1, it
can be shown that the investment rate in period t+1 is positively correlated with the
change in labor in period t. Also, because investment and labor are simultaneously
determined,
d(
I
k
)
dl
does not have a clear meaning unless we can assume some causality.
If causality were the case (for example, if ?rms adjust labor ?rst and then decide
investment according to capacity constraints) we would have a negative relationship
between the change in labor and the change in the investment rate.
38
Convex and Non-Convex Adjustment Costs
When hit by a demand or productivity shock, the ?rm decides whether to adjust
capital, labor or both, and at the same time decides the optimal level of materi-
als, energy and hours.
39
The ?rm’s problem is given by (1.4) and the optimality
38
This comes from applying the implicit function theorem where
d(
I
k
)
dl
= ?
dE
_
I
k
_
/dl
dE(
I
k
)/d(
I
k
)
.
39
The FOCs for the static optimization problem are conditional on ? and, under the full speci-
?cation of the model, given by:
h : ˆ µ(1 ??
j
)¯ zk
ˆ
?
(lh)
ˆ µ
h
?1
e
?
m
?
??w
1
lh
??1
= 0 (1.17)
e : ?(1 ??
j
)¯ zk
ˆ
?
(lh)
ˆ µ
e
??1
m
?
= p
e
(1.18)
m : ?(1 ??
j
)¯ zk
ˆ
?
(lh)
ˆ µ
e
?
m
??1
= p
m
(1.19)
42
conditions for capital and labor are given by equations (1.12), (1.13), (1.14) and
(1.15).
If we de?ne V
K
as the value of adjusting only capital, V
L
as the value of
adjusting only labor, V
LK
as the value of adjusting both labor and capital and V
N
as the value of nonadjustment, we can rede?ne the problem as a continuous choice
problem nested in a discrete choice framework. Given the ?rms decision problem in
(1.4), we can express it as V (•) = max[V
N
, V
K
, V
L
, V
LK
], where ?rms choose the
action that gives it the highest V . That is
• Firms do not adjust if V
N
> [V
K
, V
L
, V
LK
]
• Firms adjust labor if V
L
> [V
N
, V
K
, V
LK
]
• Firms adjust capital if V
K
> [V
N
, V
L
, V
LK
]
• Firms adjust capital and labor if V
LK
> [V
N
, V
L
, V
K
]
As will become clear later in the numerical analysis, the ?rms follow an (S,s) policy
in both capital and labor. An interesting issue left for future work is to prove the
validity of this result analytically. The di?culty of this proof comes from the joint
determination of capital and labor, making an (S,s) rule dependent not only on the
shocks and states but on the choice variables.
The model presented cannot be solved analytically because of the non-convex
nature of the decision rules. Therefore, a numerical solution is needed. It is in this
sense that the main di?culty associated with the model is the state space: there
?(z, k, l) and j = labor, capital, capital and labor (adjustment type) and ?
j
= 0 if there is no
adjustment.
43
are three
40
continuous state variables (shocks, capital and labor) and one discrete
choice variable (margin of adjustment). In the next section I show an illustrative
calibration, explain the numerical procedure used to solve the model, numerically
analyze the decision rules, and explore the quantitative implications that emerge
from this model.
1.4 Capital and Labor Adjustment: A Numerical Analysis of the
Proposed Model
The purpose of this paper is ultimately to analyze how ?rms make dynamic
joint decisions about capital and employment. Given the evidence and the model
presented above, this section describes the ?rms’ decision rules with respect to cap-
ital and employment adjustment, and numerically analyzes whether these decision
rules are able to generate simulated economies that reproduce the facts observed
in the data. Speci?cally, I look at inaction periods, lumpy adjustment and the dy-
namic interrelation of capital and labor, and the correlation between factor inputs.
Importantly, I want to determine what is the main force generating these behaviors;
speci?cally, whether it is the interaction e?ects in the adjustment process or the
type of the adjustment costs faced by ?rms.
I use numerical simulations of the model as the main tool to answer to these
questions. First, I explain the computational methods used to solve the model
numerically. Second, I parameterize the model with adjustment cost parameters
that appear to be ex-ante reasonable, illustrating the di?erent behavior the ?rm-level
model exhibits with respect to capital and labor dynamic adjustment when demand
40
Four if the shocks are di?erentiated between demand and productivity.
44
and productivity shocks are the main source of perturbation in the modeled economy.
Third, I show and analyze the decision rules that the model implies, presenting time
series realizations under several con?gurations of adjustment costs, in order to give
an idea of the ergodic distribution of the state variables and which decision rules
the ?rms visit more often. Finally, I analyze the quantitative response of the model
using di?erent adjustment cost con?gurations.
1.4.1 Numerical Methods
The equation to solve is the Bellman equation given in (1.4). The solution
must give the ?rm’s optimal choices for hours, energy, materials, investment and
employment given the vector of shocks z, capital k and previous employment level
l
?1
. The optimal level of hours, energy and materials are a function of the state space
(z, k, l
?1
) and this problem can be solved analytically every period as a function of
this state space conditional on the disruption cost ?
j
as is shown in footnote (39).
The variables left to solve are capital and labor, for which a numerical procedure
should be used given the dynamic links and non convexities that they exhibit in the
model.
In the solution of this equation, three basic choices should be made: (i) the
procedure for maximization over the state space, (ii) the procedure to solve the
unknown value function V (z, k, l
?1
) and (iii) the procedure to solve for the integral
over the shocks that represents the ?rm’s expectation about the future value V (•)
For (iii), I integrate using quadrature methods as in Tauchen and Hussey
45
(1991). This quadrature is solved with Hermite polynomials, which are the best for
this situation since the shocks are assumed (and estimated from the data) as AR(1)
log-processes with lognormal error terms. I discretize the shock distribution into
3 states for the productivity shock and 2 states for the demand shock. I assume
independence of both shocks such that the shock calibrated in the model is the result
of the multiplication of those two.
For (ii) I use value function iteration. While I also solved the model with
policy iteration, the existence of kinks in the value function did not assure reliable
results for the full range of parameters.
The simplest method for (i) would be a grid search, restricting the values
that the state space variables can take to the points in the grid; however, this
method is very imprecise given the large state space faced in this speci?c problem.
Moreover, since I am looking at inaction periods and spikes in investment and capital
adjustment, this grid would need to be very ?ne, which would soon result in the
curse of dimensionality. Instead, I choose a small number of points for the state
space (3 for the productivity shock, 2 for the demand shock, 70 for the capital
stock and 30 for the number of workers) and use a golden section search method
to determine the maximum over the entire state space, bracketing ?rst the optimal
region and then using linear interpolation of the optimal values to the values in the
grid. This method allows very precise calculations for the value function in each
grid point and also allows faster simulation of the model. The code is written in
Matlab and C, linking the programs through MEX-?les.
46
1.4.2 About the Parameters: Estimation and Calibration
There are two sets of parameters: those that can be directly estimated without
imposing an economic model (reduced form parameters) and those that need to be
calibrated or estimated with some simulation procedure (structural parameters).
In the ?rst group we have: the production function coe?cients ?, ?, ?, and ? for
capital, labor, energy and materials respectively; the demand shock process X
it
; the
technology shock process A
it
; and the elasticity of demand ?. In the second group
we have the adjustment cost parameters (?
j
for the convex cost, F
j
for the ?xed
cost, ?
j
for the disruption cost and {p
I
, p
sell
} for the price of capital), the discount
factor ?, the depreciation rate ? and the hours wage elasticity ?. The dataset does
not contain capital prices. Although I can calculate the mean input prices from the
data in the case of employment, energy and materials, I choose to calibrate them
because of the lack of capital prices in order to put all the factor prices on equal
footing. The calibrations come very close to the relative prices calculated from the
data for energy and materials. I do not compare the wage calibration with the data,
and capital prices are not available.
The estimates for production function coe?cients, the demand and technology
shock processes and the elasticity of demand are taken from Eslava et al. (2004).
They use information on prices to estimate an output-based KLEM production
function with demand shift instruments
41
in order to ?nd the production function
41
They use the Syverson (2005) insight that using demand as an instrument for input factors
in production function estimation can get rid of the endogeneity problems that are well known in
such situations. They do so by creating downstream demand shift instruments selected with Shea
(1997) relevance and exogeneity criteria.
47
coe?cients and the technology shock process. An advantage of their methodology
is that the price information allows them to isolate a ?rm speci?c price de?ator,
so that TFP estimations do not use a common price de?ator that, as Klette and
Griliches (1996) and Foster et al. (2005) illustrate, would bias the estimates of the
production function coe?cients. The estimations are carried over for all ?rms in
Colombia and are not di?erentiated by industry as a simplifying assumption, even if
the factor shares may di?er by industry. The coe?cients are 0.213 for capital, 0.303
for labor, 0.176 for materials and 0.2752 for energy. Next, Eslava et al. (2004) take
advantage of the price information and estimate a downward sloping demand curve
similar to the one assumed here, instrumenting output using the calculated TFP,
obtaining the demand elasticity ? = 2.28 and the demand shocks as the residuals
of the regression.
In the calibration of the model, I assume that the demand shocks and the
technology shocks follow an AR(1) lognormal process such that (with lower case
letters meaning logs and dropping the subindex i):
a
t
= ?
a
a
t?1
+ u
t
(1.20)
x
t
= ?
x
x
t?1
+ ?
t
(1.21)
Equations (1.20) and (1.21) are estimated as in Eslava et al. (2004) using year e?ects.
The coe?cients obtained are ?
a
= 0.922, ?
x
= 0.985 and ?
a
= 0.77, ?
x
= 0.89. Given
that ?
a
2
=
?
u
2
1??
a
2
and ?
x
2
=
?
2
?
1??
x
2
, we get ?
u
= 0.297 and ?
?
= 0.151. I normalize the
mean values of the shocks to one (this normalization also a?ects the input prices).
The discount factor ? is set as 0.95, the depreciation rate ? as 0.1 and the hours
48
wage elasticity as 1.1.
Before I discuss the calibration of the input prices, I want to emphasize that
even though those prices can be an important source of ?uctuations and relative
changes in input adjustment, this paper focuses on the ?rm’s responses to demand
and productivity shocks. This is the reason to look for an “average” input price in
each case, and this guides the calibration of the prices.
Energy and materials prices are calculated by solving the FOCs of the problem
without adjustment costs (equations (1.8) and (1.9) respectively). The values for
capital, labor, energy and materials plugged into these equations are the means of
the actual values. It is interesting to note that the implied prices are very close to
those obtained by dividing energy expenditure and materials expenditure by physical
amounts. The labor payment parameters w
0
and w
1
are obtained by solving the
system composed of the FOC for hours and labor in the problem without adjustment
costs (equations (1.6) and (1.7)) and using again mean values. The investment price
is obtained by solving the dynamic problem in the case of no uncertainty and no
adjustment costs.
42
Finally, I treat investment as reversible, but with the capital
resale price equal to 70% of the price of buying capital.
For this illustrative parameterization, I chose the adjustment cost parameters
in an arbitrary manner such that the adjustment costs are the same for all types
of costs and collectively account for either 4% or 20% of average pro?t. From this
point on, I focus on the congestion e?ect because it is the one that is later supported
42
The implicit assumption for the calculation of the prices is that the frictionless FOCs hold “on
average”.
49
by the data. Table 1.12 shows the chosen parameters for the adjustment costs and
the average adjustment cost as a proportion of the contemporaneous pro?t. These
costs do not increase proportionally from one column to the next because they were
obtained with simulations and re?ect an approximate rather than exact value. I
calculate the policy function under the parameterizations discussed above for later
simulations under di?erent realizations of the shocks
43
.
Table 1.12: Parameters Adjustment Costs
Adjustment Cost Cost/?
Adjusted Factor
Type 4% 20%
Fixed (F
l
) 0.22 1
Labor Convex (?
l
) 0.05 0.15
Disrupt (?
l
) 0.01 0.035
Fixed (F
k
) 0.01 0.044
Capital Convex (?
k
) 0.0007 0.006
Disrupt (?
k
) 0.01 0.045
Interaction E?ects: Congestion/ ? =30%
Joint Fixed (F
lk
) 5 5
Adjustment Convex (?
lk
) 0.11 0.11
(Congestion) Disrupt (?
lk
) 0.07 0.07
1.4.3 Decision Rules for Capital and Employment Adjustment
I now present the numerical results for the value function, the decision rules
(or policy functions) and its implications for ?rm behavior, given by the chosen
parametrization. The ?rm has the option to not adjust, adjust only capital, adjust
only employment or adjust both capital and employment. The decision rules are
presented in a graphical analysis over the space determined by the values of capital
43
This policy rule is invariant.
50
and labor. As expected, there is a region of inaction whose size depends on the
value of the shocks, on the type of adjustment costs and on the existence or not of
congestion e?ects in adjustment. This region of inaction determines a bi-dimensional
(S,s) policy in capital and labor depending not only on the shocks and the other state
variables, but also on the other choice variables. However, some regions are more
likely to a?ect ?rm behavior than others since the ergodic distribution of the state
space is an important point to take into account. That is the reason to consider
several time series realizations of ?rm’ behavior under di?erent con?gurations of
adjustment costs.
To illustrate the objective functions, ?gure 1.4 shows that in fact the value
function is concave with some kinks at lower values of employment(this is, L
t?1
on the x-axis). This e?ect on the value functions is due to the scale of the graph.
The decision rules are shown in Figures 1.5, 1.6, 1.7 and 1.8. With these decision
rules and the time series realizations, I will analyze the e?ects of the shocks, the
congestion e?ects and the adjustment costs. Figure 1.5 shows the policy functions
for the case where all costs are present for capital and labor (and equal to 4%) and
there are congestion e?ects in adjustment. The ?rst thing to note is that there is an
inaction region whose shape and size depends on the shock and the value of both
factors. This inaction region de?nes a bi-dimensional (S,s) policy for capital and
labor. The optimal (S,s) policy depends on the shock and the choice of the other
variable (either capital or labor).
Even though some adjustment regions for capital and labor are not convex
sets, there are de?ned zones in which it is optimal to adjust only labor and others in
51
Figure 1.4: Value functions: lateral view, labor.
0 500 1000 1500
1.37
1.375
1.38
1.385
x 10
7
low shock
Labor
0 500 1000 1500
1.38
1.4
1.42
1.44
x 10
7
shock 2
Labor
0 500 1000 1500
1.38
1.4
1.42
1.44
x 10
7
shock 3
Labor
0 500 1000 1500
1.45
1.5
1.55
x 10
7
shock 4
Labor
0 500 1000 1500
1.4
1.45
1.5
x 10
7
shock 5
Labor
0 500 1000 1500
1.7
1.8
1.9
2
x 10
7
high shock
Labor
which it is optimal to adjust only capital, especially for small values of the shock (see
?gure 1.5). In some of the policy rules there exist disjoint sets in the space capital-
labor for a given shock. For example, for the same capital to labor ratio may exist
inaction or adjustment depending on the level of capital and labor, opening the
possibility of multiple optimal regimes. According to the optimal rule, ?rms adjust
capital and labor together only if the shock is big enough (in this case, above the
mean shock). This implies that there is an implicit target for a relationship between
capital and labor, and that target changes with the shock.
With just one factor, a standard (S,s) rule would hold, with the shock being
52
the only determinant of the optimal adjustment policy. With the possibility of
adjusting capital and labor, ?rms make decisions depending on where they are with
respect to the optimal target of not just one isolated factor but a composite of capital
and labor. This is an important improvement over previous models that analyzed
just one factor at a time. This result is also related to Eslava et al. (2005), when
implement the gap approach by Caballero et al. (1995) and Caballero et al. (1997);
their empirical results suggest that ?rms adjust labor and capital depending on the
gap between desired and actual employment and labor. The structural analysis here
implies that this gap is implicitly a?ected by the gap in the other factor, resulting
in this bivariate (S,s) policy.
Figures 1.6, 1.7 and 1.8 compare the decision rules implied by the di?erent
types of adjustment costs considered one-by-one in the presence (or absence) of
congestion e?ects in the case of a bad shock, an intermediate shock and a good
shock.
With respect to the adjustment cost types, the convex cost implies a larger
region of adjustment in both capital and employment than the ?xed cost and the
disruption cost. It is important to note, as the theoretical analysis of the model
revealed above, that even with convex costs, there is a region of inaction, though
much smaller than the one present under non-convex costs.
The biggest inaction zone corresponds to the disruption cost. The ?xed cost
implies more staggered adjustment than the disruption cost, under which simulta-
neous adjustment of both factors is more frequent. The behavior implied by the
53
Figure 1.5: Decision rules. All costs in K,L.
Figure 1.6: Decision rules. Comparison among Adjustment costs. Low shock.
54
Figure 1.7: Decision rules. Comparison among Adjustment costs. Intermediate
shock.
Figure 1.8: Decision rules. Comparison among Adjustment costs. High shock.
55
disruption cost looks more in line with the empirical evidence, where positive co-
movement between capital and employment adjustment is observed.
For low values of the shock (?gure 1.6) the behavior under convex or disruption
costs does not depend much on the existence of congestion e?ects, and the only
di?erence between the behavior under convex cost and that under disruption costs
is the adjustment of only labor in a small region under convex costs. For the low
shock case, ?xed costs generate a more di?erentiated behavior, since there is no joint
adjustment of capital and employment in the case of congestion e?ects.
In the intermediate shock case (Figure 1.7) , we observe that without conges-
tion e?ects, there is more joint adjustment of capital and employment. This does
not necessarily imply a higher correlation of adjustments under this regime, how-
ever, since capital and labor can move in opposite directions. The inaction zones are
de?ned as double (S,s) bands. Interestingly, there is more joint adjustment in the
convex cost case with congestion e?ects than without them. The pattern for ?xed
costs observed in the low shock case repeats itself here: joint adjustment is rare in
the presence of congestion e?ects.
If ?rms face a high value of the shock (Figure 1.8), there is much more joint
adjustment and the behavior under convex costs and disruption costs is very similar,
with a larger inaction zone in the disruption case as expected. Again, ?xed costs
present the most di?erent pattern: in the presence of congestion e?ects, ?rms will
adjust only labor under certain circumstances.
Other important implications of di?erent con?gurations of the adjustment
costs can be seen plotting the time series realizations that the policy rules imply as
56
a way of visualizing the regions that the ?rms spend more time in. For example,
we could try to ?nd if bigger inaction regions imply less variability of investment,
or if bigger inaction regions are compensated by larger adjustments. Figure 1.9
shows the time series realization of one shock series when a ?rm faces all types of
adjustment costs comparing the case of congestion vs. no congestion e?ects, ?gure
1.10 shows the labor growth when the ?rm faces di?erent types of adjustment costs
with and without congestion e?ects and ?gure 1.11 shows the investment responses
of the same.
These time series realizations show that the presence of congestion e?ects
increases the inaction in both capital and labor adjustments in all the cases. In
the other hand, ?xed costs and disruption costs have the same e?ect on investment
rates when there is congestion e?ects, even if the decision rules are di?erent. When
congestion e?ects are not present, ?xed costs increase inaction and volatility in both
capital and labor with respect to the convex and disruption cases. When congestion
e?ects are present and ?rms face all types of adjustment costs, the volatility of labor
growth increases and the volatility of the investment rate decreases; Also, when the
congestion e?ects are present, convex costs increase the volatility of the investment
rate and decrease the volatility in labor growth compared with the case when either
?xed or disruption costs are present.
The decision rules as presented above do not say anything about the direction
of size of the adjustments. For example, capital and labor can move at the same time
57
Figure 1.9: Time Series: All Costs Present.
0 50 100
0.5
1
1.5
Shocks series
0 50 100
0
10
20
All costs, I/K, Congestion
0 50 100
0.5
1
1.5
Shocks series
0 50 100
?10
0
10
All costs Labor growth, Congestion
0 50 100
0
10
20
All costs, I/K, No Congestion
0 50 100
?10
0
10
All costs Labor growth, No Congestion
Figure 1.10: Time Series: Investment Rate, Adjustment Costs Comparison
0 50 100
0
10
20
Convex, I/K, Congestion
0 50 100
0
10
20
Convex, I/K, No Congestion
0 50 100
0
10
20
Fixed, I/K, Congestion
0 50 100
0
10
20
Fixed, I/K, No Congestion
0 50 100
0
10
20
Disruption, I/K, Congestion
0 50 100
0
10
20
Disruption, I/K, No Congestion
58
Figure 1.11: Time Series: Labor Growth, Adjustment Costs Comparison
0 50 100
?10
0
10
Convex, Labor growth, Congestion
0 50 100
?10
0
10
Convex, Labor growth, No Congestion
0 50 100
?10
0
10
Fixed, Labor growth, Congestion
0 50 100
?10
0
10
Fixed, Labor growth, No Congestion
0 50 100
?10
0
10
Disruption, Labor growth, Congestion
0 50 100
?10
0
10
Disruption, Labor growth, No Congestion
but in di?erent directions. There exist enormous non linearities in the decision rules.
Figures 1.12 and 1.13 show the decision rules for labor adjustment and investment
for several values for capital and labor and in the case of an intermediate shock with
low adjustment costs. From Figure 1.12, we observe that at low values of capital and
labor, the adjustments are in the same direction (positive), but for higher values,
?rms stagger depending on the state of (l, k); that is, under some combinations of
capital and labor, ?rms reduce capital and do not adjust labor, and under other
values they do the opposite. Figure 1.13 shows that factors can adjust in opposite
directions when the ?rm has high values of capital and low values of employment or
vice versa(higher or lower relative to their frictionless optimum). This means that
at low values for both capital and labor the correlation between their adjustments is
59
Figure 1.12: Labor and Capital Adjustment Levels. Intermediate Shock, High and
Low values for Capital and Labor
0
10
20
30
0
2000
4000
6000
0
50
100
150
200
Employment
Intermediate shock, Labor Adjustment,low L,K
Capital
L
a
b
o
r
A
d
j
u
s
t
m
e
n
t
0
10
20
30
0
2000
4000
6000
0
1
2
3
4
x 10
4
Employment
Intermediate shock, Investment,low L,K
Capital
I
n
v
e
s
t
m
e
n
t
1
1.1
1.2
1.3
1.4
x 10
4
1
1.2
1.4
1.6
x 10
7
?15000
?10000
?5000
0
Employment
Intermediate shock, Labor Adjustment,high L,K
Capital
L
a
b
o
r
A
d
j
u
s
t
m
e
n
t
1
1.1
1.2
1.3
1.4
x 10
4
1
1.2
1.4
1.6
x 10
7
?15
?10
?5
0
x 10
6
Employment
Intermediate shock, Investment,high L,K
Capital
I
n
v
e
s
t
m
e
n
t
likely to be positive, while at higher values this correlation is likely to be negative.
Thus, we have di?erent possibilities of ?rm behavior depending on if ?rms
face good or bad shocks, whether they face congestion e?ects in the adjustment and
depending on the type of dominant adjustment cost. In summary, the main features
of these decision rules are:
i. The decision rules for capital and employment adjustment exhibit a non-linear
pattern with inaction zones, zones of joint adjustment and zones of single factor
adjustment. That is, the decision rules present a non linear (S,s) rule in both
capital and labor. Adjustment or inaction in capital and labor depend not only
60
Figure 1.13: Labor and Capital Adjustment Levels. Intermediate Shock, Mix of
High and Low values for Capital and Labor
0
5
10
15
20
1
1.2
1.4
1.6
x 10
7
0
50
100
150
200
Employment
Intermediate shock, Labor Adjustment, high K low L
Capital
L
a
b
o
r
A
d
j
u
s
t
m
e
n
t
0
5
10
15
20
1
1.2
1.4
1.6
x 10
7
?15
?10
?5
0
x 10
6
Employment
Intermediate shock, Investment, high K low L
Capital
I
n
v
e
s
t
m
e
n
t
1
1.2
1.4
1.6
x 10
4
0
2000
4000
6000
?15000
?10000
?5000
0
Employment
Intermediate shock, Labor Adjustment, high L,low K
Capital
L
a
b
o
r
A
d
j
u
s
t
m
e
n
t
1
1.2
1.4
1.6
x 10
4
0
2000
4000
6000
0
1
2
3
4
x 10
4
Employment
Intermediate shock, Investment, high L,low K
Capital
I
n
v
e
s
t
m
e
n
t
on the states, such as the productivity and demand shocks and the capital to
labor ratio, but also on the choices of capital and labor.
ii. Persistent bad shocks and ?xed costs lead to a less frequent joint adjustment
in capital and employment. Good persistent shocks increase the joint employ-
ment and capital adjustment.
iii. In general, the presence of convex costs tends to increase the likelihood of
joint adjustment for capital and labor, while the presence of ?xed costs tends
to reduce this joint adjustment. Disruption costs can accommodate a richer
type of adjustment, depending on the capital to labor ratio a ?rm has. This
does not translate directly into measures of correlation since the adjustment
61
of capital and labor can occur in opposite directions.
iv. Under intermediate or high shocks, congestion e?ects in the adjustment in-
crease the likelihood of joint adjustment. Under low shocks, this is only true
if ?xed costs are dominant.
v. Even under convex costs, there may be inaction regions. These inaction zones
are also present and larger when ?rms face disruption or ?xed costs. How-
ever, in the case of ?xed costs, inaction zones can present disjoint sets, which
opens the possibility for multiple optimal regimes of capital and labor for the
same capital to labor ratio. Inaction zones are more important in the case of
intermediate shocks, being almost non existent for bad shocks and smaller for
good shocks.
vi. Congestion e?ects increase the inaction in both capital and labor adjustments
in all the cases; when congestion e?ects are not present, ?xed costs increase
inaction and volatility in both capital and labor with respect to the convex
and disruption cases; when congestion e?ects are present, convex costs increase
the volatility of the investment rate and decrease the volatility in labor growth
compared with the case when either ?xed or disruption costs are present; how-
ever, when congestion e?ects are present and ?rms face all types of adjustment
costs, the volatility of labor growth increases and the volatility of the invest-
ment rate decreases.
vii. It is straightforward to conclude that the decision rules presented show a model
62
that can accommodate at the same time smooth, lumpy, and infrequent ad-
justment, depending on the value of the shocks, the state of the ?rms in terms
of capital and labor, the type of adjustment costs di?erent ?rms face and
the presence or absence of congestion e?ects. The model is able to incorpo-
rate di?erent types of behavior depending on the combination of the variables
above.
Since the decision rules imply a wide range of possibilities of adjustment, the
next section simulates the response of ?rms to a speci?c realization of the technology
and demand shocks in order to analyze the types of adjustment observed under the
current parameterization.
1.4.4 Congestion E?ects and Adjustment Costs: A Simulation ex-
ploration
Given the parameters and the average e?ects they produce in the model, I show
in this subsection the results of some simulation exercises for a particular realization
of the shocks extending the analysis started in the previous section. I choose to
analyze one simple realization because this is not a formal calibration, but instead
an example of the di?erent possibilities that the adjustment costs can accommodate
with respect to ?rm behavior. In particular, I look at the inaction zones and spikes
in investment and employment adjustment, at the correlation among factor inputs
and at the dynamic interrelations expressed in a one-lag VAR across di?erent sets
of parameters. The idea behind the numerical simulations is to complement the
analysis of the decision rules and to understand, given the model and a speci?c
63
realization of the shocks, how ?rms respond to shocks in technology and demand,
how input factors move and comove and what is the role of congestion e?ects. Along
the way, we will see how well the model replicates the stylized facts observed in the
data.
I do not analyze the behavior of materials, hours and energy because they are
not the main focus of this paper. However, the model does a mixed job in replicating
the hours, materials and energy movements observed in the data. Inaction in these
factors occurs on average 20% of the time and spikes occur 30% of the time, and
the correlation between labor and hours is always negative because of the functional
form assumed in the model (see footnote (30) for the wage function assumption and
footnote (36) for the FOCs for labor and hours in the case of no adjustment costs).
The correlation between materials and energy is always above 90% and their VAR
coe?cients in the investment equation are larger than 100. The other statistics are
more reasonable. The positive side of this is that ?rms in the model adjust along
several margins and are not restricted to adjust only capital and employment.
The ?rst simulated statistics are presented in Table 1.13, which shows the per-
centage of inaction episodes, the percentage of positive and negative spike episodes,
and the di?erent responses of capital and employment to shocks. The time series
have 500 periods and I drop the ?rst 50. In this table we can see that the congestion
e?ects have an e?ect on ?rms’ adjustment behavior, making inaction more likely in
the case of low adjustment cost value and when costs are high, in most cases, at
least for capital. The increase in cost when ?rms adjust both factors may prevent
?rms from adjusting either factor as often as they would like.
64
In general, the model can replicate the basic features of inaction and spikes
in investment and labor adjustment. As seen in Table 1.13, the magnitude of the
?xed and disruption costs have a greater e?ect on capital than on employment
adjustment. This means that capital is more sensitive to the adjustment costs in the
model. Finally, with respect to the response of the variables to shocks, labor growth
has a very stable response to shocks when no congestion e?ects are present, but
the response is higher when congestion e?ects exist. Investment growth responds
negatively to shocks in some cases, which may indicate that ?rms over-invest in
some periods, that they replace capital with labor in some good periods or that
they simply sometimes disinvest once they receive a bad shock.
It is also interesting to note that even with convex costs, the percentage of
simulated observations that display inaction in both capital and labor is positive
and high, but not nearly as high as in other cases. This implies that ?rms have the
possibility of staggering adjustment of capital and employment, as discussed before.
This is left to future work.
Table 1.14 shows the simulated contemporaneous correlations between labor
and capital adjustment. It is interesting to note that the best ?t comes from the
high congestion e?ect-low adjustment cost case when all costs are present in capital
and labor. It is also important to note that the correlation between labor and
capital is negative in the case of high convex costs and low congestion e?ects, as
the analysis of the model predicted as a theoretical possibility. Moreover, when
only labor adjustment is costly, this correlation is also negative in the case of low
adjustment costs. The correlation between investment and labor growth increases
65
Table 1.13: Basic simulated statistics
Investment Labor
Adj. Inaction Pos Neg ?(
I
K
, z) Inaction Pos Neg ?(
?L
L
, z)
Cost C/? data 0.189 0.298 0.018 0.10 0.134 0.12 0.11 0.05
Type
NC 0.30 0.25 0.18 -0.03 0.23 0.18 0.11 0.13
K
0.04
C 0.34 0.29 0.16 -0.09 0.29 0.11 0.10 0.14
and NC 0.47 0.27 0.14 0.01 0.38 0.08 0.06 0.15
L
0.2
C 0.60 0.21 0.08 -0.05 0.21 0.17 0.12 0.10
NC 0.14 0.07 0.02 -0.11 0.23 0.00 0.00 0.15
0.04
C 0.03 0.12 0.08 0.08 0.00 0.12 0.09 0.21
Convex
NC 0.09 0.03 0.06 -0.12 0.18 0.02 0.02 0.16
0.2
C 0.09 0.04 0.02 0.07 0.10 0.06 0.05 0.23
NC 0.44 0.21 0.15 0.15 0.31 0.10 0.11 0.16
0.04
C 0.58 0.12 0.09 0.27 0.30 0.10 0.12 0.13
Fixed
NC 0.65 0.08 0.07 0.25 0.35 0.09 0.08 0.17
0.2
C 0.67 0.06 0.06 0.28 0.38 0.07 0.07 0.17
NC 0.43 0.20 0.15 0.18 0.29 0.13 0.10 0.17
0.04
C 0.64 0.15 0.11 0.21 0.34 0.09 0.10 0.18
Disrupt
NC 0.60 0.09 0.11 0.24 0.35 0.08 0.09 0.16
0.2
C 0.55 0.10 0.08 0.26 0.36 0.08 0.08 0.15
NC 0.20 0.30 0.22 0.10 0.28 0.15 0.10 0.19
K but
0.04
C 0.38 0.28 0.17 -0.02 0.25 0.15 0.10 0.14
not L NC 0.48 0.15 0.16 0.07 0.32 0.10 0.11 0.23
0.2
C 0.56 0.18 0.08 -0.10 0.21 0.15 0.13 0.12
NC 0.13 0.28 0.24 0.02 0.26 0.14 0.13 0.11
L but
0.04
C 0.32 0.30 0.20 0.04 0.23 0.16 0.12 0.16
not K NC 0.23 0.26 0.15 -0.08 0.23 0.17 0.13 0.13
0.2
C 0.37 0.26 0.16 0.08 0.26 0.14 0.11 0.13
NC: No Congestion E?ects present. C: Congestion E?ects present (30%). C/?: Adjustment
cost/Pro?t
a lot when ?xed and disruption costs are present.
Table 1.15 shows the coe?cients of a VAR(1) for the investment rate and
labor growth. Several parameterizations perform well, among them the one with all
costs in capital and labor and with low adjustment costs but high congestion e?ects.
Congestion e?ects do not seem to have much e?ect on the convex cost speci?cation,
but they do in the other cases, switching the signs at times. This suggests that
congestion e?ects may be important in determining the dynamic behavior of the
66
Table 1.14: Correlation(
I
K
, ?L)
Data 0.057
(Adj cost)/? 4% 20%
(Congestion E?ects)/? 4% 30% 4% 30%
All Costs in K,L 0.039 0.054 -0.030 0.005
Convex 0.035 0.203 -0.033 0.385
Fixed 0.205 0.313 0.429 0.466
Disrupt 0.325 0.365 0.421 0.421
Adj. Costs in K, not in L 0.193 0.016 0.107 0.002
Adj. Costs in L, not in K -0.058 -0.070 0.015 -0.080
Table 1.15: Simulated V AR(1)
Data C/? = 4% C/? = 20%
-0.008 -0.008 No Compl. Compl=30% No Compl. Compl=30%
0.037 -0.147 I/K ?L I/K ?L I/K ?L I/K ?L
(I/K)
?1
0.008 0.137 -0.055 0.019 -0.005 -0.005 -0.002 0.002
All Cost
?L
?1
0.013 -0.551 0.048 -0.320 -0.020 -0.387 0.480 -0.077
(I/K)
?1
-0.025 -0.061 -0.004 0.000 -0.007 -0.03 0.032 0.000
Convex
?L
?1
0.017 -0.269 0.012 0.065 0.026 -0.272 0.007 -2.918
(I/K)
?1
-0.005 0.000 0.005 0.000 -0.011 0.001 0.054 0.000
Fixed
?L
?1
1.088 -0.431 -0.465 0.341 0.408 -0.329 -3.812 -0.165
(I/K)
?1
0.001 0.001 0.006 0.001 0.037 0.000 -0.006 0.001
Disrupt
?L
?1
-1.010 -0.644 -0.254 -0.197 -3.496 -0.244 0.324 -0.210
(I/K)
?1
-0.016 0.000 -0.020 -0.013 0.000 0.000 -0.010 0.009
All K
?L
?1
-0.062 -0.233 0.085 -0.111 0.001 -0.239 0.018 -0.028
(I/K)
?1
-0.005 0.004 0.009 0.000 -0.009 0.024 0.030 -0.006
all L
?L -0.051 -0.330 0.233 -0.355 0.023 -0.435 0.687 -0.318
?rms’ factor adjustment. Congestion e?ects may act by letting the ?rm adjust one
input at a time, creating other types of dynamics in the economy. It is important
to note that even if the coe?cient on lagged capital is small in the employment
equations, very small movements in capital have a huge e?ect on the number of
workers because of scale e?ects.
What conclusions can we draw from this calibration exercise? First, this pa-
rameterization shows that considering capital and labor interrelation in adjustment
67
costs a?ects the dynamic behavior of labor and capital adjustment. Second, none of
the adjustment costs taken alone can completely explain the moments observed in
the data, and in fact, it is the combination of these costs that allows one to match
the facts. Third, this model also presents a high number of negative investment
spikes and. It seems that a higher degree of non-reversibility than the one assumed
here is needed to match the rarity of negative spikes in the data. Fourth, even with
a model of only convex costs we can have inaction zones due to the existence of
other margins of adjustment. Fifth, the combination of parameters that best ?ts
the data is the low adjustment cost-high congestion e?ects case with all forms of
adjustment costs present in capital and labor.
Sixth, the model calibrations show di?erent results if the costs are present in
one factor alone; this point is important because it suggests that considering one
factor at a time may lead to misleading estimates of adjustment costs, since the es-
timated costs for one factor may incorporate information on costs from the omitted
factors. The estimations of models with one factor which is costly to adjust, may
incorporate costs from the other in the productivity shocks or in the estimated para-
meters. And, ?nally, congestion e?ects in adjustment costs are important and they
imply, according to the model, di?erent behavior in capital and labor adjustment
than that observed when each input is considered separately.
The next section will calculate these adjustment cost parameters in a more
formal way. This will give a clearer idea of the questions asked here; this is, if
there are congestion e?ects in capital and labor adjustment and if the nature of this
interrelation comes from non-convexities in the adjustment cost process.
68
1.5 Structural Estimation of the Adjustment Cost Parameters
In this section, I estimate the adjustment cost parameters from the model.
Speci?cally, I use a minimum distance algorithm to match the moments from the
data to the moments from a simulated panel generated with the model. My main
assumption is that the model is a good approximation of the way ?rms make de-
cisions about labor and capital. I discuss the methodology and then present the
results.
1.5.1 Methodology
The methodology to apply is the Method of Simulated Moments, in the spirit of
McFadden (1989), Pakes and Pollard (1989), and (1996) and Hall and Rust (2003)
among others. The choice of this estimation method is made for computational
feasibility, given that other methods, such as maximum likelihood, would require an
enormous amount of computing power.
The parameter set to be estimated is composed of ?xed, convex and disruption
costs for capital, labor and joint capital-labor adjustment, and the resale price of cap-
ital. These are represented by a vector ? = [(F
k
, F
l
, F
lk
), (?
k
, ?
l
, ?
lk
), (?
k
, ?
l
, ?
lk
), p
i
]
The algorithm consists of solving the dynamic programming problem given a
set of parameters ?, getting the policy functions for that speci?c parametrization,
simulating a panel of plants, calculating the chosen moments from that panel and
comparing them with the moments from the data. The function that depends on
69
the parameters and must be minimized is given by:
min
?
J(?) = {M
data
?M
simulated
(?)}
W {M
data
?M
simulated
(?)} (1.22)
where M is a vector of moments, W is a weighting matrix and ? is a vector of
parameters to be estimated. To ?nd standard errors, there are two options. The
?rst option is to carry on a Montecarlo simulation, repeating the procedure under
di?erent realizations of the stochastic shock. The second option to calculate the
standard errors is by obtaining the asymptotic distribution of the estimator, like
in Hall and Rust (2003); this is the method that I use which is simpler and much
faster. I construct the simulated panels with 1000 plants over 500 periods. At the
moment, I set W to the identity matrix in order to estimate the parameters, which
gives consistent but not e?cient estimates; however, in a second stage, I recalculate
W as in Hall and Rust (2003) in order to calculate the standard errors. In future
work, I plan to re-estimate the parameters with this optimal weighting matrix to
get e?cient estimates. See Hall and Rust (2003) for more details; To solve for
parameters I use the Nelder-Mead simplex algorithm.
Regarding the moments to match, the main questions are which moments re-
?ect variation in the parameters and which moments are worth matching given their
relevance in understanding ?rm behavior. The empirical evidence in the second sec-
tion presented characteristic distributions for capital and labor. In particular, the
distributions showed highly irreversible capital and lumpy adjustment and inaction
zones for both capital and labor. However, given the arbitrary de?nition of inac-
tion and the implications for di?erent types of capital
44
, I choose not to match this
44
For example, a hammer, some special cutting tools and a milling machine are capital goods,
70
feature. Instead, I focus on the lumpiness of the distributions and match the adjust-
ments above the 90
th
and below the 10
th
percentile in the distribution of capital and
labor adjustment (i.e. the fraction of positive and negative spikes). The VAR(1)
illustrates the dynamic interrelations of capital and labor and it is an important fea-
ture to consider. On the other hand, the model highlights the importance of shocks
in the movements of capital and labor; the correlation between adjustments and
shocks is therefore the other important moment. Finally, the correlation between
capital and labor adjustment is of prime interest in the paper and it completes the
set of moments I attempt to match (11 total).
1.5.2 Adjustment Costs Parameters: Fitting the Data
In order to analyze whether congestion e?ects in the adjustment for capital
and labor are important, I ?rst match the moments assuming that all parameters are
present, including the congestion e?ects parameters (F
kl
, ?
kl
, ?
kl
), and compare the
results with those obtained not including the congestion e?ect terms in the model.
In order to analyze which type of adjustment costs are important, I compare the
results of the full speci?cation model with the results of models that shut down a
particular type of adjustment cost. It is worth emphasizing that since I am not
using the optimal weighting matrix but instead the identity matrix, this value is
understated. The calculated moments are presented in table 1.16, and table 1.17
presents the calculated parameters with the standard errors for the full speci?cation.
and de?ning an investment rate lower than 1% as inaction would not considered the investment in
small but important units of capital.
71
Table 1.16: Simulated Moments
Simulated Moments
MOMENTS DATA Convex+Fixed+Disruption Convex
Complem. No complem.
Positive Spikes 0.61 < (I/K) 0.1 0.181 0.3 0.38
(90
th
percentile) 0.23 < (?L/L) 0.1 0.133 0.27 0.25
Negative Spikes 0 > (I/K) 0.1 0.152 0.21 0.26
(10
th
percentile) ?0.22 > (?L/L) 0.1 0.105 0.19 0.21
bkk -0.008 -0.009 -0.014 -0.003
bkl -0.008 -0.016 0.21 0.065
VAR coe?cients
blk 0.037 0.068 0.045 0.005
bll -0.147 -0.203 -0.073 -0.866
?
(
I
K
,
?L
L
)
0.057 0.049 0.139 0.203
Correlations ?
(
I
K
,z)
0.1 0.089 0.03 0.074
?
(
?L
L
,z)
0.05 0.135 0.154 0.297
J(?) N.A. 0.022 0.152 0.745
Two important facts emerge from table 1.16:
45
First, the model that considers
congestion e?ects does better in several dimensions than the model that does not. In
particular, one of the ?tted VAR coe?cients in the case without congestion e?ects
has the wrong sign relative to the data, and the contemporaneous correlation be-
tween capital and employment adjustment is too high in the case without congestion
e?ects. This suggests that when ?rms adjust both factors they pay a price instead of
having a bene?t of adjusting them together. It is important to emphasize that even
if the ?rms pay an extra cost of adjusting capital and labor together, the discounted
expected net bene?t can still be higher than if ?rms adjust one factor each period.
The second important fact from table 1.10 is that the model that considers convex
costs as the only cost faced by ?rms when adjusting does the worse job in explaining
the data moments.
45
These results should be taken with care, however; the minimization routine is susceptible to
getting local minima as solutions. More starting points for the algorithm are needed to con?rm
the ?ndings presented here.
72
Table 1.17: Calculated Adjustment Cost Parameters
Convex+Fixed+Disruption Convex
Congestion E?ects No Congestion E?ects
P
sell
0.42*pi (0.7307) 0.57*pi pi
F
k
0.0002 (0.0021014) 0.0065 NA
F
l
0.007 (0.090392) 0.013 NA
F
lk
0.14 (0.40376) NA NA
?
k
0.000006 (0.0000004)** 0.000016 0.092
?
l
0.0009 (0.0045079) 0.0000571 0.0134
?
lk
0.016 (0.0065368)* NA 0.024
?
k
0.0002 (0.0000182)** 0.00065 NA
?
l
0.0215 (0.0043362)** 0.092 NA
?
lk
0.046 (0.0199720)* NA NA
Standard errors in parentheses; **/* signi?cant at 1% and 5%
Table 1.17 has important information about the size of the adjustment costs
and about the statistical signi?cance of the estimates.With respect to the size of the
estimates, the high degree of irreversibility of the capital in Colombia is observed in
the lower selling price of capital for all the models except in the benchmark convex
case (by assumption p
sell
= p
buy
in this case). This irreversibility is much bigger
than the one found by Cooper and Haltiwanger (2005) for the U.S. This degree of
irreversibility is consistent with the asymmetric distribution for the gross investment
observed in the Colombian census. The high costs of adjusting both factors at the
same time are somewhat surprising. However, the functional form for the congestion
e?ects case does not allow for a direct comparison between the individual costs and
the congestion cost. The adjustment costs are not large, but ignoring them does
not allow a good match of the moments in the data.
With respect to the statistical signi?cance of the estimates, the procedure
allows to accept statistically the disruption costs for capital and labor, the convex
73
costs for capital but not for labor and the congestion e?ect present in the convex
cost joint parameter and the disruption cost joint parameter. The low statistical
signi?cance of the ?xed costs may be due to the fact that the disruption cost takes
all its e?ects. Also, according to the procedure, I can not reject the possibility that
the convex costs are present in the Colombian ?rms when they adjust capital or
when they adjust capital and labor at the same time.
1.5.3 Non-formal Tests of Goodness of Fit
After getting the parameters, the following exercises look to determine how
well the model can, using the estimated parameters, ?t the distributions of adjust-
ment and other moments not considered in the estimation procedure.
Figure 1.13. replicates the distributions of adjustments generated using the
model and the estimated parameters. The simulated distributions are more lumpy,
but the main characteristics observed in the data are present here. In particular,
the continuous adjustment in materials and energy contrast with the lumpy pattern
observed in the distributions of adjustments of capital and labor. It is interesting
to notice the asymmetry in the capital adjustment distribution and the symmetry
in the labor adjustment distribution.
Table 1.18. tries to replicate the logit estimates for the probability of spikes
in adjustment or inaction given spikes of adjustment or inaction in the other fac-
tor. In order to do so, I generated a panel with 1000 ?rms and 500 periods using
the estimated parameters, dropping the ?rst twenty observations in each simulated
74
Figure 1.14: Distributions of Factor Adjustments for the Simulated Series. Percent-
age of observations (y-axis) in a range of adjustments (x-axis).
Gross Investment Rate
0
5
10
15
20
25
30
-
0
.
5
-
0
.
4
-
0
.
3
-
0
.
3
-
0
.
2
-
0
.
1
-
0
0
.
0
6
0
.
1
4
0
.
2
2
0
.
3
0
.
3
8
0
.
4
6
I/K
%
o
f
o
b
s
e
r
v
a
t
i
o
n
s
Wks growth
0
5
10
15
20
25
30
-
0
.
5
-
0
.
4
-
0
.
3
-
0
.
3
-
0
.
2
-
0
.
1
-
0
0
.
0
6
0
.
1
4
0
.
2
2
0
.
3
0
.
3
8
0
.
4
6
Workers growth
%
o
f
O
b
s
e
r
v
a
t
i
o
n
s
Energy Growth
0
5
10
15
20
25
30
-
0
.
5
-
0
.
4
-
0
.
3
-
0
.
3
-
0
.
2
-
0
.
1
-
0
0
.
0
6
0
.
1
4
0
.
2
2
0
.
3
0
.
3
8
0
.
4
6
Energy growth (log difference)
%
o
f
o
b
s
e
r
v
a
t
i
o
n
s
Materials Growth
0
5
10
15
20
25
30
-
0
.
5
-
0
.
4
-
0
.
3
-
0
.
3
-
0
.
2
-
0
.
1
-
0
0
.
0
6
0
.
1
4
0
.
2
2
0
.
3
0
.
3
8
0
.
4
6
Materials Growth (log difference)
%
o
f
O
b
s
e
r
v
a
t
i
o
n
s
75
Table 1.18: Probability of inaction/adjustment conditional on Inaction/adjustment
of the other factor: Simulated data
Investment Employment growth
Variable x P(inaction/x) P(Spike/x) P(inaction/x) P(Spike/x)
0.026 ** -0.021**
Inaction
(0.007) (0.007)
Investment
-0.017* -0.001
Spike
(-0.008) (-0.008)
0.031** -0.035**
Employment
Inaction
(0.008) (0.008)
Growth -0.003 -0.008
Spike
(-0.008) (0.008)
Observations 49000 49000 49000 49000
†/*/** signi?cant at 10%, 5% and 1%. Shocks in regression
Dummies for inaction are de?ned as 1 if abs(x) < 0.01 and dummies for spikes are de?ned as 1 if
x > 0.2
series. The logit estimated using the simulated panel does a mix job matching the
empirical coe?cients, but it is worth to notice that the de?nition of small or large
adjustment is arbitrary and given the lumpier nature of the simulated panel, these
de?nitions can a?ect the results. In particular, there is a signi?cant and negative
probability of adjusting capital and labor when there is inaction in the other factor,
which is not observe in the data. Even if it will be worth to incorporate this set
of moments in the estimation, the problem would come from the de?nition of large
and small adjustments. This is left for future work.
1.6 Conclusions
In this paper I have used the Census of Manufacturing Firms in Colombia to
analyze if labor and capital adjustments are interrelated, whether there are conges-
76
tion e?ects in the adjustment process, and what is the nature of the adjustment
costs.
Empirically, ?rms adjust employment and capital in an interrelated way, using
several margins of adjustment in the process. As is the case for U.S. ?rms, there is a
distribution of adjustment that is at the same time lumpy and infrequent for capital
and labor, being more frequent in the case of materials and energy. These patterns
suggest that to understand the e?ect of policies such as tax investment incentives or
reductions in the ?ring/hiring costs, a model of joint capital and labor adjustment
is needed.
I argue that these patterns can be explained with a dynamic model in which
labor and capital are costly to adjust. The adjustment cost structure is chosen to
match some facts observed in the data, such as the decrease in output after the
adjustment, the cost of hiring and ?ring workers, the cost of installing capital and
a convex component to capture the mix of smooth and lumpy adjustment.
The proposed model is ?rst calibrated taken the adjustment costs parame-
ters in an arbitrary way to serve as example and then estimated with a minimum
distance procedure. The analysis of the decision rules for ?rms’ capital and labor
adjustment shows that the adjustment patterns are highly nonlinear and they can
be characterized as a bidimensional (S,s) policy where adjustment depends not just
of the states of the system but also on the choices. The calibrated model is able to
replicate some features from Colombian ?rms’ adjustment patterns, but none of the
di?erent adjustment cost types ?t the data when considered alone. We also observe
that a model with adjustment costs only in capital or in labor predicts di?erent
77
behavior. Importantly, models with high congestion e?ects more closely resemble
the data.
Finally, I estimate the deep parameters of the model using a structural ap-
proach with a minimum distance algorithm. This method reveals that a model that
incorporates congestion e?ects ?ts the data best and the structural methodology al-
lows me to reject statistically the existence of ?xed costs and to accept the existence
of disruption costs for capital and labor, the existence of convex costs for capital
but not for labor and the existence of congestion e?ects.
The main conclusion is that labor and capital adjustment should be analyzed
together. This is supported both by theory and by facts. The data show an inter-
related adjustment pattern. Moreover, a model that incorporates adjustments for
both capital and labor, generates sharply di?erent predictions if adjustment costs
are assumed for one factor alone.
The main advantage of the type of methodology proposed in this paper is that
several policy experiments can be analyzed. The e?ects of taxes on capital and
employment and the aggregate e?ects of these policies are among the main ones.
Also, Colombia undertook several market liberalization reforms at the beginning of
the 1990s, so it would be interesting to use this structural framework to explore
how the reforms a?ected ?rm behavior in terms of factor adjustment. And ?nally,
it may be worth exploring sectoral di?erences in ?rm behavior, especially since the
parameters and functional forms may not be the same for all types of industries. This
paper took an aggregate approach to this problem, but a more micro-level analysis
may prove useful, particulary if micro level behavior is the key to understanding
78
aggregate responses.
79
Chapter 2
Costs of Adjusting Production Factors: The Case of a Glass Mould
Company
2.1 Introduction
In chapter 1, I proposed and estimated a model to explain the main empiri-
cal ?ndings observed in the distributions of factor adjustments for the Colombian
Census of Manufacturing Firms. This explanation relied on the existence of a wide
range of adjustment costs for capital and labor and in the interrelation of such ad-
justments. The present chapter presents direct evidence for the adjustment costs
proposed in chapter one, in order to relate these rather abstract concepts about
adjustment costs and interrelation to a concrete ?rm. The approach of this chapter
is simply to observe the internal records of a ?rm and determine directly how much
this ?rm has to pay for adjusting production factors
1
. Using these observed adjust-
ment costs, the chapter also evaluates how well the generic model presented in the
previous chapter can ?t a speci?c ?rm.
Ever since the work of Holt, Modigliani, Muth and Simon (1960), economists,
under the pro?t maximizing agent paradigm, have tried to derive optimal production
decision rules and to test these rules with actual data from operating plants. Despite
their e?ort, the number of di?erent production factors, the heterogeneity in di?erent
1
In some cases, the adjustment costs analyzed in the previous chapter are not directly observed,
but the numbers presented in this section are either directly observed or part of a reduced form
data analysis; in the former case, the reduced form analysis does not pretend to uncover the
structural parameters because of endogeneity problems, and are simply aimed to illustrate the
concepts developed in chapter one.
80
production processes and the mathematical complexities of the problem, in addition
to the di?culty in accessing the data, have been and still are a big challenge for
economists.
Production decisions are taken in an uncertain and dynamic environment
where decisions today a?ect the decision tomorrow. At the ?rm level, the usual
approach to the problem of deriving optimal decision rules for production factors
was to specify a quadratic cost function and derive the optimal decision rules. The
choice of a quadratic function was to simplify the mathematical problem. At the
aggregate level, this quadratic function was implemented to ?t the smooth series
observed in the data capturing the fact that it takes time to adjust production
factors.
Despite its simplicity, the quadratic adjustment cost implies continuous adjust-
ment, a feature that is not observed in the adjustment of many production factors at
the ?rm level, and in particular, not observed in the adjustment of employment and
capital. Instead, at the micro level, we observe infrequent and lumpy adjustments.
The main explanation for this ?rm behavior is that there are non-convex costs of
adjusting production factors, which translate into discrete payments or costs, like
the cost that a ?rm has to pay to hire or ?re a worker, or the resources in time and
money that a ?rm has to allocate to adjust capital.
Adding to the debate, this chapter presents direct and detailed evidence of
the type of costs a ?rm has to pay when hiring/?ring a worker or when adjusting
capital, using detailed monthly data from a glass container mould ?rm in Colombia.
At this frequency, we observe a ?xed cost when the ?rm hires or ?res workers
81
and an adjustment cost that comes from the disruption in the production process
during periods of adjustment, which increases when the adjustment is simultaneous
in capital and employment. These adjustment costs are directly related to the ones
proposed in chapter one’s model and are speci?c examples of such adjustment costs.
It is important to emphasize that the adjustment costs present here are not estimated
as in the previous chapter uncovering the structural parameters, but instead they
are directly observed and analyzed using reduced form equations.
The observed magnitudes of the adjustment costs are important. Hiring a
new worker costs $1, 320 US dollars and ?ring an existing worker costs $53, 000 US
dollars, a striking asymmetry. The existence of a powerful union increases the cost
of adjusting the number of workers through contractually established fees for ?ring
in addition to high legal costs. With respect to the disruption costs, hiring a worker
increases the production time by 1.02% a month and installing new units of capital
requires on average 1,417 hours a month, which correspond respectively to 0.073%
and 1.6% of total monthly sales. The disruption cost of installing capital is increased
by 0.86%, to 1.614% of total sales, when there is simultaneous adjustment of capital
and employment.
Besides presenting direct evidence on the di?erent types of adjustment costs,
this paper examines the pertinence of using the model developed in the previous
chapter that ?ts the average factor adjustment behavior of ?rms in Colombia, to
describe and predict the actual decision rules for this particular ?rm. In order to
do so, I use the available data on production and adjustment costs for this ?rm to
calibrate the model.
82
The model matches many of the qualitative features of the data and pro-
vides a good ?t quantitatively in other dimensions. Speci?cally, it is able to closely
match the correlation between capital and employment adjustment and productiv-
ity shocks. However, it falls short in explaining the e?ects of employment growth
in investment. There are some conceptual issues described later with respect to the
type of production process the model in the previous section describes compared to
the production process in this speci?c ?rm, but in any case it is useful to link the
direct evidence of adjustment costs obtained in this ?rm with a generic model that
?ts the macro level. Overall, the level of detail and the quality of the data, together
with the particularities of the ?rm, help us understand, on the one hand, the nature
of the adjustment costs observed at the ?rm level, and on the other hand, the the
ability of a model estimated at the macro level to ?t the data for a micro level ?rm
The paper has 5 sections. Section 2 describes the ?rm and the production
process. Section 3 presents the data and calculates adjustment costs, while section
4 describes the model, estimates the remaining parameters needed for the simulation
and presents the results, discussing the validity of simulating the model from the
previous chapter without any modifycation. Section 5 concludes and gives directions
for future research.
83
2.2 Description of the ?rm and the production process
2.2.1 History of Moldes Medellin
The ?rm used in this study is a glass mould company called Moldes Medellin.
This ?rm is a subsidiary of Ross Mould International and it is located in Medellin,
Colombia. Ross Mould International is the largest glass bottle mould company in
the world, owning plants in Colombia, England, Hungary, South Africa and U.S.
2
Moldes Medellin started operations in 1999. Before that, it was called Met-
alicas Peldar and it was a division of Peldar, a subsidiary of Owens Illinois located
in Medellin and Bogota. Peldar (Owens Illinois) sold Metalicas in 1999 to Ross
Mould International, a long term US Owens Illinois’ supplier.
3
Ross Mould made a
big initial investment, represented not only by machinery and land but also in the
form of knowledge of the production process (embodied in local labor with years of
experience); since then, no other big investments have been made.
The main customers for Moldes Medellin and for Ross International are the
two worldwide leading companies in the glass industry: Owens Illinois and Saint
Govain. Owens Latin America (Colombia, Peru, Venezuela, Ecuador, Dominican
Republic and Puerto Rico) has an special agreement with Moldes Medellin to supply
90% of their needs for the next 10 years
4
. As a consequence, the ?rm’s investment in
2
Ross Mould International has four US subsidiaries: Ross Mould, Penn Mould, OMCO mould
and Brockway Mould. Together, these operations design and built moulds for virtually every
glass bottled product on the U.S. market, including those for leading food, beverage, cosmetics
manufacturers such as Kraft, Gerber, General Foods, Coca Cola, Avon, and many others.
3
The Glass industry requires high levels of capital. These industries used to be vertically
integrated with their supply chains, and it was common to ?nd units within the ?rms in charge of
supplying the moulds required for glass production.
4
Ross International has similar agreements with Owens all around the world.
84
publicity and marketing is almost zero, allowing the company to focus on production
and service.
It is important to point out that Ross Mould does not have competitors in
Colombia and there are very few companies in Europe and America able to manu-
facture this kind of product
5
. As a result, it is very di?cult to ?nd quali?ed labor
and the company needs to provide most of the speci?c training for new workers.
2.2.2 The Production Process
Moldes Medellin produces moulds primarily for glass container companies.
A glass mould consists of several parts, each creating a stage in glass container
manufacturing process, giving the shape to the containers in a progressive way.
Glass moulds require high precision in the dimensions and high technology both in
design and manufacturing.
This company uses machine tools directed by computer programs which are
adapted for each batch. The operator of the machine tools has to do a special
mounting for each job, then charges and proofs the programs and measures the ?nal
result. Maintenance also plays a very important role since a production disruption
caused by a machine breakdown can have a considerable impact on service costs
and time.
Manufacturing the moulds has two phases: planning and production. The
planning phase starts with the designing of the mould using CAD (Computer As-
5
PEREGO and CISPER are perhaps the most signi?cant competitors that Ross Mould has to
face in Europe and America.
85
sisted Design). Once the design is done, the engineers program the production
process and write codes to program the machines for each step in the process, using
special engineering programming software (CNC- Computer Numerical Control and
CAM -Computer Assisted Machining). The next step is to assign the tools and
cutting conditions.
The production phase starts with an initial machining to the raw cast iron
material, and then a special welding process is applied to a part of the mould.
Depending of the shape of the mould, di?erent machining processes are applied
afterwards. In order to guarantee the precision of the product, a Coordinate Measure
Machine is used during the process to measure results. Each piece is analyzed by
this machine and the dimensional report is sent directly to the customer.
For each batch, the machine tools have to be set using di?erent tools depending
on the job. These tools last between 6 to 12 months and are very expensive. Also,
there are special additional elements added to the machine tools in order to execute
special processes which are called ?xtures.
In the next subsection I will describe the type of adjustment costs the company
faces when adjusting machines for new jobs and when hiring new workers. Later,
these costs are quanti?ed with ?rst-hand data on costs from the internal records of
the ?rm.
86
2.3 Data: Production process, Factor Adjustment Dynamics and Ad-
justment Costs
2.3.1 Data
I have three years of monthly data from Moldes Medellin, from January 2003
until December 2005. The data set has information on production (sales in US
dollars and quantities by item), investment (book values in Colombian pesos, cal-
culated as in Eslava et al (2004)), energy (quantities and prices), materials (prices
and quantities by job), labor hours and number of workers (production and non
production), and total labor costs in US dollars
6
. There is also data on setup times
in man-hours. I consider setup times are to be an adjustment cost for reasons I will
discuss later. All prices are converted to December 2005 US dollars using the o?cial
exchange rate and the US CPI series from the BLS.
My measure of capital consists of two parts. The ?rst part is the book values
of capital excluding land and vehicles. The second component consists of the tools
that the company uses to produce the moulds which have an approximate lifetime
of 6 months in Moldes Medellin and are not including in the book value measure of
capital
7
.
6
The calculation of labor costs is done by the plant manager day by day, converting payments
in colombian pesos to dollars using the daily o?cial exchange rate
7
These two types of capital have di?erent depreciation rates. The depreciation rate for the ?rst
type, following Oliner (1996), was set equal to the 9.5% annual depreciation rate for numerically
controlled machine tools In the second type, the depreciation taken was 35% monthly, implying a
scrap value of 12% in 6 months and a zero value in 12 months. The average selling price Moldes
Medellin gets is 12%.
87
2.3.2 A First look at the Production and Factor Adjustment Dynam-
ics
This section explores how Moldes Medellin adjusts its input factor choices
when production changes. Speci?cally it looks at the behavior of production in
sales and units, the number of production and non production workers, production
labor hours and the costs and units of materials and energy.
I start by describing basic statistics and graphing time series, then discuss
volatility and comovement among the variables in levels and in percentage terms.
Although the sample size is very small (36 observations), it is still useful to look at
these numbers to get an idea of the behavior of the ?rm.
8
Table 2.1 shows the mean
and standard deviation of the levels and growth rates of these variables. We can see
from this table that Moldes Medellin is not a very big ?rm. Monthly sales are less
than a million dollars on average and there are only 82 workers with a capital stock of
7.5 million dollars. Almost all the capital consists of machine tools, 23% of the total
workers are engineers and 89% of the production workers are high skilled workers.
The ?rm does not hold inventories because all jobs made made to order. It is also
worth noticing that the plant was underutilized during the entire sample period
which indicates no shortage of capacity. Finally, the company had an interesting
downsizing process in December 2003 in output and labor, since the management
started to build another plant to get rid of the ?nancial burden imposed by the
union; this can be seen in ?gure 2.1. This regime change plays an important role
8
A small sample size can a?ect the standard deviation of the variables and the statistical
signi?cance of the correlations.
88
Table 2.1: Basic Statistics. Monthly values
Levels Growth
Mean Std Mean (%) Std
Sales 906 229 1.84 0.21
Production Workers 53 2 0.02 0.02
Nonproduction Workers 29 2 -0.34 0.03
Total Workers 82 3 -0.12 0.02
Energy 8.4 2.0 7.23 0.34
Materials 306 115 3.96 0.30
Units produced 7.8 1.9 4.18 0.30
Hours 7.2 1.8 2.79 0.22
Energy (thousand Kw) 125 9 1.19 0.08
Capital 7571 420
Capital Tools 65 26
Investment 59 80
Investment Tools 23 19
Investment Rate (I/K) 0.80 0.01
Inv. Tools/ Capital 0.30 0.00
Inv.Tools/Capital Tools 33.88 0.11
Sales, Capital, Investment, Energy and Materials in thousand of 2005 US$ dollars.
Hours and Units produced in thousands
and it is considered later in the estimations.
Figure 2.1 shows the series for employment and labor hours, investment and
capital, energy in units (Kw) and monetary values, materials, total costs, total
sales and total units produces. Figure 2.2 shows the factor adjustment graphs at a
monthly frequency. The peaks observed in production and non production workers
adjustment and the lumpiness in their adjustment suggest the presence of non-
convex adjustment costs to change the number of workers. Hours, energy and mate-
rials, move much more often than employment. Total investment has some inaction
months mixed with some peaks. In the case of the long term tools, which depreciate
quickly, investment is always positive, with a peak that represents a special ?xture
the company bought to produce a special mould part.
89
Figure 2.1: Production Factors Series
Capital (thousand US$)
6000
6500
7000
7500
8000
8500
J
a
n
-
0
3
A
p
r
-
0
3
J
u
l
-
0
3
O
c
t
-
0
3
J
a
n
-
0
4
A
p
r
-
0
4
J
u
l
-
0
4
O
c
t
-
0
4
J
a
n
-
0
5
A
p
r
-
0
5
J
u
l
-
0
5
O
c
t
-
0
5
Labor cost (pdn) thousand US$
0
10
20
30
40
50
60
J
a
n
-
0
3
A
p
r
-
0
3
J
u
l
-
0
3
O
c
t
-
0
3
J
a
n
-
0
4
A
p
r
-
0
4
J
u
l
-
0
4
O
c
t
-
0
4
J
a
n
-
0
5
A
p
r
-
0
5
J
u
l
-
0
5
O
c
t
-
0
5
Labor (pdn) thousand hours
0
2
4
6
8
10
12
14
J
a
n
-
0
3
A
p
r
-
0
3
J
u
l
-
0
3
O
c
t
-
0
3
J
a
n
-
0
4
A
p
r
-
0
4
J
u
l
-
0
4
O
c
t
-
0
4
J
a
n
-
0
5
A
p
r
-
0
5
J
u
l
-
0
5
O
c
t
-
0
5
Energy (thousand US$)
0
2
4
6
8
10
12
14
J
a
n
-
0
3
A
p
r
-
0
3
J
u
l
-
0
3
O
c
t
-
0
3
J
a
n
-
0
4
A
p
r
-
0
4
J
u
l
-
0
4
O
c
t
-
0
4
J
a
n
-
0
5
A
p
r
-
0
5
J
u
l
-
0
5
O
c
t
-
0
5
Energy units (thousand KW)
100
110
120
130
140
150
160
170
J
a
n
-
0
3
A
p
r
-
0
3
J
u
l
-
0
3
O
c
t
-
0
3
J
a
n
-
0
4
A
p
r
-
0
4
J
u
l
-
0
4
O
c
t
-
0
4
J
a
n
-
0
5
A
p
r
-
0
5
J
u
l
-
0
5
O
c
t
-
0
5
Materials (thousand US$)
0
100
200
300
400
500
600
700
J
a
n
-
0
3
A
p
r
-
0
3
J
u
l
-
0
3
O
c
t
-
0
3
J
a
n
-
0
4
A
p
r
-
0
4
J
u
l
-
0
4
O
c
t
-
0
4
J
a
n
-
0
5
A
p
r
-
0
5
J
u
l
-
0
5
O
c
t
-
0
5
Production (Sales thousand US$)
0
200
400
600
800
1000
1200
1400
1600
J
a
n
-
0
3
A
p
r
-
0
3
J
u
l
-
0
3
O
c
t
-
0
3
J
a
n
-
0
4
A
p
r
-
0
4
J
u
l
-
0
4
O
c
t
-
0
4
J
a
n
-
0
5
A
p
r
-
0
5
J
u
l
-
0
5
O
c
t
-
0
5
Production units (thousand)
0
2
4
6
8
10
12
14
J
a
n
-
0
3
A
p
r
-
0
3
J
u
l
-
0
3
O
c
t
-
0
3
J
a
n
-
0
4
A
p
r
-
0
4
J
u
l
-
0
4
O
c
t
-
0
4
J
a
n
-
0
5
A
p
r
-
0
5
J
u
l
-
0
5
O
c
t
-
0
5
Production jobs
0
50
100
150
200
250
J
a
n
-
0
3
A
p
r
-
0
3
J
u
l
-
0
3
O
c
t
-
0
3
J
a
n
-
0
4
A
p
r
-
0
4
J
u
l
-
0
4
O
c
t
-
0
4
J
a
n
-
0
5
A
p
r
-
0
5
J
u
l
-
0
5
O
c
t
-
0
5
Investment (thousand US$)
-200
-100
0
100
200
300
400
500
J
a
n
-
0
3
A
p
r
-
0
3
J
u
l
-
0
3
O
c
t
-
0
3
J
a
n
-
0
4
A
p
r
-
0
4
J
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l
-
0
4
O
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t
-
0
4
J
a
n
-
0
5
A
p
r
-
0
5
J
u
l
-
0
5
O
c
t
-
0
5
Capital Tools (thousand US$)
0
40
80
120
160
200
J
a
n
-
0
3
A
p
r
-
0
3
J
u
l
-
0
3
O
c
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-
0
3
J
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-
0
4
A
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0
4
J
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0
4
O
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-
0
4
J
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0
5
A
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-
0
5
J
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-
0
5
O
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-
0
5
90
Figure 2.2: Production Factors Adjustment
Production growth (Sales)
-60%
-40%
-20%
0%
20%
40%
60%
80%
J
a
n
-
0
3
A
p
r
-
0
3
J
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l
-
0
3
O
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t
-
0
3
J
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0
4
A
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4
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4
O
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J
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0
5
A
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-
0
5
J
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-
0
5
O
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-
0
5
Production Units Growth
-80%
-40%
0%
40%
80%
120%
J
a
n
-
0
3
A
p
r
-
0
3
J
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3
O
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3
J
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4
A
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4
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4
O
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4
J
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0
5
A
p
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-
0
5
J
u
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-
0
5
O
c
t
-
0
5
Materials Growth
-80%
-40%
0%
40%
80%
120%
J
a
n
-
0
3
A
p
r
-
0
3
J
u
l
-
0
3
O
c
t
-
0
3
J
a
n
-
0
4
A
p
r
-
0
4
J
u
l
-
0
4
O
c
t
-
0
4
J
a
n
-
0
5
A
p
r
-
0
5
J
u
l
-
0
5
O
c
t
-
0
5
Workers growth
-6%
-4%
-2%
0%
2%
4%
6%
8%
10%
J
a
n
-
0
3
A
p
r
-
0
3
J
u
l
-
0
3
O
c
t
-
0
3
J
a
n
-
0
4
A
p
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-
0
4
J
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-
0
4
O
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-
0
4
J
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-
0
5
A
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r
-
0
5
J
u
l
-
0
5
O
c
t
-
0
5
Production Workers growth
-6%
-4%
-2%
0%
2%
4%
6%
8%
10%
12%
J
a
n
-
0
3
A
p
r
-
0
3
J
u
l
-
0
3
O
c
t
-
0
3
J
a
n
-
0
4
A
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-
0
4
J
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-
0
4
O
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t
-
0
4
J
a
n
-
0
5
A
p
r
-
0
5
J
u
l
-
0
5
O
c
t
-
0
5
Non Production Workers growth
-12%
-8%
-4%
0%
4%
8%
12%
J
a
n
-
0
3
A
p
r
-
0
3
J
u
l
-
0
3
O
c
t
-
0
3
J
a
n
-
0
4
A
p
r
-
0
4
J
u
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-
0
4
O
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t
-
0
4
J
a
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-
0
5
A
p
r
-
0
5
J
u
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-
0
5
O
c
t
-
0
5
Hours Growth
-80%
-40%
0%
40%
80%
J
a
n
-
0
3
A
p
r
-
0
3
J
u
l
-
0
3
O
c
t
-
0
3
J
a
n
-
0
4
A
p
r
-
0
4
J
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-
0
4
O
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-
0
4
J
a
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-
0
5
A
p
r
-
0
5
J
u
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-
0
5
O
c
t
-
0
5
Energy Kw Growth
-30%
-20%
-10%
0%
10%
20%
30%
J
a
n
-
0
3
A
p
r
-
0
3
J
u
l
-
0
3
O
c
t
-
0
3
J
a
n
-
0
4
A
p
r
-
0
4
J
u
l
-
0
4
O
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t
-
0
4
J
a
n
-
0
5
A
p
r
-
0
5
J
u
l
-
0
5
O
c
t
-
0
5
Energy Cost Growth
-80%
-40%
0%
40%
80%
120%
160%
J
a
n
-
0
3
A
p
r
-
0
3
J
u
l
-
0
3
O
c
t
-
0
3
J
a
n
-
0
4
A
p
r
-
0
4
J
u
l
-
0
4
O
c
t
-
0
4
J
a
n
-
0
5
A
p
r
-
0
5
J
u
l
-
0
5
O
c
t
-
0
5
Investment Rate (I/K)
-2%
-1%
0%
1%
2%
3%
4%
5%
6%
J
a
n
-
0
3
A
p
r
-
0
3
J
u
l
-
0
3
O
c
t
-
0
3
J
a
n
-
0
4
A
p
r
-
0
4
J
u
l
-
0
4
O
c
t
-
0
4
J
a
n
-
0
5
A
p
r
-
0
5
J
u
l
-
0
5
O
c
t
-
0
5
Investment rate (Tools / K)
0.0%
0.2%
0.4%
0.6%
0.8%
1.0%
1.2%
1.4%
1.6%
1.8%
J
a
n
-
0
3
A
p
r
-
0
3
J
u
l
-
0
3
O
c
t
-
0
3
J
a
n
-
0
4
A
p
r
-
0
4
J
u
l
-
0
4
O
c
t
-
0
4
J
a
n
-
0
5
A
p
r
-
0
5
J
u
l
-
0
5
O
c
t
-
0
5
Investment rate (Tools / Ktools)
0%
10%
20%
30%
40%
50%
60%
70%
80%
J
a
n
-
0
3
A
p
r
-
0
3
J
u
l
-
0
3
O
c
t
-
0
3
J
a
n
-
0
4
A
p
r
-
0
4
J
u
l
-
0
4
O
c
t
-
0
4
J
a
n
-
0
5
A
p
r
-
0
5
J
u
l
-
0
5
O
c
t
-
0
5
91
Table 2.2: Correlation among the levels of the variables
Pdn Nonpdn Total K Units
Sales Wks Wks Wks K Tools Energy Materials pdn
Sales 1.00
Pdn Workers 0.26 1.00
Nonpdn Wks 0.36 0.32 1.00
Total Wks 0.37 0.87 0.75 1.00
K -0.46 0.01 -0.71 -0.36 1.00
K Tools 0.06 -0.41 0.38 -0.09 -0.32 1.00
Energy -0.47 -0.18 -0.69 -0.49 0.83 -0.19 1.00
Materials 0.95 0.37 0.29 0.41 -0.37 -0.07 -0.48 1.00
Units pdn 0.82 0.32 0.04 0.25 -0.10 -0.14 -0.21 0.87 1.00
Hours 0.86 0.18 0.30 0.28 -0.38 0.05 -0.34 0.76 0.61
Table 2.3: Correlation among the Growth of the variables
Pdn Nonpdn Total
I
K
Itools
K
Itools
Ktools
Units
Sales Wks Wks Wks Energy Mat. pdn
Sales 1.00
Pdn Wks -0.07 1.00
Nonpdn Wks 0.17 0.30 1.00
Total wks 0.05 0.82 0.79 1.00
I
K
-0.21 -0.08 -0.05 -0.08 1.00
Itools
K
0.13 -0.26 -0.01 -0.17 -0.03 1.00
Itools
Ktools
0.26 -0.19 0.00 -0.13 -0.01 0.75 1.00
Energy -0.11 -0.01 0.00 0.00 0.08 -0.01 0.01 1.00
Materials 0.94 -0.09 0.11 0.00 -0.16 0.01 0.17 -0.18 1.00
Units pdn 0.87 -0.04 0.03 -0.01 -0.19 -0.05 0.07 -0.08 0.91 1.00
Hours 0.78 -0.10 0.09 -0.01 -0.09 0.19 0.38 0.16 0.63 0.64
Table 2.2 shows the correlation among variables and Table 2.3 shows the cor-
relation among adjustments. It is interesting to notice the positive and strong
correlation between hours growth and investment in long lived tools and between
hours and energy and materials. This ?rm chooses to adjusts hours rather than
workers since workers adjustment is very costly.
The dynamic correlations between adjustments are presented in Table 2.4,
which shows a VAR of factor adjustments. Having in mind the small sample size
and the fact that this is just an empirical exercise, the only statistically signi?cant
correlations are between lagged hours growth and investment in long lived tools, and
between hours growth and lagged energy growth. The same interrelation between
capital and labor is observed at the aggregate level in other studies using the number
92
Table 2.4: VAR for Growth of the variables
Itools
Ktools
?M
M
?e
e
?h
h
-0.192 0.009 -0.186 0.001
(
Itools
Ktools
)
?1
-0.169 -0.238 -0.176 -0.165
0.228 -0.288 -0.138 0.181
(
?Materials
Materials
)
?1
-0.173 -0.244 -0.18 -0.169
0.096 0.082 -0.505 0.017
(
?Energy
Energy
)
?1
-0.149 -0.21 (0.156)** -0.146
0.632 0.402 0.239 0.016
(
?Hours
Hours
)
?1
(0.276)* -0.389 -0.288 -0.27
-2.34 -0.541 -0.36 -0.98
(
?TFP
TFP
)
?1
(0.767)** -1.08 -0.8 -0.75
Constant 0.395 -0.009 0.074 -0.007
(0.059)** -0.083 -0.061 -0.058
Observations 34 34 34 34
R-squared 0.4 0.09 0.29 0.1
of workers. It is possible that at this frequency and with the high adjustment costs
in employment this ?rm faces, the utilization of labor, re?ected in the production
hours, is more closely related to investment than the number of workers.
This descriptive evidence suggests that given the constraints this ?rm faces on
adjusting workers or the capital stock, it instead uses intensively other margins of
adjustment such as hours, materials and energy. The low capacity utilization gives
the ?rm larger cushion to adjust these factors both upwards and downwards. With
respect to investment, even if Moldes Medellin faces high costs of capital adjustment
due to setup costs for its tools, it still invests almost continuously, but in a lumpy
way as seen in ?gure 2.2. The next section presents direct evidence on the costs
that this ?rm has to pay when adjusting capital and labor.
93
2.3.3 A Description and Calculation of the Adjustment Costs faced
by the Company
This section discusses the type of adjustment costs that Moldes Medellin faces,
at a monthly frequency, when it decides to change its production factors, speci?cally
capital and employment in response to changes in demand. The methodology used
in this section is descriptive, meaning that the adjustment costs are directly observed
as payments or increases in costs that the ?rm incurs when adjusting. I use some
reduced form regressions to isolate individual e?ects of the adjustment costs.
Adjustment Costs in Capital
When Moldes Medellin has to manufacture a batch of moulds, it must set up
the machine tools for that speci?c job. Setting the machines involves three stages:
the ?rst stage is to charge the programs into the machine’s computer; the second
stage consists of adding elements and structures to the machine in order to position
the pieces (known as “?xtures”) and the tools in the process; and the third stage is
to set up the speci?c tools for the job.
These ?xtures and tools should be considered as investments because they are
used in several jobs to produce several pieces, and are literally interchangeable parts
of the machine. They have a lifetime of around six months. They are not materials
and are not counted as materials.
This setup process takes a considerable amount of time and disrupts the pro-
duction process. In Moldes Medellin all these steps are timed and they represent
between 10% to 35% of the total time in man-hours depending on the month and
94
on the past and current job, and between 1% to 3% of the total sales in a month
(1.6% on average). Figure 2.3 shows the total setup time in hours and the average
setup time per job, the setup time as a percentage of the total time, and the setup
time as a percentage of the total sales and the total costs. Around 20% of the total
time it takes to produce a mould in the plant is devoted to installing the new capital
required for the production; it is clearly observed in this ?gure that the ?uctuations
are not generated only by ?uctuations in sales or total costs.
Figure 2.3: Setup Costs
cost man hour cost setup total cost sales Setup cost / Total cost Setup cost / Sales
12 16 548 906 3.0% 1.8%
12 22 830 1170 2.7% 1.9%
12 22 805 1040 2.7% 2.1%
11 21 1077 1372 2.0% 1.6%
11 17 747 929 2.4% 1.9%
11 13 784 972 1.7% 1.4%
11 16 943 1245 1.8% 1.4%
11 13 913 1308 1.5% 1.1%
11 17 934 1397 1.9% 1.2%
11 15 758 1107 2.0% 1.4%
11 10 606 900 1.8% 1.2%
11 12 293 459 4.3% 2.7%
10 11 273 476 4.1% 2.4%
8 9 500 784 1.9% 1.2%
7 7 504 847 1.5% 0.9%
7 13 469 781 3.1% 1.8%
7 14 412 688 3.6% 2.2%
7 14 396 669 3.9% 2.3%
7 14 495 777 3.1% 2.0%
7 12 502 767 2.7% 1.8%
7 12 494 751 2.7% 1.8%
7 10 527 821 2.2% 1.4%
7 11 499 705 2.4% 1.7%
7 8 438 646 2.0% 1.3%
7 10 416 637 2.7% 1.8%
7 10 429 644 2.7% 1.8%
5 7 363 513 2.1% 1.5% 0.203704
7 12 444 628 3.1% 2.2%
7 12 559 806 2.4% 1.7%
7 7 487 681 1.8% 1.3%
7 7 587 841 1.5% 1.0%
7 7 565 816 1.4% 0.9%
7 8 600 854 1.5% 1.0%
7 6 549 749 1.4% 1.0%
7 6 498 704 1.5% 1.1%
7 13 501 700 2.9% 2.1%
308 435 20744 30089 1 1
Setup cost as percentage of Total Cost and as
percentage of Total Sales
0.5%
1.0%
1.5%
2.0%
2.5%
3.0%
3.5%
4.0%
4.5%
J
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Setup cost / Total cost Setup cost / Sales
Setup Costs
(Dec 2005 prices, thousand of dollars)
7
9
11
13
15
17
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21
23
25
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Setup time
(Thousand of hours)
0.5
0.7
0.9
1.1
1.3
1.5
1.7
1.9
2.1
2.3
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(hours)
1
11
21
31
41
51
61
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81
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setup hours per job time per job
95
The fact that the disruption in the production process due to the machine
setup is quanti?ed, and that it can be translated into forgone pro?ts due to the
adjustment, gives ?rst hand support for the modeling mechanism adopted in the
literature of adjustment costs in which a decrease in productivity is observed during
the adjustment of capital or labor, which translates into longer production times.
It is important to notice that the setup costs in capital presented here are an
upper limit for the disruption costs caused by adjustment in capital, since some jobs
require only to re-align a set of tools without buying any new tools. However, the
short life of the tools and the speci?city of the jobs make this disruption costs to be
associated very often with investment episodes. In a related matter, sometimes it is
enough for the ?rm to change the computer programs but not necessarily the tools
it operates when a new job arrives, and in other cases it is necessary to change the
programs and the tools. This relates to the ideas of ?xed costs of adjustment and
”disruption costs”, but these are more like job speci?c investments, or ?xed costs.
This is an important di?erence with the model in chapter one, since that model
really does treat investment as an addition to long term capital stock, and not as a
job speci?c investment or short run ?xed cost of production.
Adjustment Costs in Employment
There are 3 types of observable adjustment costs in employment: (i) the direct
costs that ?rms have to pay to hire and to ?re a worker and (ii) the costs of shifting
resources from other workers to train the new ones, and (iii) the lower productivity
96
Table 2.5: Legal Firing Costs in the Colombian Legislation
Contract Type Firing Fee
Fixed term contract Time left to expiration
Contracts for the duration of the job Maximum between the time left to expiration or 15 days
Workers with less than 45 days
1 year of continuous service
Workers with more than 1 year 45 days and 15 more for every year after
and less than 5 years of continuous service the ?rst year and proportional for each fraction of year
Workers with more than 5 years 45 days and 20 more for every year after
and less than 10 years of continuous service the ?rst year and proportional for each fraction of year
Workers with more than 10 years 45 days and 40 more for every year after
of continuous service the ?rst year and proportional for each fraction of year
of the new workers compared with the old ones
9
.
The ?rst type of costs have received the most attention in the literature since
they are more directly observable. They are typically modeled as ?xed costs. The
second type of costs are known in the literature as disruption costs.
The average payment to ?re a worker in Moldes Medellin is around US$ 53,000,
which includes legally mandated ?ring costs and the union agreement cost. Because
of the strength of the union, the ?ring cost is more than four times the legally
mandated payment for laying o? a worker. Table 2.5 shows these legal fees. In
the case of Moldes Medellin this translates into 71 dollars per day of legal payment
(assuming an average hourly wage of US$8.9) which means that, accounting for
the average tenure time of 6 years, the average legally mandated ?ring cost is about
US$10,300. The rest of the ?ring cost (US$42,700) comes from the union agreements.
In order to hire a worker, the ?rm pays around US$1,320. This money is
spent on medical and psychological examinations, training costs and increases in
production times (reduction in productivity) while the new worker learns the job.
The training costs are a form of disruption costs since the ?rm shifts resources to
9
The main hiring costs are psychological, medical and ability tests, and the ?ring costs are the
legal ?ring costs and the union agreement fees.
97
train new workers using old workers; in total, this training takes 6 shifts of 8 hours
each. Given the average hourly rate (US$8.9), the total training cost has been
quanti?ed to be US$427
10
. The increase in the production time is calculated to be
2% during the ?rst month after a new worker is hired according to the manager
of the ?rm; to test this number, I ran a regression in logs of the production hours
on the number of workers and controlling for the number of units produced, which
con?rmed the manager’s estimate: an increase of 1% in the labor force increases the
total production time by 1.02%
11
. Given the average production hours per month
(7,240), this represents a cost of US$657 assuming that the worker is fully productive
after the ?rst month. Finally, the medical and psychological examinations cost
US$240 according to the company records.
Summarizing, there are two important points with respect to employment ad-
justment in this ?rm. The ?rst one is that the disruption cost is the most important
adjustment cost that ?rms face when hiring. The ?xed cost of hiring is per-se rela-
tively very low. The second point is that there exists a big asymmetry between the
hiring and the ?ring cost. In the case of Moldes Medellin this asymmetry is even
bigger because of the existence of the union, but in any case, the legally mandated
?ring cost is much higher than the hiring cost
12
.
10
This number is just an approximation, since during some periods the worker’s marginal pro-
ductivity may be higher (or lower) than the wage, causing a higher (or lower) disruption cost.
11
This regression controls for tfp (the solow residual, which is calculated and explained later in
the paper) and the level of capital. It also controls for the change in regime observed in December
2003 using a dummy variable. The standard deviation of the coe?cient is 0.27, meaning a statistical
signi?cance of 1%
12
The hiring cost is about 2.5% of the ?ring cost or 12.9% if we consider only the legal payments.
98
Interaction E?ects in the Adjustment Costs
Besides the individual adjustment costs that Moldes Medellin has to pay when
adjusting capital or employment, it is worth investigating whether the cost of ad-
justing capital increases or decreases when the ?rm adjusts employment simultane-
ously. As it was analyzed in chapter one, I call this interaction e?ects, which could
be positive (complementarities) or negative (congestion e?ects). In chapter one,
the parameters governing this interaction e?ect were uncovered with a simulation
procedure. In this section, the approach is di?erent and a reduced form regression
is ran in order to illustrate the e?ects. This reduced form analysis does not pretend
to uncover the structural parameters governing the interaction e?ects, since there
are some endogeneity problems; instead, the empirical analysis of the interaction
e?ects is aimed to clarify the concepts presented in chapter one and give ?rst-hand
empirical support for the existence of interaction e?ects. Although I do not have a
series of the employment adjustment costs, I have the series for the setup costs paid
by the ?rm every month when adjusting capital, which, as was mentioned above,
gives an upper limit for the disruption adjustment costs.
In order to ?nd out if employment growth a?ects the disruption adjustment
costs for capital (i.e. if the disruption adjustment costs are higher or lower than
average during periods of worker adjustment), I ran regressions of the logs of capital
set-up costs and capital set-up hours on the change in employment level. The
coe?cient should be interpreted as the e?ect of employment growth on disruption
cost growth (set-up cost or set-up time growth). If it is cheaper to adjust both
99
Table 2.6: E?ect of a Change in the Number of Workers on the Capital Disruption
Adjustment Cost
Dependent Variable
log Set-up costs log Set-up time
1.17 0.255
? Workers
(2.04) (2.174)
1.128 0.579
? Non Pdn Workers
(1.323) (1.412)
-0.173 -2.226
? Pdn Workers
(2.123) 9.661
R-squared 0.51 0.52 0.31 0.31
Other Controls: tfp, lagged tfp, dummy at Dec 2003 (regime change)
and log of units produced. Standard errors in parenthesis
capital and employment at the same time, this coe?cient will have a negative sign
and it will be positive otherwise.
Table 2.6 shows the results of this regression. With respect to the sign of the
e?ect, we can see from this table that an increase in the number of workers increases
the adjustment costs for capital, suggesting the existence of congestion e?ects in the
adjustment costs (an extra cost of adjusting both factors together). Moreover, we
can see that it is the increase in the number of non production workers that increases
the setup costs. The same happens in the case of the set-up time. However, the
the coe?cients are not statistical signi?cant. Overall, this result may be due to the
small variation on the number of nonproduction workers or due to the nature of the
production process. In this particular production process the set-up of the machine
tools depends on the planning made by the non production workers: the engineers
have to plan the times and the speci?c ways the tools and ?xtures are placed.
I have shown the factor adjustment behavior of Moldes medellin and the cost
that it has to pay when adjusting. The next section explores to what extent a
100
model that closely matches the factor adjustment moments of the whole Census of
Manufacturing ?rms in Colombia is able to reproduce the adjustment of production
factors in Moldes Medellin.
2.4 How Well the Model from Chapter One Can ?t this Particular
Firm?
The objective of the previous section was to illustrate with a concrete example
the adjustment costs de?nitions proposed in chapter one. In particular, we could
observe in the data the costs that Moldes Medellin has to pay when hiring or ?ring
a worker (?xed costs), the increases in production time and the reallocation of re-
sources that the ?rm has to make when adjusting capital and labor(disruption costs),
and the increase in capital setup time when the ?rm adjust at the same time the
number of workers (congestion e?ects). This section looks to link the generic model
?tted for the Colombian ?rms to the particular production process that Moldes
Medellin has. As in chapter one, the objective of this model is to understand the
existence of infrequent and lumpy adjustment across input factors and especially in
labor and capital. The explanation given for this behavior lies in the di?erent ad-
justment costs a company faces when adjusting production factors. The model also
captures the observed interrelation between capital and labor adjustment. The pa-
rameters for the adjustment costs are taken directly from the evidence collected from
Moldes Medellin. The other parameters needed to simulate the model, such as the
production function elasticities and the productivity shocks, are directly estimated
from the data using the same methodology I applied in chapter one.
101
2.4.1 Model
The model is a dynamic ?rm problem with adjustment costs in employment
and capital, where ?rms decide how much input factors to use in response to changes
in demand and productivity. The main di?erence with previous adjustment cost
models in the literature is the existence of a complementarity e?ect which makes the
joint adjustment of capital and labor more expensive (or cheaper, since no restriction
is imposed) than the individual adjustments. What motivates the ?rm to adjust
capital and employment together is the gain of the joint adjustment compared with
the opportunity cost of adjusting only one or no factors.
Equation (2.1) describes the general problem. In this equation I
t
= k
t+1
?
(1 ??) k
t
represents investment and ? represents depreciation. C(•) is the cost of
adjustment, which takes di?erent parameter values depending on whether the ?rm
adjusts employment, capital or both. ? is the discount factor and the integral term
represents the expected value of the ?rm subject to shocks z. This shock distribution
f(z
/z) is parameterized as an AR(1) process estimated using the Solow residual
from the production function estimation. For notation reasons, this shock includes
materials and energy, which are chosen optimally every period in a static fashion
13
.
V (z, k, l
?1
) = max
k
,l
_
?(z, l
?1
, l, k, k
) +?
_
V (z
, (1 ? ?)k + I, l)f(z
/z)dz
_
= max
k
,l
{zk
?
l
µ
? w(l) ?C(z, l
?1
, l, k, k
)
+?
_
V (z
, (1 ? ?)k + I, l)f(z
/z)dz
} (2.1)
13
For more details on the model, see chapter one.
102
The cost of adjustment C(•) potentially includes disruption costs, ?xed costs
and convex costs. The following is the functional form assumed for the adjustment
costs when ?rms adjust l (labor), k (capital) or kl (capital and labor):
C (z, k, I, l, l
?1
) =
_
¸
¸
¸
¸
¸
¸
¸
¸
¸
¸
¸
¸
¸
_
¸
¸
¸
¸
¸
¸
¸
¸
¸
¸
¸
¸
¸
_
C
l
= ?
l
R(•) +F
l
l
?1
+
?
l
2
_
?l
l
?1
_
2
l
?1
if ?l = 0
C
k
= ?
k
R(•) +F
k
k +
?
k
2
_
I
k
_
2
k + p
I
? I if I = 0
C
lk
= C
l
+ C
k
+ ?
lk
R(•) + F
lk
?
l
?1
k
+
?
lk
2
_
I
k
_ _
?l
l
?1
_
?
l
?1
k if ?l ? I = 0
(2.2)
In the case of labor or capital adjustment, (C
l
and C
k
respectively) the ?rst term
?
j
R(•) represents the disruption cost, the second term involving F
j
represents
the ?xed cost and the third term involving ?
j
represents the convex cost, with
j=k(capital) and l(labor). In the case of capital adjustment, there is an extra cost
which represents the investment price, which can take values of p
I
= {p
buy
, p
sell
}
depending on if the ?rm buys or sells capital, having the selling price a negative
value. The asymmetry in the price for buying and selling capital implies that capital
is not fully reversible.
The convex cost term is the benchmark used in the cost function estimation
literature and it also appears also in this general model. In this paper, however, I
do not ?t with a quadratic function the observed adjustment costs. In fact, the data
does not show a quadratic shape. Neither do I use a ?xed capital adjustment cost,
since I do not have data on it.
In the model, if the ?rm adjusts capital and employment at the same time,
the adjustment cost is the sum of the cost of adjusting capital (C
k
), plus the cost of
adjusting employment independently (C
l
), plus a collection of terms that represent
103
the extra cost of the joint adjustment. The parameters to be inserted in the model
are the observed ones: {?
k
, ?
l
, ?
kl
} for the disruption cost, F
l
for the ?xed cost, and
p
I
for the investment price.
There are important di?erences between the production process represented
in the generic model in chapter one and the production process in Moldes medellin.
For example, Moldes Medellin “produces to order” and stochastic arrivals of orders
or ”jobs” seems like the appropriate way to model the glass mould factory. However,
the production function chosen for the generic model can be interpreted this way
if the shock processes are taken as demand shocks, or demand ?uctuations that
trigger the production factor adjustment every time they arrive. Also, many of the
adjustment costs that the glass mould company incurs are related to retooling from
one job to another, as it was said above. In this sense, the adjustment costs should
be seen as an upper limit.
2.4.2 Calibration/Estimation of the Parameters
The existence of a disruption cost takes the form of lower productivity and
can be also thought as the shift of resources in order to adjust the other factor. In
the previous section, this cost was observed to ?uctuate between 1% and 3% of the
total sales, with an average of 1.6% in the case of capital and of 1.02% increase in
the production time in the case of labor, or 0.073% of the total sales.
The ?xed adjustment cost represents the installation costs (in both time and
resources) in the case of capital and ?ring and hiring costs in the case of labor. I
104
only observe the ?xed labor adjustment cost, which is calculated to be $53,000 US
for ?ring and $240 US for hiring (out of the total of $1320 of hiring costs). This
translates into 5.8% of total monthly sales in the case of ?ring costs and 0.026% in the
case of hiring costs. Since my benchmark model assumes a symmetric adjustment
cost in employment, I use the average between the hiring and ?ring costs to be the
?xed cost parameter in the model. This cost (US$26,620) is scaled in the model by
the employment level. To get the parameter value, I consider the average number
of employees (80) as the scale value, getting a adjustment cost parameter of 333 or
0.333 in thousand dollars.
14
With respect to the selling price, this ?rm sells the used tools after a couple of
months for a recovery price which ?uctuates approximately between 10% and 20%
of the original price with an average of 12%.
Congestion e?ects in the adjustment costs are also observed in Moldes Medellin,
speci?cally in the capital disruption cost when the ?rm increases the number of work-
ers. The estimations above suggest that a 1% increase in the number of workers
increases the cost of adjusting capital by 1.17%. Table 2.7 summarizes the adjust-
ment cost parameters to be introduced in the model.
15
The values for the adjustment cost parameters calculated for Moldes Medellin
are consistent with the ones found in Chapter one using the generic model for the
Colombian ?rms. For example, the disruption cost parameter was 0.046 compared
to 0.01693 for Moldes Medellin. The ?xed cost parameter is much higher for Moldes
14
In future work, I intend to incorporate the asymmetry of these costs into the model and change
the scale value for the increment.
15
In order to make the parameters comparable with the ones in the previous chapter, I consider
capital and sales to be thousands of dollars.
105
Table 2.7: Adjustment Cost Parameters
Capital Employment
Disruption 0.016 0.00073
Fixed 0.332
Complementarity (disruption) 0.016 + 0.00073 + 0.0002 = 0.01693
Medellin than for the average ?rm in Colombia according to the estimates in chapter
one (0.332 vs. 0.007), but this may be due to several causes like the very high
cost imposed by the contractual obligations with the union, to the long tenure of
the workers in Moldes Medellin (the longer the tenure, the higher the ?ring cost),
and the failure of the model in capturing the asymmetry between hiring and ?ring
costs. On the other hand, the capital in this glass mould ?rm is very irreversible
compared with the typical Colombian ?rm (0.12 vs 0.42 times the buying price);
this is reasonable since we are dealing here with a form of capital that depreciates
very fast and is speci?c for the process.
The next step is to estimate the other parameters needed to simulate the
model in the case of Moldes Medellin. These parameters are the production function
elasticities, the wage equation parameters and the productivity shocks that will drive
the adjustment of the production factors.
What Function Can Describe the Production Process?
There may be many functional forms that can describe the production process
in Moldes Medellin. Since the objective of this section is to compare the perfor-
mance of the model proposed in the previous chapter, the natural choice is to ?t
a Cobb-Douglas production function. However, a closer look at the production
process suggests that such a choice is not a bad one. The main characteristic of
106
the Cobb-Douglas production function is that the cost shares remain constant. Fig-
ure 2.4 shows this value for Moldes Medellin. We can see that the cost shares do
not ?uctuate much, giving some support for the assumption of the Cobb-Douglas
production function. Table 2.8 shows the OLS estimates of the Cobb-Douglas pro-
Figure 2.4: Cost Shares
Cost Shares
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
J
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O
c
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O
c
t
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5
A
p
r
-
0
5
J
u
l
-
0
5
O
c
t
-
0
5
labor pdn energy materials
duction function relating sales to capital, labor costs, energy cost and materials cost.
Even if the OLS coe?cients may be biased, the fact that the observed cost shares
are similar to the coe?cients estimated with the OLS suggest that this functional
form and these coe?cients are reasonable. The cost shares are on average 0.15 for
labor (total hours), 0.48 for materials, 0.02 for energy and 0.04 in the case of the
capital (long lived tools). The cost shares for labor and materials are very close
to the OLS estimates but the energy and the capital costs are not. This may be
because variation in capacity utilization occurs through capital (energy) more than
other factor and the existence of other type of capital. Figure 2.5 shows the
107
Table 2.8: Production Function Estimates
Coe?cient. Stdandard Error
Capital 0.116 0.034
Energy 0.085 0.046
Materials 0.560 0.061
Labor 0.175 0.061
F(4,31)=126.14
Adj R-squared=0.9346
Number of obs=36
residual from the previous production function estimation. The big jump between
January and April 2004 is associated with the change in the plant management and
the downsizing of the plant in order to control the union. From this residual, I esti-
Figure 2.5: Residual Production Function
Residual production function
-0.1
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
J
a
n
-
0
3
A
p
r
-
0
3
J
u
l
-
0
3
O
c
t
-
0
3
J
a
n
-
0
4
A
p
r
-
0
4
J
u
l
-
0
4
O
c
t
-
0
4
J
a
n
-
0
5
A
p
r
-
0
5
J
u
l
-
0
5
O
c
t
-
0
5
mate an AR(1) process tfp
t
= ?
tfp
tfp
t?1
+?
t
getting an autocorrelation coe?cient
of 0.487 (std=0.134) and a ?
?
= 0.021 which in turn implies that ?
tfp
= 0.024.
The wage function is taken as wage = w
0
? e + w
1
? e ? h
(
?) and estimated
directly from the data on wages and hours.
16
The elasticity of wages with respect to
16
The numbers are given in thousands of December 2005 dollars.
108
hours is taken as 1.1, as in the previous chapter. The results from an OLS estimation
of this equation are w
0
= 1.11(std = 0.58) and w
1
= 0.12(std = 0.000).
The energy price is calculated as the average kilowatt price paid by the ?rm
across all sample months and is equal to 0.067US$. The materials price is the
average across months of the ratio of total cost to quantities (measured in pounds
of casting per unit produced) and equal to 1.4 US$. The buying price of capital is
normalized to 1. The selling price of capital is calculated as follows: The lifetime
of the tools is one year. However, they are sold when they are 6 months old by
around 12% of their value. This implies a monthly depreciation of 35%. Finally,
the discount rate is taken as 0.95 per year which implies a discount rate of 0.996 per
month.
Benchmark Moments
At this frequency, some of the variables are not as relevant to this particular
company as they are to the average Colombian ?rm observed in the annual Cen-
sus of Manufacturing ?rms. These variables are the employment growth and the
investment rate. On the other hand, some variables that are not observed in the
census play a key role describing the behavior of Moldes Medellin, like labor hours
and the investment rate in long lived tools. That is the reason why the benchmark
moments taken from the census can be compared with the moments for Moldes
Medellin for energy and materials, but not in capital and labor. Table 2.9 summa-
rizes the moments that are taken as benchmarks to compare with the simulations
of the model.
109
Table 2.9: Benchmark Moments (Monthly Values From the Data)
Wks Growth Hours Growth
T
KTools
90
th
percentile 0.013 0.229 0.444
10
th
percentile -0.013 -0.153 0.200
?(
T
KTools
, x) -0.1277 0.38372
?(x, tfp) -0.0133 0.42224 -0.0711
VAR Coe?cients
I
K
?Wks
Wks
?Hours
Hours
(
I
K
)
?1
-0.191 0.021 0.002
(
?Wks
Wks
)
?1
0.038 -0.075 0.019
(
?Hours
Hours
)
?1
0.631 -0.068 0.016
2.4.3 Simulations Results
Table 2.10 shows the simulation results using the model and the calibrated
parameters. A quick view of the results reveals that the model does not get a perfect
?t, but is able to reproduce some qualitative features of the data. In particular,
although it does not match exactly any moment exactly, it does yield the correct
sign in most cases. In particular, the model predicts the correct signs in the case of
the percentiles of workers growth, hours growth and the capital growth.
The model matches the qualitative behavior for the correlation between work-
ers, hours and investment with productivity shocks. With respect to the VAR, the
model is not able to explain the e?ect of lagged employment and hours growth on
capital, but it does a better job in explaining the e?ect of investment on employment
growth and hours growth. The best match is the correlation between the investment
rate and the productivity shock.
The lack of a good match between the simulated moments and the moments
from the data may come from di?erent explanations. First, it is possible that the
110
model does not re?ect all the variables management considers when adjusting fac-
tors. With respect to this ?rst argument, it is true that the existence of the union
imposes intangible restrictions, such as political ?ghts inside the ?rm, that the man-
agement tries to avoid, or long processes which retard the response of the ?rm to
shocks in demand or productivity. It is also hard to consider in one single model
all the factors that the management weighs when making decisions. Second, it is
possible that the ?rm does not act completely as pro?t maximizing agent. With
respect to the second argument, if it is true that the ?rm is not acting as a pro?t
maximizing agent, it must be true that it is in its best interest to modify its be-
havior. For example, the model suggests that the ?rm should respond much more
adjusting workers, hours and investment despite the high adjustment costs; it also
suggests substitution between hours and capital instead of substituting workers and
capital.
I do not view the results of the simulations as a failure. Instead I regard them
as very promising, considering this model is taken directly from a model ?t to the
average behavior of all ?rms in Colombia
17
.
Some modi?cations to the model regarding the observed asymmetry in the
?xed costs of adjusting labor, or the modeling of di?erent types of workers (i.e.
production and non production), or di?erent types of production functions, could
signi?cantly improve the ?t of the model to the data. The ?nal goal is to deliver
a model that can assist the managers of Moldes Medellin in their decision making
process.
17
The only modi?cation made was a di?erent calibration/estimation of the parameters.
111
Table 2.10: Simulations Results
Wks Growth Hours Growth
T
KTools
90
th
percentile 0.037 0.49 0.710
10
th
percentile -0.037 -0.31 0.000
?(
T
KTools
, x) -0.017 -0.059
?(x, tfp) 0.384 0.115 -0.027
VAR Coe?cients
I
K
?Wks
Wks
?Hours
Hours
(
I
K
)
?1
-0.1632 0.029 0.081
(
?Wks
Wks
)
?1
-0.033 -0.0048 0.089
(
?Hours
Hours
)
?1
-0.039 -0.006 0.103
2.5 Conclusions and Future work
In this paper, I have presented direct evidence of the costs that a glass mould
?rm has to pay when adjusting input factors using detailed production monthly
data. The observed adjustment costs come on the one hand from the disruption
in production when adjusting capital and employment, resulting from the resources
diverted to adjust these factors, and on the other hand from the ?xed costs that
the ?rm has to pay when hiring or ?ring a worker. I presented also direct evidence
of the existence of an additional cost for the ?rm when adjusting both factors at
the same time, since the disruption cost is higher during these periods. The most
salient features of the adjustment costs are the high asymmetry between the ?ring
and the hiring cost and the high disruption cost in both capital and employment
adjustment.
These observed adjustment costs were introduced in a model that ?t the aver-
age behavior of the manufacturing sector in Colombia. In that case, the parameters
were estimated and not observed, in contrast with this paper, where the costs are
112
observed and not estimated.
With this direct calibration, the model is able to reproduce many qualitative
features from the Glass Mould ?rm behavior, and in some cases, the qualitative re-
sults match the data, as in the response of investment and labor hours to shocks in
productivity, or in the case of the extreme percentiles (10
th
and 90
th
) of labor hours
growth. However, the overall quantitative ?t, and some qualitative features like the
dynamic relationship between capital and employment, are not good. The expla-
nations for this could come from misspeci?cation of the model or from suboptimal
behavior of the ?rm.
The model can be improved by incorporating features like the asymmetry of
the ?xed employment adjustment costs or other constrains that the management
faces because of the union. But if the model is a good approximation of the produc-
tion process in Moldes Medellin, it suggests that despite the high adjustment costs,
the ?rm should adjust employment, hours and investment more frequently and use
more the substitution margin between capital and workers.
In the future, I plan to carefully consider a speci?c model that can ?t the
operation of Moldes Medellin, introducing elements like those mentioned above.
The ?nal goal is to show to the management and the owner how they can improve
their pro?ts with modi?cations to the production choices suggested by an economic
model.
113
Chapter 3
Conclusions and Final Thoughts
In analyzing input factor decisions using the unique data sets presented in
chapters two and three, this dissertation makes three main contributions. First, it
reveals the fact that it is more costly for ?rms to adjust capital and employment at
the same time, an e?ect called congestion. This e?ect is important in explaining the
observed interrelation between capital and employment growth. Second, it provides
direct evidence of the existence of adjustment costs using data from a particular ?rm;
these adjustment costs take the form of disruption in the production process and
reallocation of internal resources to adjust the input factors, ?xed costs of adjusting
factors and complementarities in the adjustment costs as de?ned before. And third,
it proposes a model that is able to explain the empirical evidence about capital and
employment adjustment, namely the mix of smooth and lumpy adjustments, the
mix of inaction, small and large adjustments and the interrelation in capital and
employment adjustment. The key for the success of the explanation lies in the joint
analysis of dynamic capital and employment decisions with a very complete and
realistic structure of adjustment costs.
In the ?rst chapter I have used the Census of Manufacturing Firms in Colom-
bia to analyze if labor and capital adjustment are interrelated, whether there are
interrelations in this process, and what the nature of this adjustment is. The data
114
shows the same patterns observed in other data sets: mix of smooth and lumpy ad-
justments in capital and employment, mix of inaction, small and large adjustments,
continuous adjustment in energy and materials and interrelation between capital
and employment adjustment.
I argue that these patterns can be explained with a dynamic model in which
labor and capital are costly to adjust. The adjustment cost represents some facts
from the data, such as the decrease in output after the adjustment, the cost of hiring
and ?ring workers, the cost of installing capital and a convex component to capture
the mix of smooth and lumpy adjustment. The model also incorporate the fact that
the adjustment is more costly when done simultaneously in capital and employment.
The decision rules for ?rms’ capital and labor adjustment show that the adjustment
patterns are highly nonlinear and they can be characterized as a bidimensional (S,s)
policy where adjustment depends not just of the states of the system but also on the
choices. Importantly, the model with high complementarities more close resemble
the data statistics.
The main conclusion from the ?rst chapter is that labor and capital adjust-
ment should be analyzed together when considering a dynamic model of adjustment
dynamics with convex and non-convex costs. This is supported by an empirical rea-
son as well as a theoretical one. The data show an interrelated adjustment pattern.
Moreover, in a model that incorporates adjustments for both capital and labor, the
conclusions about factor movements are di?erent if adjustment costs are presented
in one factor alone. The structural methodology allows me to reject statistically the
existence of ?xed costs and to accept the existence of disruption costs for capital and
115
labor, the existence of convex costs for capital but not for labor and the existence
of congestion e?ects.
The main advantage of the type of methodology proposed in this paper is that
several policy experiments can be analyzed. The e?ects of taxes on capital and
employment and the aggregate e?ects of these policies are among the main ones.
Also, Colombia undertook several market liberalization reforms at the beginning
of the 1990s, so it would be interesting to explore with this structural framework,
how the reforms a?ected the ?rm behavior in terms of factor adjustment. And
?nally, it may be worth exploring sectoral di?erences in ?rm behavior, especially
since the parameters and functional forms may not be the same for all types of
industries. This paper took an aggregate approach to this problem, but a more
micro-level analysis may prove useful, particulary if micro level behavior is the key
to understanding aggregate responses.
In the second chapter I have presented direct evidence of the costs that a
glass mould ?rm has to pay when adjusting production input factors using detailed
production monthly data. The evidence presented con?rms part of the adjustment
cost structure proposed in chapter one. The observed adjustment costs come on the
one hand from the disruption in production when adjusting capital and employment
and from the resources used to adjust these factors, and in the other hand from the
?xed costs that the ?rm has to pay when hiring or ?ring a worker. I presented also
direct evidence of the existence of an additional cost for the ?rm when adjusting
both factors at the same time since the disruption cost is higher during these periods.
The most salient features of the adjustment costs are the high asymmetry between
116
the ?ring and the hiring cost and the high disruption cost in both capital and
employment adjustment.
The observed adjustment costs where introduced in the model from chapter
one. In chapter one, the parameters were estimated and not observed, in contrast
with chapter two, where the costs are observed and not estimated.
With this direct calibration, the model is able to reproduce many qualitative
features from the Glass Mould ?rm behavior, and in some cases the qualitative
results get close to the data as in the response of investment and labor hours to
shocks in productivity, or in the case of the labor hours growth extreme percentiles
(10
th
and 90
th
). However, the overall quantitative ?tting and some quantitative
features like the dynamic relationship between capital and employment are not good.
The explanations for this can come from the misspeci?cation of the model or from
the suboptimal behavior of the ?rm.
The model can be improved in features like the asymmetry of the ?xed em-
ployment adjustment costs or the production function or incorporating some other
constrains that the management faces because of the union. But if the model is a
good approximation of the production process in Moldes Medellin, it suggests that
despite the high adjustment costs, the ?rm should adjust more employment, hours
and investment and use more the substitution margin between capital and workers.
In the future, I plan to carefully consider a speci?c model that can ?t the
operation of Moldes Medellin, introducing elements like the mentioned above. The
?nal goal is to show to the management and the owner how they can improve
their pro?ts with modi?cations to the production choices suggested by an economic
117
model.
118
Appendix 1
Appendix Chapter 1: Complementary Analysis of the Variables
Around Spikes in Capital and Employment
This appendix has three main goals. The ?rst one is to analyze how the
adjustments of capital and employment and the levels of energy, materials, output
and productivity are interrelated before, during and after a spike in investment or
employment. The second goal is to show that the patterns of adjustment have a mix
of lumpy and smooth elements as argued in previous sections. And the third goal is
to show that TFP and output decrease after episodes of large adjustments specially
in capital, suggesting the presence of adjustment costs in the form of forgone pro?ts.
Following a similar methodology to Sakellaris (2004) and Letterie et al. (2004),
I analyze the conditional expected values of the variables of interest around the
spikes in investment and employment adjustment. Speci?cally, I create a dummy
variable for the investment spikes if the investment rate is greater than 20% and was
lower than 20% in the previous period; that is
I
t
K
t
> 0.2 and
I
t?1
K
t?1
< 0.2. In order
to make a comparison with the existing literature, and given the arbitrary nature
of the de?nition of thresholds for “large” adjustments, I also construct a dummy
variable signalling the job creation bursts if the adjustment is bigger than 10% in t
but less than 10% in absolute value in t ?1. Job destruction bursts are determined
by the same rule on the negative side (less than -10% labor adjustment in t and
more than 10% in t ?1). An important assumption is that two years of consecutive
large adjustment correspond to the same episode. Consequently, I analyze 5 years
119
around the investment episode.
The analysis is based on the following regression:
X
is
= µ
i
+ v
s
+
j=2
j=?2
?
j
? EV ENTD
t+j
is
+
st
(1.1)
X
is
is the variable of interest for ?rm i in period s. µ
i
stands for plant e?ects
to control for unobserved heterogeneity and ?
s
stands for year e?ects to control for
aggregate e?ects in the variable; EV ENTD = 1 if the event D happens in time s,
where D can be an investment spike, job creation burst or job destruction burst.
The reported coe?cients in tables A1, A2 and A3 are the ?
j
’s of equation (1.1).
They account for the conditional expected values of the adjustments in capital and
employment and the levels of energy, materials, output and productivity in the time
window composed by the two periods before and two periods after the episode of
large adjustment in capital and employment.
We should expect a statistically signi?cant coe?cient on capital and employ-
ment growth around the spikes of the opposite factor if there is an interrelation
between capital and labor adjustment. Also, if there is smooth adjustment, we
should observe a constant increase or decrease in the coe?cients before or after the
episodes; in contrast, lumpy adjustment would be seen as jumps in these coe?-
cients. If there is evidence of a disruption cost, we expect productivity and output
to decrease after the spikes.
In fact, as expected, the most relevant facts drawn from the tables A1, A2
and A3 are that there is interrelation in the adjustment, that there is evidence of
disruption costs, especially after capital adjustments and that ?rms adjust with mix
120
Table A1. Conditional Expected Values during Investment spikes episodes
I/K ?L/L log
log(k) log(L) log(E) log(M) log(TFP)t+2 0.092 0.003 0.043 0.384 0.044 0.033 0.045 -0.107
(0.013)** 0.005 (0.009)** (0.014)** (0.007)** (0.010)** (0.009)** (0.008)**
t+1 0.195 0.008 0.052 0.401 0.052 0.026 0.05 -0.107
(0.014)** 0.005 (0.010)** (0.015)** (0.008)** (0.011)* (0.010)** (0.009)**
I/K spike 0.615 0.026 0.052 -0.262 0.052 0.014 0.061 0.088
t (0.014)** (0.005)** (0.010)** (0.015)** (0.007)** 0.011 (0.010)** (0.009)**
t-1 -0.071 0.008 0.036 -0.204 0.025 -0.001 0.05 0.071
(0.014)** 0.005 (0.009)** (0.015)** (0.007)** -0.011 (0.010)** (0.009)**
t-2 -0.021 0.003 0.013 -0.167 0.013 -0.02 0.026 0.052
-0.013 0.005 0.009 (0.015)** 0.007 -0.011 (0.010)** (0.009)**
Obs. 20093 27835 26578 27946 28068 28132 26060 24410
R
2
0.13 0.01 0.18 0.25 0.03 0.08 0.23 0.1
Standard errors in parentheses* signi?cant at 5%; ** signi?cant at 1%
of smooth and lumpy adjustment. These coe?cients are particular for the episodes
of capital and employment spikes, but the analysis in the main text supports the
results found here
Table A2. Conditional Expected Values during Employment growth spikes
I/K ?L/L log
log(k) log(L) log(E) log(M) log(TFP)t+2 0.006 -0.012 -0.054 -0.068 -0.123 -0.06 -0.05 0.017
0.005 (0.003)** (0.007)** (0.012)** (0.005)** (0.008)** (0.008)** (0.007)**
t+1 0.01 -0.024 -0.037 -0.066 -0.166 -0.05 -0.024 0.034
0.005 (0.003)** (0.007)** (0.011)** (0.005)** (0.008)** (0.007)** (0.007)**
L spike=t 0.042 0.34 0.058 -0.045 0.175 0.019 0.058 0.014
(0.005)** (0.003)** (0.007)** (0.011)** (0.005)** (0.008)* (0.007)** (0.007)*
t-1 0.035 -0.023 0.075 0.035 0.13 0.041 0.076 0.008
(0.005)** (0.003)** (0.007)** (0.011)** (0.005)** (0.008)** (0.007)** -0.007
t-2 0.016 -0.008 0.074 0.093 0.11 0.037 0.07 -0.002
(0.005)** (0.003)** (0.007)** (0.012)** (0.005)** (0.008)** (0.008)** -0.007
Obs. 19770 27800 26578 27946 28068 28132 26060 24410
R
2
0.03 0.43 0.19 0.19 0.16 0.09 0.24 0.09
Standard errors in parentheses* signi?cant at 5%; ** signi?cant at 1%
121
Table A3. Conditional Expected Values during Negative Employment growth
spikes
I/K ?L/L log
log(k) log(L) log(E) log(M) log(TFP)t+2 0.002 0.005 0 0.005 0.086 0.019 0.013 -0.028
0.005 0.003 0.007 0.012 (0.005)** (0.008)* 0.008 (0.007)**
t+1 0 0.016 -0.02 0.027 0.124 0.009 -0.01 -0.053
0.006 (0.003)** (0.007)** (0.012)* (0.005)** 0.008 -0.008 (0.007)**
-L spike -0.017 -0.36 -0.11 0.036 -0.243 -0.07 -0.103 -0.026
t (0.006)** (0.003)** (0.007)** (0.012)** (0.005)** (0.009)** (0.008)** (0.007)**
t-1 -0.02 0.033 -0.101 0.005 -0.176 -0.078 -0.107 -0.019
(0.006)** (0.003)** (0.007)** -0.012 (0.005)** (0.009)** (0.008)** (0.007)**
t-2 -0.006 0.015 -0.087 -0.034 -0.139 -0.071 -0.084 -0.011
-0.006 (0.003)** (0.008)** (0.013)** (0.006)** (0.009)** (0.008)** -0.007
Obs. 19770 27800 26578 27946 28068 28132 26060 24410
R
2
0.02 0.42 0.19 0.18 0.17 0.09 0.24 0.09
Standard errors in parentheses* signi?cant at 5%; ** signi?cant at 1%
122
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