Labor Study on Labor reallocation, Productivity and Output Volatility in Japan

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Productivity has many benefits. At the national level, productivity growth raises living standards because more real income improves people's ability to purchase goods and services, enjoy leisure, improve housing and education and contribute to social and environmental programs.

ABSTRACT
Title of dissertation: LABOR REALLOCATION, PRODUCTIVITY
AND OUTPUT VOLATILITY IN JAPAN
Naomi N. Gri?n, Doctor of Philosophy, 2005
Dissertation directed by: Professor John Haltiwanger
Department of Economics
The dissertation o?ers an analysis of the labor reallocation process in Japan and sheds
light on its relationship with productivity and output volatility during the 1990s, the period of
sluggish growth. The ?rst chapter provides descriptive statistics of job reallocation rates among
relatively large Japanese ?rms. The main results show that job reallocation follows a steady
decline in volatility between 1967 and 1997 and exhibits little deviation from its long-run trend in
the 1990s. At the same time, the idiosyncratic e?ects of job reallocation appear to counteract the
sectoral/aggregate e?ects during the 1990s in the manufacturing sector. Finally, the contribution
of net entry to overall productivity growth has decreased during this period, mainly through exits
by relatively productive ?rms.
The second chapter investigates the labor input and inventory responses to demand shocks
in both the Japanese manufacturing sector as a whole, and the Iron and Steel industry. The main
results show that ?rst, demand shocks increased in volatility after 1992 in both the manufacturing
sector and the Iron and Steel industry. Second, for the manufacturing sector, the adjustment
mechanism shifted from an intensive use of inventories to more of a reliance on employment and
work hours after 1992. Finally, for the Iron and Steel industry, the employment and inventory
adjustments do not exhibit any systematic changes while the work hour adjustment has become
more intense since 1992.
The third chapter provides a theoretical examination of the impact of the Employment Ad-
justment Subsidy (EAS). A partial equilibrium industry model with heterogeneous establishments
and aggregate uncertainty shows that the EAS lowers labor productivity, while reducing job ?ows
and increasing average ?rm-level employment. While the directly measured impact on productiv-
ity is proportional to the fraction of subsidized workers, the indirect e?ects of the subsidy on output
and employment volatility can be substantially larger. The subsidy can lead to a sizable increase
in output ?uctuations over the business cycle by symmetrically increasing the output response to
shocks, while still meeting its primary objective of reduced employment volatility.
LABOR REALLOCATION, PRODUCTIVITY
AND OUTPUT VOLATILITY IN JAPAN
by
Naomi N. Gri?n
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
2005
Advisory Committee:
Professor John Haltiwanger, Chair/Advisor
Professor John Shea, Advisor
Professor Michael Pries, Advisor
c Copyright by
Naomi N. Gri?n
2005
FOREWORD
Chapter 1 of the dissertation, entitled “Evaluation of the Reallocation Mechanism during
the ‘Lost Decade’ of the 1990s,” represents joint work between Naomi Gri?n and Kazuhiko Odaki
at the Financial Services Agency of the Japanese government. Naomi’s examining committee has
determined that she has made a substantial contribution to this joint work. This work is included
in this thesis with the approval of Prof. John Haltiwanger, the chair of Naomi’s dissertation
committee, and of Prof. John Shea, a member of Naomi’s committee and the Director of Graduate
Studies for the Department of Economics.
ii
This dissertation is dedicated to Ed.
ACKNOWLEDGMENTS
I would like to express my profound gratitude to my advisors, Prof. John Haltiwanger,
Prof. John Shea and Prof. Michael Pries, for their faith and con?dence in me, and their support
and encouragement which has been tremendously important for the completion of this thesis. I
want to thank Prof. John Haltiwanger for providing direction, guidance, and inspiring my thesis
topic, Prof. John Shea for generously sharing his creativity in approaching and solving economic
problems, and meticulously reviewing and commenting on earlier versions of these papers, and
Prof. Michael Pries for guiding me towards a topic in the initial stages of my dissertation and for
his generous assistance with technical problems.
I would also like to thank Prof. Je?rey Smith for his valuable suggestions, Prof. Kyoji
Fukao at Hitotsubashi University for providing the JIP database, and the sta? at the Employment
Security Bureau of Japanese Ministry of Health, Labor and Welfare for preparing the information
on the Employment Adjustment Subsidy. I would also like to thank my friends, Ana Maria Oviedo,
Akie Takeuchi, Andri Chassamboulli and Ariko Oka, for their friendship and many valuable and
honest suggestions, and my former professors, Prof. Makoto Nagawara for pushing me to pursue
an advanced degree and Prof. Cristino Arroyo for introducing me to the ?eld of economics.
Lastly, I would like to thank my father and mother, Otomatsu and Yasumi Nakaguchi, for
always encouraging me to pursue my goals and be proud of who I am, my father- and mother-
in-law, Jerry and Linda Gri?n, for their understanding, unconditional love and support, and my
husband, Edward Gri?n, for being supportive, always believing in me, and not complaining (too
much) during this long process.
iv
TABLE OF CONTENTS
List of Tables vi
List of Figures viii
1 Evaluation of the Reallocation Mechanism during the ‘Lost Decade’ of the 1990s 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Description of the Dataset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.3 Job Reallocation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.4 Productivity Decomposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2 Input and Output Responses to Demand Shocks using an Interrelated Factor Demand Model 21
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.2 Description of the Interrelated Factor Demand Model . . . . . . . . . . . . . . . . 26
2.3 Description of the Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.4.1 Manufacturing Sector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.4.2 Iron and Steel Industry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3 Labor Adjustment, Productivity and Output Volatility: An Evaluation of Japan’s Employ-
ment Adjustment Subsidy 47
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.2.1 Summary of the EAS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.2.2 Overview of the Iron and Steel Industry . . . . . . . . . . . . . . . . . . . . 57
3.3 An Industry Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
3.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
3.4.1 Basic Setup and Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
3.4.2 Stationary Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
3.4.3 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
3.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
A Construction of Variables using the Nikkei Financial Dataset 94
B Examination of the Impact of Higher Volatility of Shocks on Subsidy Applications 95
C Industry Correspondence used for the Construction of the Demand Instrument 99
Bibliography 101
v
LIST OF TABLES
1.1 Descriptive statistics of ?rm level employment in the Nikkei ?nancial dataset for
1965?1997, for all ?rms, entering ?rms and exiting ?rms. . . . . . . . . . . . . . . 7
1.2 Correlation matrix of the various measures of job reallocation in the manufacturing
sector for 1965?1997. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.3 Correlation matrix of the various measures of job reallocation in the non-manufacturing
sector for 1965?1997. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.4 Variance decomposition results for the manufacturing and the non-manufacturing
sector for 1967?1997, based on two-digit and three-digit Nikkei industry classi?cations. 12
1.5 Productivity decomposition results for the manufacturing sector using labor pro-
ductivity and TFP for 1969?1996. . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.1 The estimates of the interrelated factor demand model in the manufacturing sector,
9-month forecast horizon. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.2 The estimates of the interrelated factor demand model in the manufacturing sector,
6-month forecast horizon. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.3 The estimates of the interrelated factor demand model in the manufacturing sector,
12-month forecast horizon. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.4 The estimates of the interrelated factor demand model in the Iron and Steel industry,
9-month forecast horizon. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.5 The estimates of the interrelated factor demand model in the Iron and Steel industry,
6-month forecast horizon. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.6 The estimates of the interrelated factor demand model in the Iron and Steel industry,
12-month forecast horizon. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
2.7 The estimates of the output elasticity with respect to demand shocks in the Iron
and Steel industry, 9-month forecast horizon. . . . . . . . . . . . . . . . . . . . . . 42
2.8 The estimates of the output elasticity with respect to demand shocks in the Iron
and Steel industry, 6-month forecast horizon. . . . . . . . . . . . . . . . . . . . . . 43
2.9 The estimates of the output elasticity with respect to demand shocks in the Iron
and Steel industry, 12-month forecast horizon. . . . . . . . . . . . . . . . . . . . . . 44
3.1 Share of subsidy bill by industries for 1990?2002. . . . . . . . . . . . . . . . . . . . 56
3.2 Parameter values used to obtain stationary distributions with annual frequency. . . 79
3.3 Summary statistics of stationary distributions without aggregate volatility: ? = 2.7. 84
3.4 Summary statistics of stationary distributions with aggregate volatility: ?
g
= 3.13,
?
b
= 2.27. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
vi
3.5 Summary statistics obtained from simulation exercises with low adjustment costs:
?
h
= 0.8, ?
f
= 0.8. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
3.6 Summary statistics obtained from simulation exercises with high adjustment costs:
?
h
= 1, ?
f
= 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
B.1 Parameter values used to obtain stationary distributions with monthly frequency. . 95
B.2 Summary statistics of stationary distributions with low and high aggregate volatility. 98
C.1 Concordance of industry classi?cations between JIP dataset, Indices of Industrial
Production (METI), and CGPI. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
vii
LIST OF FIGURES
1.1 Annual job creation and job destruction rate (in percentage) in the manufacturing
sector calculated using the Nikkei ?nancial dataset for 1965?1997. . . . . . . . . . 9
1.2 Annual job creation and job destruction rate (in percentage) in the non-manufacturing
sector calculated using the Nikkei ?nancial dataset for 1965?1997. . . . . . . . . . 9
2.1 Monthly series on shipments, employment, work hours and inventories (in logs)
in the manufacturing sector for January 1978?November 2004. Data source: the
original series of shipment and inventory indices are taken from Indices of Industrial
Production while the data on employment and work hours for establishments with
more than 30 employees are taken from Monthly Labor Statistics. . . . . . . . . . . 31
2.2 Monthly series on shipments, employment, work hours and inventories (in logs) in
the Iron and Steel industry for January 1978?November 2004. Data source: the
original series of shipment and inventory indices are taken from Indices of Industrial
Production while the data on employment and work hours for establishments with
more than 30 employees are taken from Monthly Labor Statistics. . . . . . . . . . . 36
2.3 Monthly series on the demand instrument in the Iron and Steel industry for January
1978?November 2004. Data source: JIP database, Indices of Industrial Production
and CGPI. See the text for the construction method used. . . . . . . . . . . . . . 41
3.1 Annual total subsidy bill (in billions of yen) by three types of activities for 1975?2001.
Data source: the Employment Security Bureau of Japanese Ministry of Health, La-
bor and Welfare. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.2 Annual real gross output in the Iron and Steel industry (in billions of yen). Data
source: JIP database. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3.3 Annual employment in the Iron and Steel industry (in thousands), which include
both permanent and temporary workers for all establishments with more than ?ve
employees. Data source: Employment Trend Survey. . . . . . . . . . . . . . . . . 58
3.4 Estimated annual number of workers who are unutilized for production via EAS in
the Iron and Steel industry. Data source: the information on subsidy was provided
by the Employment Security Bureau of the Japanese Ministry of Health, Labor and
Welfare. Other data used for the estimation is provided in the text. . . . . . . . . 60
3.5 TFP (1990?2001) in the Iron and Steel industry. Data source: Annual Report on
National Account for the output and capital stock, Employment Trend Survey for
annual employment, and Monthly Labor Statistics for average work hours. See the
text for the estimated annual number of subsidized workers. . . . . . . . . . . . . . 61
3.6 TFP (1973?1998) in the Iron and Steel industry. Data source: the JIP database for
the output and capital stock, Employment Trend Survey for annual employment,
and Monthly Labor Statistics for average work hours. See the text for the estimated
annual number of subsidized workers. . . . . . . . . . . . . . . . . . . . . . . . . . . 62
3.7 Employment decision rule. It shows the optimal choice of employment given the
previous level of employment. The diagonal line represents the circumstance in
which employment remains the same. . . . . . . . . . . . . . . . . . . . . . . . . . . 66
viii
3.8 Employment and production decision rule for an unsubsidized ?rm. Since e
t
is
constrained to be less than n
t
, this represents the circumstance in which the subsidy
take-up does not take place. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
3.9 Employment and production decision rule for a subsidized ?rm. Firms apply when
the optimally chosen e
t
is strictly below n
t
. . . . . . . . . . . . . . . . . . . . . . . 67
3.10 Optimal subsidy coverage. This graph shows the distance between n
t
and e
t
in
?gure (3.9) for n
t
strictly greater than e
t
. . . . . . . . . . . . . . . . . . . . . . . . 68
3.11 EV vs. ?ring costs. Firms decide to exit from the market when the expected loss of
staying in the market is greater than the cost of ?ring its entire workforce. EV (2)
corresponds to a higher level of pro?tability shock compared to EV (1). . . . . . . 75
3.12 Cumulative distribution functions of three stationary distributions. The solid line
shows the cdf of ?rm level employment when the subsidy is set equal to zero. The
dashed line shows the cdf of employment when the subsidy is set equal to 2/3 of
wage. The dotted line shows the stationary distribution in terms of utilized workers
when subsidy is set equal to 2/3 of wage. . . . . . . . . . . . . . . . . . . . . . . . 86
B.1 Subsidy application decision rules with volatility for the good aggregate state. The
higher number of volatility measures indicates higher volatility and the higher num-
ber of idiosyncratic shocks represents more favorable conditions. . . . . . . . . . . 96
B.2 Subsidy application decision rules with volatility for the bad aggregate state. The
higher number of volatility measures indicates higher volatility and the higher num-
ber of idiosyncratic shocks represents more favorable conditions. . . . . . . . . . . 97
ix
Chapter 1
Evaluation of the Reallocation Mechanism during the ‘Lost Decade’ of the 1990s
1.1 Introduction
This chapter provides descriptive statistics that highlight the labor reallocation mechanism,
a critical component for understanding the business cycle, in Japan. In particular, we use a
?rm level dataset (the Nikkei ?nancial dataset) to investigate the annual rates of job creation and
destruction between 1965 and 1997 among relatively large, publicly traded ?rms. The primary
interest of this exercise is to investigate the characteristics of job reallocation during the 1990s, a
period of sluggish economic growth, relative to other periods. In addition, we conduct productivity
decomposition exercises to examine if the cleansing e?ect of recessions (i.e. downsizing/exit of the
least productive ?rms) was in place during the ?rst half of the 1990s. The main results show that
job reallocation, the sum of job creation and job destruction, follows a steady decline in volatility
between 1967 and 1997. We conjecture that this is associated with a decline in the trend employ-
ment growth rate, as job reallocation dynamics in Japan are mainly creation driven. Whereas
the job reallocation rate exhibited little deviation from its long-run trend in the 1990s, we observe
that the dominance of the idiosyncratic component relative to the sectoral/aggregate component
in explaining overall reallocation dynamics declines during the 1990s in the manufacturing sector.
The idiosyncratic e?ects also appear to counterbalance the sectoral/aggregate e?ects during this
period. Finally, the productivity decomposition exercises reveal that the contribution of net entry
to overall productivity growth has decreased in recent years. In particular, exit by relatively
productive ?rms constitute this reduction in the contribution of net entry.
The 1990s marked the ?rst decade of sluggish economic growth for the Japanese economy
since the end of the Second World War. The deterioration of Japan’s economic performance,
which persisted over a decade, has interested many macroeconomists, yet not enough evidence has
1
been unmasked to generate a consensus regarding the factors that have contributed to the lengthy
recovery. The early stage of the preceding discussion centered around policy failures in the area
of demand management, notably highlighted by a “liquidity trap” hypothesis or “credit crunch”
problem. However, formal evidence in support of these hypothesis has not yet been found.
The proponents of the “liquidity trap” hypothesis claim that the monetary authority’s
inability to stimulate investment by lowering interest rates, or consumer spending by creating
in?ationary expectations, unnecessarily prolonged the recovery phase. On the other hand, the
“credit crunch” hypothesis speculates that the poor ?nancial condition among many Japanese
banks was leading to the banks’ reduced lending to pro?table projects, thereby contributing to
lower investment. However, Motonishi and Yoshikawa (1999), using the Bank of Japan di?usion
indices of “real pro?tability” and “banks’ willingness to lend,” ?nd that except for 1997 when the
government ?nally allowed some big banks to fail, drops in investment were unrelated to banks’
willingness to lend and were mainly driven by a fall in real pro?tability.
1
Furthermore, using
growth accounting, Hayashi and Prescott (2002) argue that the economic stagnation during the
1990s in Japan is largely explained by a fall in exogenous TFP growth.
More recent literature identi?es the reallocation issue as the primary problem. For example,
Peek and Rosengren (2003) ?nd the evidence of misallocation of credit by Japanese banks as
they engaged in “evergreening” loans. Namely, they claim that ?nancially troubled ?rms were
more likely to obtain further loans from banks than their healthier counterparts during the 1990s,
as banks sought to manipulate their balance sheets by making ?nancially troubled ?rms look
arti?cially solvent. Likewise, using stock returns, Hamao, Mei and Xu (2003) suggest that there
was a lack of resource reallocation in Japan during the 1990s. In particular, when a ?rm’s
idiosyncratic risk is measured as the deviation of its stock return from the average response to
the market rate, they show that the role of idiosyncratic risk in explaining the total time-series
volatility of ?rm stock returns decreased during the 1990s. Consequently, they point out that
this apparent increase in homogeneity of corporate performance may have hindered the ability of
1
Woo (1999) ?nds similar results.
2
investors and managers to distinguish high quality ?rms from low quality ?rms, and discouraged
capital formation.
These ?ndings indicate that misallocation, or the lack of reallocation, may provide us with
a better understanding of the problem. In fact, a considerable amount of research relates real-
location to economic performance and growth over the business cycle. The theoretical aspects
of the literature often focus on Schumpeter’s idea of “creative destruction.” Aghion and Howitt
(1992), for instance, construct an endogenous growth model in which old technology is immedi-
ately destroyed with the emergence of new technology, thereby constituting the underlying engine
of economic growth through the introduction of a competitive research sector that generates ver-
tical innovations. In a similar spirit, Caballero and Hammour (1994, 1996) created a model in
which only entering ?rms have access to the latest vintage of capital, and therefore the destruction
of ?rms with old vintages facilitates the ?ow of new entries and is productivity enhancing.
On the empirical front, Davis and Haltiwanger (1992) and Davis, Haltiwanger and Schuh
(1996) have demonstrated, using a longitudinal plant level dataset from the US manufacturing
sector, that recessions are associated with volatile job reallocation as a result of excessive job
destruction compared to job creation, and much of the variation in job reallocation is explained
by the idiosyncratic component. Consequently, the empirical study in this chapter looks at the
reallocation aspect of Japanese ?rms’ performance during the recessionary years. In particular,
we highlight the job reallocation process among relatively large, publicly traded ?rms.
2
The Nikkei ?nancial dataset between 1964 and 1997 shows that the variation in the job
reallocation rate has been declining during this period. This is because job creation plays the
largest role in driving job reallocation dynamics in Japan, and variation in job creation declined
over time as the trend employment growth rate declined. Moreover, we do not observe any obvious
changes to the declining trend of job reallocation during the 1990s. While there is a mild increase
2
The studies on the characteristics of job reallocation in Japan are limited primarily due to a lack of a dataset
as comprehensive as the Longitudinal Research Database used by Davis and Haltiwanger (1992), and as a result,
an in-depth cross-country comparison with the facts on the reallocation activities of the U.S. manufacturing sector
has not yet been possible.
3
in the job destruction rate during the 1990s, it was o?set by a reduction in the job creation rate of
a similar magnitude. As a result, in contrast to what one might expect given evidence from the
US manufacturing sector, the dramatic and persistent reduction in the growth rate which started
in 1992 was not accompanied by a sudden rise in the job reallocation rate. These results are
observed in both the manufacturing and the non-manufacturing sector, but relatively speaking,
the role of job destruction is even smaller in the non-manufacturing sector when compared to the
manufacturing sector.
The general ?nding is consistent with a study done by Genda (1998), which computes job
creation and destruction rates during the ?ve-year interval between 1991 and 1995 for continuing
establishments from the Employment Trend Survey.
3
He emphasizes the relatively large role
played by job creation in driving reallocation dynamics during this period of economic downturn,
thereby highlighting potential di?erences in the labor adjustment mechanism between the U.S.
and Japan in response to negative shocks.
4
While we do not observe any major change in the long-run trend of the variation in the
job reallocation rate during the 1990s, the characteristics of the components comprising job real-
location changed dramatically during the 1990s in the manufacturing sector. More speci?cally,
we decompose job reallocation rates into an idiosyncratic component and a sectoral/aggregate
component in order to examine the relative importance of these two components in explaining the
overall variation of job reallocation. The results show that, in the manufacturing sector, the rel-
ative dominance of the idiosyncratic component over the sectoral/aggregate component declined
in the 1987?1997 period. This result is similar to the ?nding by Hamao, Mei and Xu (2003)
that heterogeneity in corporate performance as measured by stock returns declined during the
1990s. Furthermore, the correlation between the idiosyncratic and the sectoral/aggregate compo-
3
The approximate number of sample establishments of the survey used in Genda (1997) varies from 10,000 to
12,000 each year.
4
Although Foote (1998) shows that the relative importance of job destruction as opposed to job creation in
driving cyclical dynamics can depend on employment trend growth, it seems that the di?erence in trend growth
rates alone cannot explain the low job reallocation in Japan during the 1990s.
4
nent was signi?cantly negative in the period 1987?1997. Similar changes were not observed in
the non-manufacturing sector.
Finally, we conduct productivity decomposition exercises to examine whether or not the
cleansing e?ect of recessions was taking place via downsizing and exits by ine?cient ?rms. Foster,
Haltiwanger and Krizan (1998) show that, in the US manufacturing sector, the contribution of
reallocation in explaining aggregate productivity growth through the replacement of relatively
ine?cient establishments by more productive ones is signi?cant, and entry/exit dynamics play an
important role. Similar exercises done for Japanese manufacturing ?rms using the Nikkei ?nancial
dataset show that while some downsizing of ine?cient ?rms took place and contributed to overall
productivity growth between 1988 and 1997, the contribution of net entry is weak during this
period. In particular, the TFP growth decomposition shows that exit of ine?cient ?rms is not
observed during this period. Thus, the overall results indicate rather slow reallocation dynamics
among large Japanese ?rms during the 1990s prior to 1997. The observed lack of exit among
the least e?cient ?rms match the ?nding by Peek and Rosengren (2003) that banks deliberately
helped ?nancially troubled ?rms to stay in business.
1.2 Description of the Dataset
The main dataset used in this chapter is the Nikkei ?nancial dataset from 1964 to 1998. It
contains about 2500 relatively large non?nancial ?rms, and the primary advantage of the dataset
is that it allows us to examine changes in reallocation dynamics over time. Firms included are
those that are listed on the Tokyo Stock Exchange, JASDAQ and other regional stock markets,
leading unlisted companies submitting ?nancial reports to the Ministry of Finance, and other
leading unlisted companies that are not included in the above mentioned categories but submit
reports to their shareholders. The dataset has ?nancial as well as employment data, with some
corporate information.
The dataset is an unbalanced panel, in which 70% of the 78,670 observations are based on
annual reports while the remainder are mostly based on semi-annual reports. The number of ?rms
5
covered in the dataset increases over time, as the number of entries into the dataset are much larger
than the number of exits from the dataset. There are two unusually large ?ows of entries into the
dataset in 1965 and 1970. The increase in 1965 is likely to be associated with part of the initial
data collection process, while the increase in 1970 is related to the inclusion of ?rms listed on other
stock markets.
5
Firms in the dataset are classi?ed according to their Nikkei industry classi?cation,
which does not always clearly match the standard government classi?cation. Industry categories
excluded in this dataset are banks, investment banks, and insurance companies.
6
Table (1.1) provides descriptive statistics of ?rm level employment in the Nikkei ?nancial
dataset. Note that the ?gures correspond to the average of the annual statistics in each time
interval. Also, the annual average employment ?gure is used for ?rms which submit reports semi-
annually. The top part of the table gives descriptive statistics of the entire dataset. As we can
see, the average ?rm size in terms of employment falls while the average number of ?rms increases
over time, most likely re?ecting the incorporation of smaller size ?rms, or the spin o? of divisions
into separate business entities.
The middle part of the table gives the descriptive statistics of ?rm level employment for
entering ?rms only. Note that entry into the dataset does not necessarily imply entry into the
market, but rather has more to do with being listed on a stock exchange. The privatization of
Nippon Telegraph and Telephone (NTT) in 1986 as well as Japan Railway (JR) in 1988 generate
a signi?cant jump in the average size and standard deviation of entering ?rms for the period
1985?1989. The bottom part of the table identi?es statistics for ?rms that dropped from the
dataset. Again, dropping from the dataset does not necessarily mean exit from the market, as
it could imply either bankruptcy, merger, or restructuring as a private entity. Compared to the
number of entering ?rms, the average number of ?rms that exit from the dataset is relatively
5
Only ?rms listed on the Tokyo Stock Exchange (TSE) were included in 1964. Firms listed on Osaka and Nagoya
stock exchanges were incorporated in 1970, other listed ?rms from smaller regional stock markets were incorporated
in 1975, and leading unlisted companies submitting ?nancial report to the Ministry of Finance or reports to their
shareholders were added in 1977.
6
131 out of 140 three-digit industries and 32 out of 36 two-digit industries, according to their Nikkei classi?cation,
are included in the dataset.
6
Table 1.1: Descriptive statistics of ?rm level employment in the Nikkei ?nancial dataset for
1965?1997, for all ?rms, entering ?rms and exiting ?rms.
Average Average
Average standard Average Average number of
Period Mean median deviation minimum maximum ?rms
A. Entire dataset
1965?1969 2616 1051 5675 24 80870 1406
1970?1974 2590 1018 6017 24 86566 1696
1975?1979 2333 888 5486 10 77344 1853
1980?1984 2116 801 5031 12 73732 2042
1985?1989 2173 773 7423 7 249295 2195
1990?1997 2220 812 6992 6 223009 2344
B. Entering ?rms
1965?1969 665 394 790 48 3503 41
1970?1974 1181 456 1969 85 7256 66
1975?1979 662 439 864 33 6381 58
1980?1984 502 341 506 43 2323 34
1985?1989 3052 261 13429 25 79276 38
1990?1997 657 472 613 194 1822 18
C. Exiting ?rms
1965?1969 5167 4773 3806 2752 8348 3
1970?1974 1809 951 2800 196 8651 7
1975?1979 786 399 796 181 2174 6
1980?1984 709 537 843 58 2291 7
1985?1989 1100 500 1672 93 4297 5
1990?1997 1094 800 1089 294 2978 6
small.
Since entries and exits into the dataset may not be related to the state of the economy,
employment growth rates constructed with the Nikkei dataset with and without entries/exits are
compared with the employment growth rates given by the Labor Force Survey, which includes
employment for the entire economy.
7
The correlation between the two is 0.5089 when all entering
and exiting ?rms are excluded from the calculation, and falls to 0.4742 when they are included.
There are exceptionally large ?ow of entries in 1965, 1970, 1977 and 1978. Moreover, the privati-
7
The time series employment data from Labor Force Survey is available at the following website:
http://www.stat.go.jp/data/roudou/longtime/03roudou.htm. Total employment growth is constructed using the
‘total number of employees’ from Table 1.
7
zation of NTT in 1986 and JR in 1988 a?ects the employment growth rate of the Nikkei dataset
signi?cantly. When those entries are excluded from the computation while including other en-
tries/exits, the correlation goes up slightly to 0.5053. Therefore, we will employ this adjustment
with entries and exits incorporated for our analysis of job reallocation.
Finally, out of 2531 ?rms with employment data, approximately 59% belong to ‘Manu-
facturing’, 16% to ‘Wholesale, Retail Trade, Eating and Drinking Places’, 8% to ‘Construction’,
5.5% to ‘Transport and Communication’, 6.5% to ‘Service’, and 3.5% to ‘Financing, Insurance
and Real Estate’.
8
The examination of ?rm level job reallocation will be executed for both the
manufacturing sector (1487 ?rms) and the non-manufacturing sector (1044 ?rms). Productivity
decomposition exercises are only done for the manufacturing sector, however, since the sectoral
de?ators provided by the Bank of Japan (CGPI) are available only for manufacturing industries.
1.3 Job Reallocation
The annual job creation, job destruction and job reallocation rates are constructed following
Davis and Haltiwanger (1992) and Davis, Haltiwanger and Schuh (1996):
JC
t
=
I
t

i,g
it>0
(E
it
/E
t
)g
it
, JD
t
=
I
t

i,g
it<0
(E
it
/E
t
)g
it
, and JR
t
= JC
t
+JD
t
(1.1)
where I
t
is the total number of ?rms at time t, g
it
= (E
it
?E
it?1
) /E
it
, E
it
= (E
it
+E
it?1
) /2
and E
it
is employment of ?rm i at year t. Also note that the average ?gures of employment for
each year are used for ?rms that submit reports semi-annually.
Figure (1.1) and ?gure (1.2) show the percentage rates of job creation and job destruction
for ?rms in the manufacturing and non-manufacturing sectors between 1965 and 1997.
9
Both
?gures show a larger share of variability arising from job creation before the mid-1970s. Job
destruction is particularly stable relative to job creation in the non-manufacturing sector. The
larger role of job creation in driving job reallocation dynamics in this sector may be attributed to
8
There are also very small number of ?rms which belong to ‘Fisheries’, ‘Mining’, and ‘Electricity, Gas, Heat and
Water Supply’.
9
Note that observations from the ?rst year (1964) and the last year (1998) of the dataset are not used for the
analysis as the data appears to be incomplete in these years.
8
0
1
2
3
4
5
6
7
8
1965 1970 1975 1980 1985 1990 1995
Job creation rate Job destruction rate
Figure 1.1: Annual job creation and job destruction rate (in percentage) in the manufacturing
sector calculated using the Nikkei ?nancial dataset for 1965?1997.
0
1
2
3
4
5
6
7
1965 1970 1975 1980 1985 1990 1995
Job creation rate Job destruction rate
Figure 1.2: Annual job creation and job destruction rate (in percentage) in the non-manufacturing
sector calculated using the Nikkei ?nancial dataset for 1965?1997.
9
the sectoral employment trend growth rate which is higher in the non-manufacturing sector than
the manufacturing sector, as described by Foote (1988).
Table 1.2: Correlation matrix of the various measures of job reallocation in the manufacturing
sector for 1965?1997.
JC
t
JD
t
JR
t

JR
t
JR
t
?

JR
t
JC
t
?JD
t
JC
t
1.000
JD
t
-0.506 1.000
JR
t
0.747 0.195 1.000

JR
t
0.735 0.142 0.945 1.000
JR
t
?

JR
t
0.456 0.229 0.695 0.423 1.000
JC
t
?JD
t
0.917 -0.808 0.420 0.436 0.206 1.000
Table 1.3: Correlation matrix of the various measures of job reallocation in the non-manufacturing
sector for 1965?1997.
JC
t
JD
t
JR
t

JR
t
JR
t
?

JR
t
JC
t
?JD
t
JC
t
1.000
JD
t
-0.397 1.000
JR
t
0.878 0.091 1.000

JR
t
0.741 0.128 0.871 1.000
JR
t
?

JR
t
0.569 -0.026 0.604 0.135 1.000
JC
t
?JD
t
0.938 -0.691 0.658 0.536 0.458 1.000
Table (1.2) and (1.3) show the correlation matrix of the various measures of job reallocation
in the manufacturing and the non-manufacturing sector, respectively, between 1965 and 1997. As
expected, JR
t
has a higher correlation with JC
t
than JD
t
, and this pattern is much stronger
for the non-manufacturing sector. JC
t
and JD
t
are negatively correlated, but the correlation is
stronger for the manufacturing sector. Furthermore, as a result of higher volatility in job creation,
job reallocation (i.e. JC
t
+ JD
t
) and net job creation (i.e. JC
t
?JD
t
) are positively correlated:
the correlation is 0.42 for the manufacturing sector and 0.66 for the non-manufacturing sector.
As mentioned earlier, this evidence is consistent with Genda (1997) for continuing establishments
10
between 1991 and 1995, while it stands in contrast with the evidence from the U.S. manufacturing
sector that job destruction is more volatile than job creation and that, therefore, job reallocation
moves countercyclically.
10
Next, following Davis and Haltiwanger (1990, 1992), the job reallocation rate, which is the
sum of the job creation and destruction rates, is decomposed into a sectoral/aggregate component
and an idiosyncratic component to examine their relative importance in driving the time variation
of job reallocation. Let g
it,i?j
be the employment growth rate of ?rm i in industry j at time t,
and decompose it in a linear fashion as g
it,i?j
= ¯ g
it
+g
jt
, where g
jt
is the employment growth rate
of sector j, and ¯ g
it
is the residual idiosyncratic component. The idiosyncratic component of job
reallocation is given by

JR
t
=
I
t

i
(E
it
/E
t
) | ¯ g
it
| . (1.2)
The sectoral/aggregate component of job reallocation is JR
t
?
¯
JR
t
. The correlation matrix table
shows that, both for manufacturing and non-manufacturing, the correlation of job reallocation
is higher with the idiosyncratic component than the sectoral/aggregate component for the entire
sample period.
Furthermore, using the identity JR
t
=

JR
t
+(JR
t
?

JR
t
), the variance of job reallocation
is decomposed as follows:
var(JR
t
) = var(

JR
t
) +var(JR
t
?

JR
t
) + 2cov(

JR
t
, JR
t
?

JR
t
) (1.3)
This decomposition allows us to identify the fraction of variation in job reallocation arising from
the variation in the idiosyncratic and sectoral/aggregate components, while controlling for the
covariance between the two. Table (1.4) gives the results for the variance decomposition exercise for
both the manufacturing and non-manufacturing sectors. The sample period is divided into three
10
Also, Motonishi and Tachibanaki (1999) use establishment level data for 1988, 1990 and 1993 from “Census of
Manufacturers,” which includes all establishments with more than four employees constructed by the Ministry of
International Trade and Industry, to calculate job creation and destruction rates and they ?nd that, during this
period of economic downturn, the reduction in job creation rate is more dramatic than the increase in the job
destruction rate. Job creation (destruction) rate is 6.16% (5.3%) for 1988?1990 and 4.23% (5.59%) for 1990?1993.
11
Table 1.4: Variance decomposition results for the manufacturing and the non-manufacturing sector
for 1967?1997, based on two-digit and three-digit Nikkei industry classi?cations.
Manufacturing Non-manufacturing
1967? 1977? 1987? 1967? 1977? 1987?
1977 1987 1997 1977 1987 1997
3-digit classi?cation
V ar(JR
t
) 3.984 0.370 0.057 1.429 0.269 0.134
Fraction of variance accounted for by
–Idiosyncratic e?ects 0.516 0.663 2.203 0.421 1.650 1.199
–Sectoral/aggegate mean e?ects 0.110 0.314 2.683 0.393 0.131 0.483
–Covariance e?ects 0.373 0.022 -3.886 0.186 -0.781 -0.682
2-digit classi?cation
V ar(JR
t
) 3.984 0.370 0.057 1.429 0.269 0.134
Fraction of variance accounted for by
–Idiosyncratic e?ects 0.514 0.885 2.723 0.597 1.289 1.289
–Sectoral/aggegate mean e?ects 0.112 0.317 2.668 0.186 0.093 0.539
–Covariance e?ects 0.374 -0.203 -4.391 0.217 -0.382 -0.827
sub-periods to track the change over time: 1967?1977, 1977?1987 and 1987?1997. Furthermore,
the sectoral growth rate, g
jt
, is measured both at the three-digit and two-digit level of the Nikkei
industry classi?cation. The results are similar for both the two- and three-digit classi?cations.
First, notice that the variance of the job reallocation rate declines over time. As mentioned
previously, this most likely relates to the decline in the trend growth rate over time, since job
reallocation in Japan has mostly been creation-driven.
The manufacturing sector experiences a signi?cant change in the 1987?1997 period. Prior to
this, the idiosyncratic component played a dominant role in the overall variation in job reallocation.
However, the 1987?1997 period is characterized by a smaller and equally signi?cant role for the
idiosyncratic component respectively, for the three-digit and the two-digit classi?cation. More
interestingly, the covariance between the idiosyncratic and the sectoral/aggregate components
became considerably negative during this period. The correlation between the two is ?0.80 for
the three-digit case and ?0.81 for the two-digit case, statistically signi?cant at the 1% level in
both cases. On the contrary, we do not observe any dramatic change for the non-manufacturing
12
sector during the 1987?1997 period. The relative dominance of idiosyncratic e?ects continues, and
unlike the manufacturing sector, the correlation between the idiosyncratic and sectoral/aggregate
e?ects is negative in all cases after 1977 as shown by the covariance terms. However, most of them
are statistically insigni?cant at the 10% level.
11
The decline in the relative dominance of the idiosyncratic component in the manufacturing
sector seems consistent with the ?nding by Hamao, Mei and Xu (2003) that the heterogeneity
of corporate performance measured in terms of idiosyncratic risks decreased during the 1990s, or
put di?erently, the aggregate market return has become increasingly important relative to idiosyn-
cratic risks in assessing ?rms’ stock returns. However, a similar change was not observed in the
non-manufacturing sector. The negative covariance term indicates that higher sectoral/aggregate
disturbances were associated with smaller idiosyncratic reallocation activity. Accordingly, the
idiosyncratic e?ects appear to “counteract the impact of aggregate and sectoral e?ects” on job
reallocation particularly in the manufacturing sector during the 1987?1997 period.
12
It will be
interesting to investigate the sources which resulted in this change, but this particular agenda is
merely noted here as a topic of future research.
1.4 Productivity Decomposition
Using plant level data from the Census of Manufactures, Foster, Krizan and Haltiwanger
(1998) show that reallocation of outputs and inputs across establishments as well as reallocation
through entry and exit play an important role in explaining aggregate productivity growth. In
this section, we conduct similar productivity decomposition exercises using the Nikkei ?nancial
dataset in order to explain productivity dynamics among relatively large Japanese ?rms.
Two types of decomposition exercises, following Foster, Krizan and Haltiwanger (1998), are
conducted. Denoting ?P
jt
as the productivity growth of industry j between t ? 1 (beginning
11
The only decomposition with statistically signi?cant correlation between the idiosyncratic and sec-
toral/aggregate e?ects is the three-digit level case for the 1977?1987 period. The correlation is 0.84.
12
Davis and Haltiwanger (1992), p.853.
13
period) and t (ending period), the ?rst decomposition is given by the following equation:
?P
jt
=

i?C
s
it?1
?p
it
+

i?C
(p
it?1
?P
jt?1
)?s
it
+

i?C
?s
it
?p
it
(1.4)
+

i?N
s
it
(p
it
?P
jt?1
) ?

i?X
s
it?1
(p
it?1
?P
jt?1
)
where s
i
is the share of ?rm i in industry j, p
i
and P
j
are the indices of productivity for ?rm and
industry respectively, and C, N and X indicate the set of continuing ?rms, entering ?rms and
exiting ?rms respectively. The second decomposition is given by
?P
jt
=

i?C
s
it
?p
it
+

i?C
(p
it
?P
jt
)?s
it
(1.5)
+

i?N
s
it
(p
it
?P
jt
) ?

i?X
s
it?1
(p
it?1
?P
jt
)
where a bar over a variable indicates the value averaged over t ?1 and t.
The ?rst term in both equation 1.4 and 1.5 shows contribution of the ‘within’ ?rm pro-
ductivity growth to aggregate productivity growth. On the other hand, the second term shows
the contribution arising from reshu?ing of inputs or outputs across ?rms, or the ‘between’ ?rm
e?ect. Here, the changes in shares are weighted in both cases by the deviation of ?rm produc-
tivity from the corresponding industry productivity index. The index in the ?rst decomposition
uses beginning period industry productivity, P
jt?1
, while the second decomposition uses industry
productivity averaged over the beginning and ending period. The last two terms represent the
contribution of entry and exit respectively. Note that a ?rm’s entry into the dataset raises ag-
gregate productivity when its productivity is above the industry productivity index. Likewise,
a ?rm’s exit from the dataset raises aggregate productivity when its productivity is below the
industry productivity index.
As we can see, the share weight used for the ‘within’ e?ect and the productivity weight used
for the ‘between’ e?ect in the second decomposition given by equation 1.5 are average ?gures and
therefore, the interaction e?ect between changes in share and changes in productivity is already
incorporated in the ?rst two terms, while the ?rst decomposition given by equation 1.4 explicitly
controls for this e?ect with the third ‘cross’ term. While the ?rst method provides a more
14
accurate decomposition, it is more sensitive to measurement errors as discussed in Foster, Krizan
and Haltiwanger (1998), and therefore, the results using both decomposition methods will be
presented.
13
Two types of productivity measures, labor productivity and total factor productivity (TFP),
are constructed for the decomposition exercises. Since the Nikkei dataset does not have information
on manhours, the labor productivity measure used here is the log di?erence of real gross output
and employment. Note that the real gross output ?gures were summed over each year when
?rms submit reports more than once a year, while the average employment ?gures are used for
these ?rms. Furthermore, since the industry level price indices used to de?ate gross output and
materials were available only for the industries within manufacturing, the decomposition exercises
are restricted to the manufacturing sector.
The index of TFP is measured simply as follows:
lnTFP
it
= lnY
it
??
M
lnM
it
??
L
lnL
it
?(1 ??
M
??
L
) lnK
it
(1.6)
where Y
it
is real gross output for ?rm i at year t, M
it
is real materials, L
it
is employment, K
it
is
the real capital stock, ?
M
is material’s share of total cost, and ?
L
is labor’s share of total cost.
14
Detailed explanations of the construction of real gross output, real materials, and real capital stock
using the Nikkei ?nancial dataset are provided in the appendix.
Note that the notations for the material cost share ?
M
and the labor cost share ?
L
are
simpli?ed here, as the shares actually used vary across three-digit Nikkei industry classi?cations,
although not over time. The material and labor cost shares are ?rst calculated at the ?rm level
by a taking simple average across time, and are then aggregated at the industry level using the
?rm level mean employment as a weight. When aggregated across all ?rms in the dataset, the
13
For instance, a measurement error in labor input generates spuriously high negative correlation between the
change in share and labor productivity growth. This, in turn, raises the ‘within’ e?ect. Similarly, a measurement
error in output, in the case of conducting decomposition with TFP for instance, generates a spuriously high positive
correlation between the change in share and TFP growth. This reduces the ‘within’ e?ect. Since the second
method uses the average ?gures, it is less sensitive to this type of measurement error.
14
Again, material input values are summed over a year for ?rms which submit reports more than once a year.
15
material cost share is 67.5%, while the labor cost share is about 16.1% and the capital cost share
is about 16.4%.
The time horizon over which we investigate productivity growth is set between 8 to 10
years. This time horizon indicates the distance between the subscript t and the subscript t ?1 in
equations 1.4 and 1.5. Accordingly, the analysis decomposes productivity growth dynamics over
the long-run. Ideally, the starting period and the ending period should encompass the full business
cycle. This allows us to compare the results across di?erent time periods while avoiding short-run
business cycle e?ects on productivity. Hence, we divided the entire productivity series into three
sub-periods based on the following business cycle considerations: 1) a high growth period (from
the peak of 1969 to the peak of 1979), 2) the bubble economy period (from the peak of 1979 to
the peak of 1988) and 3) the sluggish growth period (from the peak of 1988 to the peak of 1996).
Table (1.5) shows the results of productivity decompositions using labor productivity and
TFP. The measure of the share (s
it
) used for labor productivity is employment, while that used for
TFP is real gross output. The top part of the table shows the results using the ?rst decomposition
method and the bottom part of the table shows the results using the second decomposition method.
To begin with, the ?rst column shows that the ‘within’ component explains almost all
the productivity growth, except for TFP growth during the period of sluggish growth. The
signs of the ‘between’ e?ect for labor productivity are not consistent across time periods. A
negative ‘between’ implies that ?rms with labor productivity below the industry average expanded
more in terms of employment. This result is not necessarily puzzling if, among the ?rms in the
dataset, high productivity sites characteristically increased in capital intensity over time while
reducing employment. Accordingly, the expansion for these ?rms may have been taking place
through capital deepening instead of employment, with an increase in capital-labor ratio. Since
the negative ‘cross’ term implies a negative correlation between labor productivity growth and
employment growth, this may also be capturing the e?ect of increased capital intensity at the high
productivity sites. This can also take place via an increase in TFP among downsizing ?rms.
Since the e?ect of capital accumulation on output is taken into account in the calculation
16
Table 1.5: Productivity decomposition results for the manufacturing sector using labor productivity
and TFP for 1969?1996.
A. Decomposition 1
Within Between Cross Entry Exit (Net entry) Overall Num. of ?rms
(1) (2) (3) (4) (5) (4)-(5) growth (entries/exits)
LP
1969?1979 71.8% 4.1% -7.1% 4.2% 1.2% 3.1% 71.8% 1274 (312/43)
1979?1988 51.5% -2.1% -1.0% 2.3% 0.3% 2.0% 50.4% 1346 (115/43)
1988?1996 30.9% 1.2% -2.7% 0.0% 0.4% -0.3% 29.1% 1360 (57/22)
TFP
1969?1979 15.1% -7.1% 0.4% 1.8% -0.7% 2.5% 10.8% 1148(263/41)
1979?1988 13.0% -3.6% -0.3% 0.5% -0.7% 1.1% 10.2% 1262 (91/42)
1988?1996 4.6% -0.5% 2.2% 0.5% 0.4% 0.1% 6.4% 1304 (55/21)
B. Decomposition 2
Within Between Cross Entry Exit (Net entry) Overall Num. of ?rms
(1) (2) (3) (4) (5) (4)-(5) growth (entries/exits)
LP
1969?1979 68.2% 2.2% 1.6% 0.1% 1.5% 71.8% 1274 (312/43)
1979?1988 51.0% -2.2% 1.4% -0.1% 1.5% 50.4% 1346 (115/43)
1988?1996 29.6% -0.1% -0.1% 0.3% -0.4% 29.1% 1360 (57/22)
TFP
1969?1979 15.3% -6.9% 1.6% -0.8% 2.4% 10.8% 1148(263/41)
1979?1988 12.9% -3.8% 0.4% -0.8% 1.2% 10.2% 1262 (91/42)
1988?1996 5.7% 0.6% 0.4% 0.3% 0.1% 6.4% 1304 (55/21)
of TFP, the negative ‘between’ and ‘cross’ e?ects for TFP are more puzzling. Technically, the
negative ‘between’ e?ect implies faster output growth at sites whose total factor productivity is
below the industry average, and the negative ‘cross’ term indicates that positive growth of TFP
is associated with negative output growth. The latter may be true if many ?rms in the dataset
had spun o? less e?cient product lines or subsidiaries as part of their restructuring. While the
‘between’ e?ect is negative in almost all cases, the negative relationship between TFP growth and
output growth is observed only during the bubble economy period.
Overall, we do not ?nd any conclusive evidence for a misallocation among the group of
17
continuing ?rms examined in this exercise. Compared to the 1977?1988 period, the between
and cross e?ects are larger in most cases during the 1988?1996 period. Therefore, downsizing
of relatively ine?cient ?rms may have been more active during this latter period than the earlier
period.
Next, we discuss changes in ‘entry’ and ‘exit’ e?ects over time. Note here that the positive
sign on the ‘exit’ e?ect indicates a negative contribution to the overall growth rate, in accordance
with equation 1.4 and equation 1.5. The ‘net’ entry e?ect is the di?erence between the ‘entry’
e?ect and the ‘exit’ e?ect. For the TFP decomposition, the estimated ‘entry’ and ‘exit’ e?ects are
very similar across two types of decomposition for all periods.
When using labor productivity, the table shows ‘net’ entry reduces total productivity growth
by about 0.3% or 0.4% during the sluggish period, while in prior periods, it boosted overall produc-
tivity growth by 1.5% to 3.1%. Both entry and exit contributions were weak during the sluggish
growth period, but the ‘entry’ e?ect falls sharply during the sluggish growth period. Consequently,
exit by relatively more pro?table ?rms by itself accounts for much of the ‘net’ entry e?ect during
the 1988?1996 period.
For TFP, the ?rst result is that again, the ‘net’ entry e?ect is very small during the period
of sluggish growth. However, the ‘entry’ e?ect did not change at all in the 1988?1996 period
in comparison with the 1979?1988 period. Therefore, the reduction is entirely brought about
by the drop in the contribution of the ‘exit’ e?ect. Here, we observe that the contribution of
the ‘exit’ e?ect becomes suddenly negative (as the sign turns positive) during the sluggish growth
period. The negative ‘exit’ e?ect implies that quite few ?rms with a TFP level higher than
the industry average exited during this period. In both decompositions, the positive contribution
made by entering ?rms during the sluggish period is still signi?cant, constituting about 7% of total
productivity growth, while the exit of relatively more productive ?rms during the same period leads
to a reduction in productivity of approximately 5 ?6% of total productivity growth.
Overall, these results indicate the following. The results for ‘between’ and ‘cross’ e?ects
are somewhat puzzling and inconclusive. Certainly, these results may be driven by an increase in
18
capital intensity or spinning o? of ine?cient subsidiaries, which partly account for the cross-period
di?erences. However, we do not ?nd any obvious evidence which suggests that the 1990s were a
particularly bad period in terms of the reallocation of labor input and output among continuing
?rms. At the same time, there has been a change in the contribution of net entry during the
sluggish growth period. In particular, much of the reduction in TFP growth was attributed to
the drop in ‘exit’ e?ect, as the ‘entry’ e?ect remained strong. The implications of these results
are discussed in the next section.
1.5 Conclusion
Job reallocation exercises performed using the Nikkei ?nancial dataset showed that job
reallocation dynamics among large Japanese ?rms are mainly driven by job creation, and this
job reallocation pattern does not seem to have changed much during recent years of sluggish
economic growth. Moreover, the smaller role played by job destruction is more prominent in the
non-manufacturing sector. When the job reallocation rate is decomposed into an idiosyncratic
component and a sectoral/aggregate component, the dominance of the idiosyncratic component
over the sectoral/aggregate component in driving the overall variation of job reallocation declined
in the 1987?1997 period in the manufacturing sector. As mentioned before, the larger in?uence of
the sectoral/aggregate component during this period appears consistent with the ?ndings on stock
return volatility by Hamao, Mei and Xu (2003). At the same time, the correlation between the
idiosyncratic and the sectoral/aggregate components turned suddenly and signi?cantly negative in
the 1987?1997 period in the manufacturing sector, suggesting that idiosyncratic e?ects started to
counterbalance sectoral/aggregate e?ects during this period. This may be caused by protective
measures used by the government in response to negative sectoral/aggregate disturbances, but
identifying the sources of this change will require further investigation.
The productivity decomposition exercises reveal that among continuing ?rms, we do not ?nd
strong evidence of the cleansing e?ect of recessions, as the results for ‘between’ and ‘cross’ e?ects
do not suggest that the reallocation was poor during the sluggish growth period. Neither is the
19
evidence found in the behavior of entering ?rms, as they seem to have made a strong contribution
to the overall TFP growth rate during the sluggish growth period. However, exits of relatively
more productive ?rms underscore that the cleansing e?ect is not at work. In other words, the
malfunction of the reallocation mechanism seems to manifest itself in the exiting behavior of ?rms.
These results also relate to the ?ndings of Peek and Rosengren (2003) that ?nancially troubled
and heavily indebted companies had less di?culty accessing credit from major Japanese banks, as
those banks sought to manipulate their balance sheets rather than fund their ?nancially healthier
counterparts. This type of ?nancial practice may have led to the survival of the least productive
?rms, at the expense of less heavily indebted and more productive ?rms. Moreover, the strong
and positive contribution of entry implies that the ‘credit crunch’ may not have been so signi?cant.
This is consistent with the ?ndings by Motonishi and Yoshikawa (1999).
Within the framework of a search model, a dramatic increase in job destruction leads to
a long period of high unemployment and lengthy recovery from recession, as job creation takes
time due to the existence of search costs.
15
The examination of job reallocation using the Nikkei
?nancial dataset revealed that the sluggish growth in Japan during the 1990s was not accompanied
by a dramatic rise in job destruction. This fact can also be con?rmed by the unemployment rate,
which followed a gradual and mild increase instead of a sudden rise during this period. At the
same time, the exit behavior of ?rms suggests an insu?cient resource reallocation from less to
more productive ?rms. Accordingly, this may possibly have extended the length of the sluggish
growth period.
In the next chapter, I examine the nature of the labor input adjustment mechanism in Japan
during the 1990s from a di?erent angle. More speci?cally, I investigate the aggregate labor input
responses to demand shocks in the manufacturing sector and the Iron and Steel industry, sectors
whose employment has declined in recent years.
15
For example, see Mortensen and Pissarides (1994).
20
Chapter 2
Input and Output Responses to Demand Shocks using an Interrelated Factor
Demand Model
2.1 Introduction
This chapter investigates the labor input and inventory responses to demand shocks in the
Japanese manufacturing sector, as well as the Iron and Steel industry, the largest bene?ciary of the
Employment Adjustment Subsidy (EAS), using an interrelated factor demand model developed in
Topel (1982). I use monthly industry-level time-series data between January 1978 and November
2004. In order to evaluate changes in the adjustment mechanism in recent years, the entire
series was divided into two parts after identifying a natural breakpoint in the demand shock
processes. Subsequently, the responses of employment, work hours and inventories to demand
shocks are compared between the period preceding and following the natural break point, which
was identi?ed as May 1992. The main ?ndings are the following. First, demand shocks appear
to have increased in volatility after 1992 in both the manufacturing sector and the Iron and Steel
industry. Second, for the manufacturing sector, the adjustment mechanism shifted from one using
inventories intensively to reliance more on employment and work hours. Finally for the Iron and
Steel industry, the employment and inventory adjustments do not exhibit any systematic changes,
while the work hour adjustment has become much more prevalent in recent years.
Topel (1982) provides a theoretical framework which relates inventory costs and temporary
layo?s, and also provides an empirical model for testing. The theory predicts that, other things
being equal, lower inventory costs and therefore active inventory adjustments are associated with
less frequent layo?s, recalls and work hour adjustments to meet short-run demand ?uctuations.
Similarly, higher hiring/layo? costs increase the cost of frequent layo?s, and encourage more active
inventory adjustments. While Topel (1982) does not estimate inventory costs and hiring/layo?
21
costs, the prediction of an inverse relationship between inventory adjustment and temporary layo?s,
in turn, is supported by his empirical results comparing several US manufacturing sectors between
1958?75.
1
Hashimoto (1993) applies Topel’s empirical framework to compare the labor adjustment
mechanism of the manufacturing sector in two countries, the US and Japan. He uses monthly time
series data from January 1967 to December 1986 for Japan, and from January 1961 to December
1984 for the US, and ?nds that while employers in the US manufacturing sector adjust employment
to accommodate short-run ?uctuations in demand, Japanese employers rely less on employment
adjustment and more on the adjustment of work hours. His estimates of interrelated factor
demand show that the employment elasticity to unanticipated demand shocks is much stronger in
the US than in Japan (0.146 as opposed to 0.065) and the elasticity of work hours with respect to
anticipated demand shocks is much weaker in the US in comparison with Japan (0.024 as opposed
to 0.141).
Furthermore, Hashimoto splits the series in order to evaluate the impact of the Employment
Insurance Law, which was enacted in 1975. The objective of this law was to encourage ?rms
to sustain employment during temporary unfavorable shocks via the Employment Adjustment
Subsidy (EAS) in order to prevent a rise in unemployment. Since ?rms are subsidized when they
adjust output through a reduction in work hours instead of employment, mainly through temporary
business closures, the subsidy program was expected to reduce frequent layo?s and increase the
intensity of adjustment in work hours. Consequently, Hashimoto ?nds that employment became
less responsive, while work hours became more responsive to demand shocks after 1975. More
speci?cally, he ?nds that the employment elasticity to unanticipated (anticipated) current demand
shocks falls from 0.30 (0.28) to -0.27 (-0.27) while the elasticity of work hours to unanticipated
(anticipated) current demand shocks rises from -0.28 (-0.17) to 0.41 (0.12).
As the Japanese economy has gone through a period of signi?cant transformation during
the 1990s, the changes in the estimates of the interrelated factor demand model further elucidate
1
The industries used in his analysis are Chemicals, Petroleum, Tires and Tubes, Fabricated Metals, Rubber and
Plastics, Electrical Machinery and Primary Metals.
22
the impact as well as the nature of this transformation. Accordingly, in this chapter, I ?rst
update Hashimoto’s results on the labor adjustment mechanism in the Japanese manufacturing
sector using monthly time-series data from January 1978 to November 2004. The series were
split into two parts, before and after May 1992, based on the Quandt statistic which uses Chow’s
structural breakpoint tests and the least square breakpoint estimate.
2
The results show that both
employment and work hours adjustment became more intense, while inventory adjustment became
less so after 1992.
While the 1990s marked the period of the greatest take-up of the Employment Adjustment
Subsidy, the increase in the intensity of employment adjustment in the 1990s by itself does not
invalidate Hashimoto’s conjecture that the EAS reduces employment adjustment and encourages
adjustments through work hours. This is because the changes in the underlying pattern of demand
shocks also most likely a?ected employers’ strategy for adjusting labor inputs. Furthermore,
technological improvements are likely to have reduced search/hiring costs in some industries, while
remaining high in those with high subsidy coverage, thereby limiting the aggregate impact of the
subsidy. Therefore, it is di?cult to evaluate the impact of the subsidy by comparing the results
across time, as we can not completely isolate those e?ects that are brought about by the changes
in the economic environment.
However, a more realistic explanation as to why the impact of the EAS is not visible in
the manufacturing sector is that the EAS has had a very high concentration in certain sectors
within manufacturing, and the overall size of subsidized work hours in the manufacturing sector as
a whole is quite small. This point is particularly emphasized by the fact that the Iron and Steel
sector alone took, on average, about half of the total annual subsidy bill between 1990 and 2002.
Furthermore, the estimated average annual fraction of workers who are unutilized for production
through the subsidy program in the Iron and Steel sector is only about 2%, a small fraction of the
whole. The next chapter provides a further explanation of the details of industry selection, the
subsidy coverage across industries, as well as the method used to estimate the size of subsidized
2
As described later, both tests generate similar results.
23
workers using the data on the subsidy bill.
The EAS’s high concentration in the Iron and Steel industry makes this industry an ideal
candidate for the investigation of the potential impact of the EAS on labor adjustment using an
interrelated factor demand model.
3
Here, the time-series data was again split into two parts at
May 1992, and the resulting estimates are compared across periods. As described in the next
chapter, the EAS bill dramatically increased after 1992, and therefore some of the impact of the
EAS may be observed from this comparison. However, the changes in the underlying pattern of
shock processes and the corresponding shifts in the employers’ labor adjustment strategies makes
it hard to isolate the impact of the subsidy. Albeit imperfect, one strategy would be to use
the results of the manufacturing sector as a benchmark case, and examine how the results in the
Iron and Steel industry di?er from the general trend observed by the benchmark. The results
on employment elasticity to demand shocks show that, in most cases, employment responses are
insigni?cant and weak in the Iron and Steel industry even post-1992. This result stands in sharp
contrast to that of the manufacturing sector. On the other hand, the response of work hours to
demand shocks in Iron and Steel has strengthened after 1992. While part of the di?erences may
simply be caused by institutional di?erences other than the EAS, these results do not contradict
with the prediction that the EAS reduces employment’s responses and increases the response of
work hours to shocks.
Another noteworthy result is that inventory responses to demand shocks are much larger
in size and more signi?cant in the Iron and Steel industry compared to the manufacturing sector
as a whole. This result is indicative of higher labor adjustment costs or lower inventory costs
in the Iron and Steel sector compared to the average industry within the manufacturing sector.
Higher adjustment costs, in turn, increase the bene?ts of the Employment Adjustment Subsidy
and increase the take-up rates of the subsidy. Furthermore, while inventory adjustments become
weaker and insigni?cant within the manufacturing sector after 1992, they remained strong and
3
Note that the exercise carried out here is not a direct test of the impact of the EAS, since we cannot disentangle
the institutional di?erences and the impact of the EAS. In order to test the impact of the EAS, we also need a
dataset for the pre-EAS period, as in Hashimoto (1993). This was not done in this paper due to limited data.
24
signi?cant in the Iron and Steel sector. This result reveals that labor adjustment costs continued
to be high relative to inventory adjustment costs within Iron and Steel.
4
Finally, output responses to demand shocks in the Iron and Steel sector are also investigated.
The standard procedure outlined in Topel (1982) uses a seasonally unadjusted monthly time-series
on shipments to construct the demand shock series, by decomposing the shipments series into a
predictable and an unpredictable component. In order to evaluate the output responses to demand
shocks, I used a demand instrument series constructed using the average growth rate of shipments
of downstream industries.
5
The results are mixed. When using shipments to measure output, the
output growth responses to unpredicted demand shocks rise after 1992, while when value added
was used to measure output, the output responses to demand shocks fall after 1992. However,
coe?cients are not signi?cantly di?erent from each other before and after 1992.
The demand instrument exhibits a substantial increase in volatility after 1992. Higher
volatility, in turn, can explain the rise in the subsidy take-ups, as volatility increases the need
for frequent input adjustments. The implications of higher shock volatility on subsidy take-up
decisions in the context of the theoretical framework given in the next chapter will be discussed in
the appendix.
As for the output responses to shocks, the theoretical framework in the next chapter shows
that, ceteris paribus, a rise in the number of subsidized workers increases output volatility, as
the subsidy allows ?rms to hoard workers at smaller costs and meet short-term ?uctuations in
demand more easily. Therefore, the reduced value added sensitivity to demand shocks during
the period of higher subsidy coverage contradicts the theoretical prediction. It requires a better
demand instrument, or theoretical modi?cations, or both, to ?ll the theoretical and empirical
discrepancy. One possible theoretical explanation for the reduced sensitivity of output is that
4
According to Survey on Employment Trend published by the Ministry of Labor, Health and Welfare, the share
of ?exible workers such as part-time or temporary workers is among the lowest for the Iron and Steel industry
throughout the 1990s.
5
Obviously, we cannot use shipments series to construct demand shocks when shipments are also used to measure
output, as the unpredictable component of demand shocks will be perfectly correlated with the output measure.
25
the input responses are non-linear in the size of demand shocks and/or there is a limit on the
degree of input adjustments including the use of the subsidy. In these cases, the average input
responses to shocks could decline with the volatility of shock processes. While this explains the
reduced output sensitivity to demand shocks in the presence of high volatility, whether or not such
modi?cations are necessary has not yet been discovered as empirical results on output responses
are still inconclusive. Reconciling this issue will remain a future research agenda.
2.2 Description of the Interrelated Factor Demand Model
Topel’s interrelated factor demand model captures the interdependence of input decisions
among the following three variables: employment, work hours and inventories. It also allows us
to distinguish the responses to unpredicted current shocks, predicted current and predicted future
shocks. More speci?cally, the following set of equations are used to investigate the interrelated
factor demand decision rules:
L
t
= ?
10
+?
11
L
t?1
+?
12
H
t?1
+?
13
I
t?1
+
T

?=0
?
1?
´ q
t+?
+?
1
q
u
t
+trend, (2.1)
H
t
= ?
20
+?
21
L
t?1
+?
22
H
t?1
+?
23
I
t?1
+
T

?=0
?
2?
´ q
t+?
+?
2
q
u
t
+trend, (2.2)
I
t
= ?
30
+?
31
L
t?1
+?
32
H
t?1
+?
33
I
t?1
+
T

?=0
?
3?
´ q
t+?
+?
3
q
u
t
+trend. (2.3)
Here, L
t
, H
t
and I
t
refer to employment, work hours and inventory in natural logarithms at time
t, T is the planning horizon, ´ q is the forecasted component of demand while q
u
t
captures the
unpredicted component (i.e. q
t
? ´ q
t
), and ?, ?, and ? are the impact elasticity coe?cients to be
estimated. As explained by Topel, forecasted as well as unforecasted components of shipments
drive the model.
The following propositions are given by Topel: ?rst, the speed of adjustment parameters,
given by ?
jj
, are expected to increase as the labor adjustment costs increase or inventory costs
decrease. These parameter values equal zero when inputs are freely variable and unity when they
are ?xed. Second, a rise in current predicted shipments (´ q
t
) or in current unpredicted shipments
26
(q
u
t
) increases both employment and work hours while reducing inventories. A lower cost of
inventories as well as higher labor adjustment costs increase the inventory and work hour responses
to current predicted or unpredicted shocks, whereas they reduce the employment responses to those
shocks. Employment and work hour adjustments for predicted shocks could be larger than for
unpredicted shocks, if adjustment takes time and needs to be pre-arranged. Third, a rise in
future expected shipments (

T
?=1
´ q
t+?
) should increase the demand for employment, work hours
and inventories. These e?ects are smaller the longer the planning horizon, and the higher the
inventory and labor adjustment costs.
Next, it is assumed that expected monthly demand values depend only on the past values
of shipments and not on the other endogenous variables. More speci?cally, the demand condi-
tion, characterized by the monthly series on log shipments, q
t
, follows a seasonally di?erenced
autoregressive integrated moving average (ARIMA) process of the following form:
A
a
(L)(1 ?L)(1 ?L
12
)q
t
= (1 ??L
12
)M
m
(L)u
t
(2.4)
where L represents a lag operator, A
a
(L) and M
m
(L) are polynomials of orders a and mrespectively
in the lag operator, ? is a seasonal moving average parameter, and u
t
is the white noise error term.
The best ?t model was chosen based on the Akaike information criterion, Schwartz information
criterion and correlogram.
Following Topel (1982), an additional structure is imposed on the lead distributions of ?
j?
.
Namely, it is assumed that they follow a third order Almon polynomial, thereby requiring the
shortest planning horizon to be 4 months. The planning horizons for both the manufacturing
sector and the Iron and Steel industry are set at 6, 9 and 12 months.
Finally, for the Iron and Steel industry only, the output responses to demand shocks are
investigated. Here, the demand instrument d
t
was used instead of shipments to model the demand
condition. As described in the next section, d
t
is the weighted average log growth rate of shipments
of downstream industries and not the level.
6
The demand shock was assumed to follow a seasonally
di?erenced autoregressive moving average (ARMA) model, instead of an ARIMA model. Now,
6
The shipments ?gures are normalized by the year 2000 values so that I could not use the actual level.
27
by totally di?erentiating an equation similar to the previous ones with respect to time, we can
estimate the output growth responses using the following equation:
dY
t
= ?
40
+?
41
dL
t?1
+?
42
dH
t?1
+?
43
dI
t?1
(2.5)
+?
44
dY
t?1
+
T

?=0
?
4?
´
d
t+?
+?
4
d
u
t
+trend.
Here, Y
t
refers to the log of real output, and dY
t
= Y
t
? Y
t?1
. As mentioned previously, I use
both real shipments and real value added as a measures of real output.
2.3 Description of the Data
Monthly seasonally unadjusted series on shipments, employment, work hours and inventories
within the manufacturing sector as well as the Iron and Steel industry between January 1978 and
November 2004 are used to obtain the estimates for the interrelated factor demand model. As
discussed in Topel (1982), the use of seasonally unadjusted series is important since “the transitory
and highly predictable character of seasonal ?uctuations makes them prime candidates for inventory
smoothing and temporary layo?s.”
7
The data on shipments and inventories are taken from the Indices of Industrial Production
published by the Japanese Ministry of Economy, Trade and Industry.
8
Nominal values of the
indices of shipments and inventories for each industry are de?ated using monthly Corporate Good
Price Indices (CGPI) constructed by the Bank of Japan. The data on employment and work hours
are taken from Monthly Labor Statistics provided by the Japanese Ministry of Health, Labor and
Welfare.
9
Note that the statistics on employment and work hours are based on establishments with
7
Footnote 16 in Topel (1982).
8
The series are normalized by the value for the year 2000. The historical monthly series on shipments,
value added, inventories and inventory ratio by industries within the manufacturing sector are available for
review and downloading on METI’s website in both English and Japanese. The English site is found at:
http://www.meti.go.jp/statistics/index.html
9
Note that the statistics used here are based on the old industrial classi?cation used prior to year 2004. Various
compilations of labor related data including Monthly Labor Statistics are provided on line by the Japan Institute
for Labor Policy and Training at http://stat.jil.go.jp/ in Japanese.
28
more than 30 employees. Unfortunately, monthly statistics that include smaller establishments
are available only since 1990.
10
To investigate the output responses to demand shocks in the Iron and Steel industry, a
demand instrument is constructed using the information on the activity of downstream industries.
Note that I was unable to use the actual level of shipments made by the downstream industries,
since the industrial monthly ?gures are normalized by the year 2000 values in Indices of Industrial
Production. Instead, the demand instrument is constructed as the average growth rate of shipments
of downstream industries, weighted by the annual share of consumption of the Iron and Steel
industry’s shipments.
Following Bartelsman, Caballero and Lyons (1994), the weights used to calculate the de-
mand instrument are taken from an annual input-output table, and here, by the 2-digit industry
classi?cations given by Indices of Industrial Production. More speci?cally, letting w
ij
be the ele-
ment on the ith row and jth column of the input-output table in a particular year, and dq
jt
the
log growth rate of the index of monthly shipments of industry j at time t, the monthly demand
instrument for industry i can be written as follows:
d
it
=

j=i
w
ij

j=i
w
ij
dq
jt
. (2.6)
Note that the subscript t refers to month. Although the weight w
ij
varies every year, I did not
add a subscript so as to keep the presentation simple. Since this exercise is only performed for
the Iron and Steel industry, the index i refers to Iron and Steel and j refers to other industries.
The annual input-output table is taken from the Japan Industry Productivity Database
(JIP database).
11
Nominal values of shipments are again de?ated using CGPI.
12
Since industry
classi?cations di?er between the JIP database and the Indices of Industrial Production, a matching
10
The correlation between the two statistics, one based on establishments with more than 30 employees and the
other based on establishments more than 5 employees, is very high for both employment and work hours in the
manufacturing as well as the Iron and Steel sectors.
11
The JIP database is made available both in Japanese and English by Kyoji Fukao on his website:
http://www.ier.hit-u.ac.jp/˜fukao/english/data/index.html.
12
Note that since the CGPI does not have categories for ‘furniture’, ‘leather products’ and ‘rubber products,’ the
indices for ‘other manufacturing products’ are used for each.
29
between the two classi?cations was required. Table (C.1) in the appendix shows the concordance
of industry classi?cations. Note that the broad industry classi?cation of the Indices of Industrial
Production, which is equivalent to a two-digit level classi?cation, was used for the correspondence,
as de?ators are available only at this level. Furthermore, while we can construct time-varying
weight w
ij
for each year, the JIP database ends in 1998. Hence, the weights for 1998 are used for
the remainder of the period until November 2004.
2.4 Results
2.4.1 Manufacturing Sector
First, I present results for the manufacturing sector in order to compare with Hashimoto’s
results. Figure (2.1) shows log shipments, employment, work hours and inventories from the
manufacturing sector. The ?gure on shipments shows that the reduction in the trend growth rate
occurred around 1992. Employment also starts to fall around 1992, and average work hours drop
in 1988, reaching a new steady state level in 1992. This drop in hours was arguably caused by
changes in the Labor Standards Law that gradually reduced statutory work hours from 48 hours
to 40 hours a week. However, visual inspection of shipments and employment suggests a deeper
regime change in the manufacturing sector, unrelated to the changes in the labor law, around 1992.
In order to model the time series process for demand, the best parsimonious speci?cation
which removed autocorrelation in the residuals was chosen based on the Akaike information crite-
rion.
13
Once the model was chosen, I tested for a structural break between 1989 and 1992 using
the Quandt statistic and the least squares break-date test, as the visual inspection suggested a
break around this period.
14
More speci?cally, F-statistics from Chow structural break tests are
plotted over possible structural breakpoint dates and the date with the largest value was picked
13
I experimented with a number of speci?cations with both lags ranging from one to four. The selection criterion
chosen are AR(4) and MA(4).
14
As discussed in Hansen (2001), the least squares test is a better test for the structural break, and the Quandt
statistic produces the same result as the least squares test only “in linear regression when the Chow test is constructed
with ‘homoskedastic’ form of the covariance matrix.”
30
-.8
-.6
-.4
-.2
.0
.2
.4
78 80 82 84 86 88 90 92 94 96 98 00 02 04
LNSHIP
4.45
4.50
4.55
4.60
4.65
4.70
4.75
4.80
78 80 82 84 86 88 90 92 94 96 98 00 02 04
LNEMP
4.95
5.00
5.05
5.10
5.15
5.20
5.25
5.30
78 80 82 84 86 88 90 92 94 96 98 00 02 04
LNHRS
-.4
-.3
-.2
-.1
.0
.1
.2
78 80 82 84 86 88 90 92 94 96 98 00 02 04
LNINV
Figure 2.1: Monthly series on shipments, employment, work hours and inventories (in logs) in
the manufacturing sector for January 1978?November 2004. Data source: the original series of
shipment and inventory indices are taken from Indices of Industrial Production while the data
on employment and work hours for establishments with more than 30 employees are taken from
Monthly Labor Statistics.
as the Quandt statistic. Similarly, the sum of squared errors are calculated for possible structural
breakpoint dates, and the date which minimized the residual variance was chosen as the least
squares breakpoint date.
The results are similar in both cases. The Quandt statistic reaches its peak in April 1992
and May 1992, while the sum of squared errors was the smallest in March 1992 and May 1992.
Here, I chose May 1992 as the month for a structural break.
15
In addition to the slowdown in
the trend output growth occurring around that time, the standard deviation of log shipments,
detrended by a Hodrik-Prescott ?lter, increased by 25% in comparison to the period preceding
May 1992. The higher volatility in short-run ?uctuations of output within the manufacturing
sector suggests more turbulent demand conditions during the 1990s.
15
As explained later, the same test for the Iron and Steel sector also exhibited similarly strong evidence for a
break in May 1992.
31
Table 2.1: The estimates of the interrelated factor demand model in the manufacturing sector,
9-month forecast horizon.
Employment ( L
t
) Hours (H
t
) Inventories (I
t
)
Pre-1992 Post-1992 Pre-1992 Post-1992 Pre-1992 Post-1992
Demand:
Current Unpredicted 0.002 0.027** 0.065 0.216*** -0.202*** 0.053
(0.012) (0.012) (0.060) (0.059) (0.063) (0.061)
Current Predicted 0.009 0.043*** 0.048 0.313*** -0.165*** 0.118**
(0.010) (0.012) (0.053) (0.057) (0.056) (0.059)
Future Predicted 0.001 0.030*** 0.049* 0.297*** 0.053* 0.009
(0.006) (0.008) (0.028) (0.040) (0.030) (0.041)
Lagged Dep. Variables:
L
t?1
1.017*** 0.969*** -0.499*** -0.491*** 0.451*** 0.037
(0.024) (0.018) (0.125) (0.090) (0.131) (0.093)
H
t?1
0.025 0.001 0.113 -0.067 0.115 0.048
(0.016) (0.018) (0.084) (0.091) (0.089) (0.094)
I
t?1
-0.012** 0.002 -0.090*** 0.068*** 0.916*** 0.950***
(0.006) (0.006) (0.030) (0.028) (0.032) (0.029)
Number of obs. 149 127 149 127 149 127
R-squared 0.9971 0.9996 0.9645 0.9721 0.9844 0.9702
Durbin-Watson statistics 2.12 2.02 2.13 2.22 1.67 1.93
F-statistics 2182 12091 174 184 405 173
After splitting the sample in two, I estimated various ARIMA and again chose the best
parsimonious model for each group.
16
Table (2.1) shows the estimates of the interrelated factor
demand model with the planning horizon set equal to 9 months.
17
The standard errors are
reported inside parenthesis. Note that the coe?cients for future predicted demand are the sum
of the coe?cients for future months.
Prior to 1992, employment responses to demand shocks were positive but they were small in
16
I used AR(2) and MA(3) for the ?rst period and AR(1) and MA(3) for the second period. In both cases, the
resulting disturbance terms are not autocorrelated.
17
The original interrelated factor model proposes that we include a lagged value of other factors or stocks such
as materials on the right hand side of each equation. I included ‘raw material inventory-consumption ratio’ on the
right hand side as a robustness check, but the main results did not change. The coe?cient on the raw material
ratio is signi?cant only for the work hours’ regression, and the sign is negative as expected.
32
size, and insigni?cant. However, the coe?cients for all shocks become bigger and signi?cant after
1992. The same pattern is observed for work hours, with an even greater degree of signi?cance.
Finally, the table shows that inventory adjustment becomes less responsive to demand shocks after
1992. Moreover, the coe?cients have expected signs before 1992, but they have wrong signs after
1992 for current unpredicted and predicted demand shocks. Finally, all shock response coe?cients
before and after 1992 are signi?cantly di?erent from each other at the 5% level for both employment
and work hours. For inventories, only coe?cients on current unpredicted shocks are signi?cantly
di?erent.
Table (2.2) and (2.3), respectively, show similar tables with the planning horizon set equal
to 6 and 12 months. The evidence for the change in employment responses to shocks after 1992 is
not as strong as with a 9-month forecast horizon. For employment, the coe?cients before and after
1992 are no longer signi?cantly di?erent from each other at the 5% level for current unpredicted
and current predicted shocks. The change in the sensitivity of work hours is strong in both tables
and hence robust across various planning horizons. Again, for work hours, the coe?cients before
and after 1992 are signi?cantly di?erent from each other for all shock measures. The pattern of
changes in inventory responses was also preserved across di?erent planning horizons.
Overall, these results imply that there has been a shift in the adjustment style, from heavy
reliance on inventories as opposed to employment and work hours, to reliance more on employment
and particularly work hours with less emphasis on inventories. One possible explanation is that
before 1992, the trend growth rate in the manufacturing sector was higher and consequently,
short-run ?uctuations in demand carried less weight in employers’ labor input decisions. In other
words, employers ignored the short-run ?uctuations in demand to make employment decisions,
and used inventory adjustment almost exclusively to accommodate the ?uctuations. This view
is consistent with the practice of life-time employment, which Japanese ?rms favored during the
period of post-war high economic growth. However, after the collapse of the bubble economy in
the early 1990s, employers in the manufacturing sector started to pay more attention to demand
in making employment decisions. Alternatively, lower labor adjustment costs, as re?ected by an
33
Table 2.2: The estimates of the interrelated factor demand model in the manufacturing sector,
6-month forecast horizon.
Employment ( L
t
) Hours (H
t
) Inventories (I
t
)
Pre-1992 Post-1992 Pre-1992 Post-1992 Pre-1992 Post-1992
Demand:
Current Unpredicted -0.002 0.018 0.067 0.302*** -0.205*** 0.090
(0.013) (0.013) (0.067) (0.064) (0.072) (0.069)
Current Predicted 0.0003 0.027 0.041 0.514*** -0.148** 0.215**
(0.013) (0.019) (0.067) (0.093) (0.072) (0.099)
Future Predicted 0.007 0.034*** 0.043* 0.315*** 0.030 0.050
(0.005) (0.008) (0.024) (0.036) (0.026) (0.039)
Lagged Dep. Variables:
L
t?1
1.040*** 0.967*** -0.531*** -0.480*** 0.372*** 0.088
(0.022) (0.018) (0.113) (0.088) (0.121) (0.094)
H
t?1
0.029* -0.013 0.121 -0.011 0.091 0.054
(0.017) (0.018) (0.084) (0.086) (0.090) (0.092)
I
t?1
-0.013** 0.004 -0.090*** 0.052* 0.922*** 0.945***
(0.006) (0.006) (0.030) (0.027) (0.032) (0.029)
Number of obs. 152 130 152 130 152 130
R-squared 0.9972 0.9996 0.9641 0.9725 0.9852 0.9707
Durbin-Watson stat. 2.08 2.09 2.13 2.23 1.68 2.01
F-stat. 2361 12614 176 192 436 181
increase in the use of part-time workers, may have allowed employers to accommodate short-term
?uctuations in demand more easily. Another interesting observation is that inventory began to
play a lesser role in demand bu?ering and work hours took on a much larger role. In sum, the
role of labor input adjustment started to outweigh that of inventories after 1992.
Compared to Hashimoto’s results for the period 1967?1986, I observe smaller employment
and work hours responses to current predicted and unpredicted shocks, but similar inventory
responses. However, the coe?cients for employment and work hours before 1992 are not signi?-
cantly di?erent from zero in most cases for both Hashimoto and myself. When Hashimoto splits
the sample into two, 1967?1974 and 1975?1986, he observed negative and signi?cant employment
responses to demand shocks in the latter period. This was not observed in my results for the
1978?1992 period. Furthermore, Hashimoto found that the work hours’ response to the current
34
Table 2.3: The estimates of the interrelated factor demand model in the manufacturing sector,
12-month forecast horizon.
Employment ( L
t
) Hours (H
t
) Inventories (I
t
)
Pre-1992 Post-1992 Pre-1992 Post-1992 Pre-1992 Post-1992
Demand:
Current Unpredicted 0.004 0.016 0.046 0.146*** -0.175*** 0.015
(0.012) (0.011) (0.062) (0.054) (0.065) (0.054)
Current Predicted 0.010 0.024*** 0.027 0.207*** -0.103* 0.055
(0.010) (0.008) (0.050) (0.041) (0.052) (0.041)
Future Predicted -0.012 0.030*** 0.070* 0.310*** 0.004 0.038
(0.007) (0.009) (0.038) (0.045) (0.040) (0.044)
Lagged Dep. Variables:
L
t?1
0.985*** 0.974*** -0.420*** -0.504*** 0.272* -0.001
(0.028) (0.020) (0.146) (0.097) (0.152) (0.097)
H
t?1
0.033* -0.006 0.098 -0.115 0.142 -0.002
(0.017) (0.019) (0.086) (0.095) (0.090) (0.095)
I
t?1
-0.006 0.003 -0.097*** 0.075*** 0.932*** 0.954***
(0.006) (0.006) (0.032) (0.029) (0.034) (0.029)
Number of obs. 146 124 146 124 146 124
R-squared 0.9967 0.9995 0.9641 0.9705 0.9831 0.9700
Durbin-Watson stat. 2.18 2.06 2.13 2.11 1.75 1.89
F-stat. 1886 10736 168 170 363 166
predicted shock is signi?cant for the 1975?1986 period, while this was insigni?cant in my sample
for the 1978?1992 period.
While Hashimoto’s concludes that the reduction in employment responses in the manufactur-
ing sector after 1975 may be caused by the Employment Adjustment Subsidy, my results somewhat
undermine this conclusion, as employment responses were strengthened during the 1990s, when the
subsidy bill was at its highest. As mentioned earlier, this is not to claim that the EAS does not
a?ect employment responses to shocks. Rather, the results suggest that the impact of the EAS
on the manufacturing sector as a whole is probably limited, due to small and highly concentrated
coverage relative to the size of the entire sector.
18
Given that the Iron and Steel industry receives
18
Part of the heterogeneity in subsidy receipts across industries may be related to the fact that the Japanese
government actively selected the four-digit industries to which the subsidy was targeted between 1975 and 2000.
However, the particularly high take-up rates in certain industries such as the Iron and Steel industry seems to
35
4.2
4.3
4.4
4.5
4.6
4.7
4.8
78 80 82 84 86 88 90 92 94 96 98 00 02 04
LNSHIP
4.4
4.5
4.6
4.7
4.8
4.9
5.0
5.1
5.2
5.3
78 80 82 84 86 88 90 92 94 96 98 00 02 04
LNEMP
4.96
5.00
5.04
5.08
5.12
5.16
5.20
5.24
78 80 82 84 86 88 90 92 94 96 98 00 02 04
LNHRS
4.3
4.4
4.5
4.6
4.7
4.8
78 80 82 84 86 88 90 92 94 96 98 00 02 04
LNINV
Figure 2.2: Monthly series on shipments, employment, work hours and inventories (in logs) in the
Iron and Steel industry for January 1978?November 2004. Data source: the original series of
shipment and inventory indices are taken from Indices of Industrial Production while the data
on employment and work hours for establishments with more than 30 employees are taken from
Monthly Labor Statistics.
about half of the total subsidy on average every year from 1990 to 2002 and the EAS bill started
to take on a dramatically higher level after 1992, it seems worthwhile to investigate how input
adjustment mechanism changed in this industry after 1992. While this is not a direct test of
the impact of the EAS, the contrast between the manufacturing sector is likely to highlight some
institutional factors as well as the potential impact of the EAS. This is the subject to which I
turn next.
2.4.2 Iron and Steel Industry
Figure (2.2) shows log of shipments, employment, work hours and inventories in the Iron
and Steel industry. The ?gure on shipments shows that unlike the manufacturing sector, there
is no obvious change in the trend growth rate during this period. However, employment in this
underscore its high labor adjustment costs.
36
industry has been in decline during the entire period, re?ecting an increase in capital intensity
over the long-run. As in the manufacturing sector, work hours reach a lower steady-state level
around 1992 in response to changes in the labor law.
I repeated my earlier procedures to estimate the form of the data generating process for
shipments and to search for structural breaks.
19
Both the Quandt statistic and the least squares
breakpoint tests indicated that the highest probability of a structural break was found in May
1992, and therefore the sample was split into two at this breakpoint.
20
Although the change is
smaller than in manufacturing, the standard deviation of log shipments, detrended by a Hodrik-
Prescott ?lter, increases by 11% after May 1992, thereby again indicating an increased turbulence
in demand conditions during the 1990s. Subsequently, I estimate two separate data generating
processes for the demand.
21
Table (2.4) shows the estimates of the interrelated factor demand model for Iron and Steel,
with the forecast horizon set equal to 9 months. Employment responses to current predicted and
unpredicted shocks are not signi?cant at 10% in either period. One of the coe?cients on future
predicted demand is signi?cant, but both coe?cients have the wrong sign. As for work hours, the
size of adjustment increases in response to both current predicted and unpredicted shocks, and the
increase in the size of the coe?cients as well as the degree of signi?cance is particularly dramatic
for the current predicted shock. The inventory adjustment to current predicted and unpredicted
shocks does not change much after 1992. The inventory coe?cients all have the correct sign
except for the future predicted shock before 1992. Overall, the table shows that the main change
is observed in the adjustment of work hours.
Table (2.5) and (2.6) show the estimates of the same model, but with forecast horizons set
equal to 6 months and 12 months respectively. The results are quite similar. In general, these
tables do not o?er conclusive evidence for any change in the employment response. While in all
19
Here, The Akaike information criterion selects an AR(3) and MA(4).
20
As mentioned previously, this break-date coincides with the time the EAS bill started to take on a dramatically
higher level.
21
For the ?rst half, AR(1) and MA(2) are selected while for the second half, AR(3) and MA(2) are selected by
the Akaike information criterion.
37
Table 2.4: The estimates of the interrelated factor demand model in the Iron and Steel industry,
9-month forecast horizon.
Employment ( L
t
) Hours (H
t
) Inventories (I
t
)
Pre-1992 Post-1992 Pre-1992 Post-1992 Pre-1992 Post-1992
Demand:
Current Unpredicted 0.010 0.019 0.109*** 0.150** -0.671*** -0.562***
(0.013) (0.013) (0.040) (0.058) (0.073) (0.068)
Current Predicted 0.013 0.006 0.027 0.166*** -0.431*** -0.260***
(0.012) (0.011) (0.039) (0.047) (0.071) (0.055)
Future Predicted -0.012 -0.022** 0.059** 0.051 -0.032 0.050
(0.009) (0.010) (0.027) (0.042) (0.049) (0.049)
Lagged Dep. Variables:
L
t?1
0.970*** 0.945*** 0.015 -0.352** 0.083 0.214
(0.021) (0.035) (0.068) (0.152) (0.124) (0.178)
H
t?1
0.070*** 0.026 0.664*** 0.492*** 0.045 0.108
(0.019) (0.018) (0.062) (0.080) (0.112) (0.094)
I
t?1
-0.0002 0.003 -0.085*** -0.049** 0.919*** 0.970***
(0.007) (0.006) (0.021) (0.024) (0.038) (0.029)
Number of obs. 150 125 150 125 150 125
Akaike info. Criteria -8.95 -8.76 -6.63 -5.80 -5.43 -5.48
Schwarts Criteria -8.53 -8.29 -6.21 -5.33 -5.01 -5.01
R-squared 0.9995 0.9996 0.9369 0.9120 0.8944 0.9367
Durbin-Watson stat. 2.06 1.89 2.35 2.28 1.50 1.59
F-stat. 12034 14756 96 54 55 77
cases the coe?cient on current unpredicted shocks becomes somewhat stronger, there is no robust
evidence for a change in the responsiveness of employment to current predicted shocks. As for the
adjustment in work hours in response to current predicted and unpredicted shocks, the coe?cients
become stronger in terms of size and signi?cance in all cases except for the unpredicted shock
with the 12-month forecast horizon. Finally, in all speci?cations, only work hours’ coe?cients on
current predicted shocks, before and after 1992, are signi?cantly di?erent from each other.
The evidence, overall, indicates that there are two main changes in the labor adjustment
mechanism. First, the employment response to current unpredicted shocks became somewhat
stronger after 1992. However, this result is not so conclusive because the coe?cients are only
signi?cant in one case. Furthermore, the size and the signi?cance of this increase in most cases
38
Table 2.5: The estimates of the interrelated factor demand model in the Iron and Steel industry,
6-month forecast horizon.
Employment ( L
t
) Hours (H
t
) Inventories (I
t
)
Pre-1992 Post-1992 Pre-1992 Post-1992 Pre-1992 Post-1992
Demand:
Current Unpredicted 0.006 0.032* 0.110** 0.249*** -0.659*** -0.688***
(0.014) (0.016) (0.045) (0.073) (0.084) (0.091)
Current Predicted 0.007 0.018 0.017 0.321*** -0.367*** -0.452***
(0.020) (0.017) (0.063) (0.074) (0.117) (0.093)
Future Predicted -0.005 -0.024** 0.059** 0.069 0.033 0.066
(0.008) (0.009) (0.025) (0.042) (0.046) (0.052)
Lagged Dep. Variables:
L
t?1
0.985*** 0.959*** 0.022 -0.317** 0.218* 0.088
(0.020) (0.034) (0.065) (0.152) (0.120) (0.190)
H
t?1
0.070*** 0.044*** 0.661*** 0.532*** 0.021 0.007
(0.019) (0.017) (0.061) (0.074) (0.114) (0.093)
I
t?1
-0.0005 -0.001 -0.080*** -0.063*** 0.914*** 1.018***
(0.007) (0.005) (0.021) (0.023) (0.039) (0.028)
Number of obs. 153 128 153 128 153 128
Akaike info. Criteria -8.92 -8.74 -6.61 -5.75 -5.37 -5.31
Schwarts Criteria -8.51 -8.27 -6.20 -5.28 -4.96 -4.85
R-squared 0.9995 0.9996 0.9356 0.9115 0.8890 0.9454
Durbin-Watson stat. 2.03 1.88 2.33 2.35 1.44 1.43
F-stat. 12229 15241 96 55 53 93
are smaller than in the manufacturing sector. Secondly and more importantly, work hours became
more responsive to shocks after 1992 although the magnitude of the change is not as dramatic as
that in the manufacturing. This is particularly the case for current predicted shocks. Note that
these results are not at odds with theoretical predictions of the impact of the EAS. The procedural
lags in the application process should probably make the impact of the EAS more visible for
predicted shocks than unpredicted shocks. Hence, it makes sense that the responsiveness of work
hours to current predicted shocks has increased after 1992, while that for employment became
weaker or remained insigni?cant after 1992.
Next, I present the results obtained using equation 2.5 for the estimation of the output
responses to demand shocks. Figure (2.3) plots the demand instrument measure, d
t
, between
39
Table 2.6: The estimates of the interrelated factor demand model in the Iron and Steel industry,
12-month forecast horizon.
Employment ( L
t
) Hours (H
t
) Inventories (I
t
)
Pre-1992 Post-1992 Pre-1992 Post-1992 Pre-1992 Post-1992
Demand:
Current Unpredicted 0.006 0.019 0.123*** 0.109* -0.638*** -0.442***
(0.011) (0.013) (0.036) (0.055) (0.066) (0.069)
Current Predicted 0.007 0.002 0.058** 0.163*** -0.375*** -0.130***
(0.008) (0.009) (0.026) (0.039) (0.048) (0.049)
Future Predicted -0.019* -0.019* 0.048 0.035 0.007 0.029
(0.010) (0.010) (0.030) (0.042) (0.056) (0.053)
Lagged Dep. Variables:
L
t?1
0.960*** 0.949*** 0.006 -0.404*** 0.129 0.218
(0.023) (0.035) (0.073) (0.149) (0.133) (0.187)
H
t?1
0.065*** 0.038* 0.651*** 0.353*** 0.079 0.128
(0.020) (0.021) (0.063) (0.090) (0.115) (0.113)
I
t?1
0.0002 0.003 -0.081*** -0.028 0.926*** 0.955***
(0.007) (0.006) (0.021) (0.025) (0.039) (0.031)
Number of obs. 147 122 147 122 147 122
Akaike info. Criteria -8.94 -8.75 -6.63 -5.85 -5.43 -5.40
Schwarts Criteria -8.51 -8.27 -6.21 -5.36 -5.00 -4.92
R-squared 0.9995 0.9996 0.9373 0.9166 0.8931 0.9301
Durbin-Watson stat. 2.08 1.88 2.34 2.14 1.53 1.64
F-stat. 11502 13660 94 56 53 67
January 1978 and November 2004. The structural break tests again suggest the highest probability
of a structural break in May 1992, and the standard deviation of d
t
is 45% higher after 1992.
22
Table (2.7) shows the estimates of equation 2.5 with the planning horizon set equal to 9 months.
Here, the indices of shipments and value added are used as measures of output. The correlation
between d
t
and the growth rate of shipments (value added) is 0.84 (0.60).
23
Note that while
the expected signs of the responses to current predicted and unpredicted shocks are positive for
both measures of output, this may not be so for future predicted shocks: whereas a positive sign is
22
As a comparison, the standard deviation of the growth rate of shipments (value added) is 25% (11%) higher
after 1992.
23
Furthermore, when shipments (value added) are regressed on current and lagged demand, the corresponding
R-squared is 0.71 (0.40).
40
-40
-30
-20
-10
0
10
20
30
78 80 82 84 86 88 90 92 94 96 98 00 02 04
DINST
Figure 2.3: Monthly series on the demand instrument in the Iron and Steel industry for January
1978?November 2004. Data source: JIP database, Indices of Industrial Production and CGPI.
See the text for the construction method used.
expected for value added, current shipments do not need to respond positively to future predicted
shocks.
24
When shipments are used as a measure of output, the coe?cient on current unpredicted
demand shocks becomes higher and more signi?cant after 1992, while the opposite holds when value
added is used. For current and future predicted shocks, the coe?cients are mostly insigni?cant,
and some have incorrect signs. This may be because the instrument does a poor job in capturing
the predictable component of demand. Table (2.8) and (2.9) show the estimates of the same
equation using 6-month and 12-month forecast horizons respectively. The key results on the
output responses to demand shocks are essentially the same.
The di?erence in the observed direction of change in the responsiveness of shipments and
value added is rather puzzling, but in all cases, the shock response coe?cients before and after
1992 are not signi?cantly di?erent from each other. Theory suggests that holding other things
equal, the subsidy program should lead to an increase in output volatility. This happens as the
subsidy encourages ?rms to reduce production during downturns by subsidizing labor hoarding,
while making output respond faster during upturns as ?rms avoid paying hiring costs. The
24
While it is ideal to construct the measure of gross output as ‘shipments plus change in inventories,’ it was not
done in this exercise due to the use of indices.
41
Table 2.7: The estimates of the output elasticity with respect to demand shocks in the Iron and
Steel industry, 9-month forecast horizon.
Shipment (Y
t
) Value Added (Y
t
)
Pre-1992 Post-1992 Pre-1992 Post-1992
Demand:
Current Unpredicted 0.400*** 0.565*** 0.424*** 0.345***
(0.085) (0.097) (0.072) (0.071)
Current Predicted -0.003 0.257 0.257** -0.078
(0.154) (0.189) (0.130) (0.142)
Future Predicted -0.999* -0.187 -0.545 -0.100
(0.519) (0.473) (0.425) (0.360)
Lagged Variables:
L
t?1
-0.306 -0.057 -0.301 -0.662
(0.614) (0.682) (0.486) (0.505)
H
t?1
-0.181 -0.093 0.149 -0.071
(0.193) (0.130) (0.152) (0.114)
I
t?1
0.599*** 0.669*** -0.089 -0.085
(0.087) (5.162) (0.064) (0.077)
Q
t?1
-0.288*** -0.130 -0.046 -0.256***
(0.069) (0.095) (0.089) (0.095)
Number of obs. 150 128 150 128
R-squared 0.9181 0.9350 0.8577 0.880
Durbin-Watson statistics 2.16 2.07 2.00 1.86
F-statistics 68.31 72.55 36.72 36.94
empirical counterpart to this prediction is the responsiveness of value added to demand shocks.
However, we do not ?nd any evidence that value added responses to shocks increased after 1992.
The theoretical explanation for the reduced sensitivity may be that input responses are nonlinear
in the size of the demand shock, or that there are upper limits on labor input adjustments as well
as the use of the subsidy. Yet, since the coe?cients are not signi?cantly di?erent from each other,
whether or not an alternative framework is required is unclear. Filling in these empirical and
theoretical discrepancies remains an item for future investigation.
Finally, the theoretical framework in the next chapter implies that higher volatility in shock
processes increases the subsidy take-ups by increasing labor adjustment costs and therefore the
bene?t of the subsidy program. The result of a numerical experiment is given in the appendix.
The intuitive reason for this is that the subsidy covers part of the costs for sustaining employment
42
Table 2.8: The estimates of the output elasticity with respect to demand shocks in the Iron and
Steel industry, 6-month forecast horizon.
Shipment (Y
t
) Value Added (Y
t
)
Pre-1992 Post-1992 Pre-1992 Post-1992
Demand:
Current Unpredicted 0.413*** 0.567*** 0.431*** 0.301***
(0.086) (0.096) (0.073) (0.072)
Current Predicted 0.010 0.299 0.195 0.043
(0.153) (0.182) (0.131) (0.140)
Future Predicted -1.059** 0.002 -0.586 -0.059
(0.442) (0.422) (0.373) (0.331)
Lagged Variables:
L
t?1
-0.197 -0.311 -0.300 -1.385***
(0.584) (0.635) (0.462) (0.476)
H
t?1
-0.155 -0.021 0.057 0.014
(0.187) (0.145) (0.148) (0.109)
I
t?1
0.594 0.641*** -0.073 -0.040
(0.087) (0.116) (0.064) (0.075)
Q
t?1
-0.287*** -0.148 -0.054 -0.142
(0.069) (0.088) (0.089) (0.093)
Number of obs. 153 131 153 131
R-squared 0.9175 0.9377 0.8578 0.878
Durbin-Watson statistics 2.17 2.11 2.03 1.97
F-statistics 69.41 78.16 37.62 37.42
while ?rms reduce output through reduction in work hours, so that ?rms can avoid incurring
?ring/hiring costs to accommodate demand ?uctuations. This theoretical prediction matches
comfortably with the evidence that the EAS bill started to take on a dramatically higher level
after the structural breakpoint date of 1992
2.5 Conclusion
In this chapter, I evaluate labor input and inventory responses to demand shocks in the
manufacturing sector and in the Iron and Steel industry using an interrelated factor demand
model. I also investigate the output response to demand shocks in the Iron and Steel industry.
For this, a demand instrument was constructed using the growth rates of shipments of downstream
industries. In all cases, we observe a structural break in the data generating process for demand
43
Table 2.9: The estimates of the output elasticity with respect to demand shocks in the Iron and
Steel industry, 12-month forecast horizon.
Shipment (Y
t
) Value Added (Y
t
)
Pre-1992 Post-1992 Pre-1992 Post-1992
Demand:
Current Unpredicted 0.395*** 0.548*** 0.420*** 0.324***
(0.092) (0.095) (0.079) (0.072)
Current Predicted -0.023 0.187 0.234 -0.058
(0.170) (0.188) (0.144) (0.146)
Future Predicted -0.675 -0.153 -0.464 -0.124
(0.567) (0.507) (0.472) (0.400)
Lagged Variables:
L
t?1
-0.523 -0.021 -0.363 -0.527
(0.623) (0.691) (0.503) (0.525)
H
t?1
-0.197 -0.09 0.135 -0.082
(0.201) (0.155) (0.162) (0.117)
I
t?1
0.607*** 0.608*** -0.085 -0.104
(0.088) (0.132) (0.065) (0.080)
Q
t?1
-0.290*** -0.180* -0.052 -0.237**
(0.070) (0.095) (0.091) (0.097)
Number of obs. 147 125 147 125
R-squared 0.9191 0.9386 0.8548 0.880
Durbin-Watson statistics 2.20 1.99 2.00 1.90
F-statistics 67.62 75.00 35.03 35.94
around May 1992. The volatility of demand increased substantially after the date of the structural
break.
In the manufacturing sector, the results indicate that the burden of adjustment shifted from
an inventory to the labor input. This could be because this period witnessed a decline in the trend
growth rate. During the period of high trend growth, short-run ?uctuations in demand arguably
played a smaller role in in?uencing labor input decisions, while a slower growth rate during the
1990s made short-run ?uctuations relatively more important in labor input adjustment decisions.
A reduction in labor adjustment costs could also be another factor which led to the change in the
style of labor adjustment. I also discussed that the impact of the Employment Adjustment Subsidy
is unlikely to be visible in the manufacturing sector as a whole, due to the program’s small size
and its concentration in a few industries.
44
In the Iron and Steel industry, the primary recipient of the EAS, the results showed weak
evidence for a change in the employment response to demand shocks. This deviation from the
results for the manufacturing sector matches with the theoretical predictions of reduced employ-
ment volatility via the EAS, as the program encourages ?rms to sustain employment by allowing
?rms to ‘ride out’ unfavorable shocks through subsidization. Accordingly, the results indicate an
increased response of work hours to shocks, particularly to current predicted shocks. The inven-
tory responses in this sector showed a small di?erence across periods, and there is no regularity
in the direction of the change across di?erent planning horizons. However, the magnitude of the
inventory responses in the Iron and Steel industry in general are much larger than in manufactur-
ing as a whole. This highlights the fact that the Iron and Steel industry faces much higher labor
adjustment costs and/or lower inventory costs than the average industry in the manufacturing
sector. As the theory suggests, high labor adjustment costs could be the main reason for the high
take-up rate of the subsidy within the Iron and Steel industry.
Finally, the results on the output responses to demand shocks in the Iron and Steel sector
are mixed. Whereas shipment responses to current unpredicted shocks increased, value added
responses to demand shocks fell after 1992. Yet, we ?nd that coe?cients are not signi?cantly
di?erent from each other in all cases. I also discussed that the reduction in the response of value
added does not match with the theoretical prediction, and we may have to make some modi?cations
in order to theoretically describe these results. However, whether or not such modi?cations are
necessary is yet to be discovered. Although unresolved issues still remain, the theory presented
in the next chapter can comfortably explain why subsidy take-ups rose after 1992 as a result of
increased volatility in the shock processes.
On the whole, the exercises in this section elucidate evidence of a structural change around
1992, and the corresponding reactions to this change in the manufacturing sector and the Iron
and Steel industry. The manufacturing sector as a whole seems to have embarked on a shift in
adjustment strategy to meet the more volatile shock processes, while the Iron and Steel sector,
which relies heavily on the subsidy, did less to change its employment adjustment style. The
45
theoretical implications of the EAS on long-run productivity, employment, output, as well as
employment and output ?uctuations over the business cycle are discussed in the next chapter.
46
Chapter 3
Labor Adjustment, Productivity and Output Volatility: An Evaluation of Japan’s
Employment Adjustment Subsidy
3.1 Introduction
This chapter examines the Employment Adjustment Subsidy (EAS), a core Japanese em-
ployment insurance policy since 1975.
1
The EAS program allows ?rms to reduce output dur-
ing unfavorable business conditions without laying o? workers by providing part of the costs of
sustaining excess workers. The EAS policy has not yet been formally analyzed despite recent
macroeconomic literature emphasizing job reallocation as a driving force behind business cycles.
Therefore, the primary objective of this chapter is to point out some of the key implications of the
policy through the application of a theoretical framework of heterogeneous establishments with
aggregate uncertainty. In particular, this chapter investigates the impact of the EAS on average
labor productivity, job ?ows and entry/exit rates at the steady-state. In addition, it examines the
implications of the policy for the volatility of employment, output and productivity over business
cycles.
Between 1990 and 2002, over 360 billion yen (over 3.6 billion US dollars) was spent on the
EAS. On average between January 1991 and October 2001, about 170,000 establishments were
eligible for the subsidy program.
2
According to the 1996 Establishment Census, there are about
6.5 million establishments in Japan (excluding public service) with 770,000 in manufacturing.
1
Since 1975, the employment insurance programs had three central interrelated projects: (1) an employment
stabilization project that was carried out through the Employment Adjustment Subsidy, (2) a skill development
project providing assistance to the management and development of job training centers, and (3) a workers’ welfare
project providing employment consultation. The employment stabilization project has been the most predominant
of the three.
2
Although, as described later, additional criteria set by the government in terms of past employment and output
trends must be satis?ed in order to receive the subsidy.
47
Consequently, the average number of targeted establishments corresponds to 2.6% of the total
number of establishments, or approximately 20% of manufacturing establishments. The number
of targeted establishments peaked at 411,000 in February 2000.
The EAS recipients are heavily concentrated in the manufacturing sector, with the largest
bene?ciary being the Iron and Steel industry. Between 1990 and 2002, over 93% of subsidy
recipients were in manufacturing, and approximately 40% of the total bill during that period went
to the Iron and Steel industry.
3
Although the program in principle involves the entire economy,
to illustrate the theoretical implications of the program this chapter focuses on the Iron and Steel
industry. The calibrated industry model developed later in this chapter will attempt to match
moments of key variables obtained from the data for this industry.
With respect to the empirical background, Davis and Haltiwanger (1990, 1992, 1999) and
Davis, Haltiwanger and Schuh (1996), using longitudinal data sets in the US manufacturing sector,
expose the importance of idiosyncratic di?erences across establishments in explaining business cycle
dynamics. Many theoretical frameworks analyzing industry dynamics, such as Jovanovic (1982),
Hopenhayn (1992), Hopenhayn and Rogerson (1993), Ericson and Pakes (1995) and Campbell
and Fisher (2000), also stress the importance of heterogeneity across ?rms when characterizing
?rm’s production and entry/exit decisions. To the extent that the EAS interacts with such
heterogeneity across establishments within an industry, the appropriate theoretical framework to
analyze the e?ect of the policy must also encompass similar features.
In addition, prior research concerning the implications of di?ering labor market institutions,
3
In October 2001, the Japanese government abolished industry selection completely in response to criticism
that the program was skewed toward particular industries. Accordingly, the current guidelines provide that any
establishment can receive the subsidy if speci?c and much stricter criteria are satis?ed. Namely, the monthly
average of the last six months’ production has to drop by more than 10% and employment has to be less than or
equal to, in comparison with the same months of the previous year. Previously, the monthly average of the last
three months’ production had to be strictly less, while employment had to be equal or less than the previous year.
Furthermore, the subsidy cannot be given to establishments whose unfavorable business conditions are predicted
to last for more than two years, and establishments are no longer able to receive the subsidy continuously for more
than a year. Instead, they are required to take a year long hiatus, except during severe economic circumstances.
48
particularly European employment policies, has shown that labor market policies have an impor-
tant e?ect on equilibrium job ?ows, unemployment and productivity. Hopenhayn and Rogerson
(1993), for instance, illustrate that high ?ring costs in Europe, which interfere with the process
of job reallocation, lead to a sizable reduction in employment and a drop in average productivity.
Others have stressed the interactions between a changing economic environment and labor market
policy. Ljungqvist and Sargent (1998) explain that generous unemployment bene?ts increase un-
employment rates when the skill mix demanded in the labor market is rapidly changing. Other
studies have linked multiple labor market policies. Bentola and Rogerson (1993), for example,
demonstrate that wage compression in Europe tends to generate more volatile employment ?ows,
fostering a policy that restricts the ?ring of workers. They argue that these institutional di?er-
ences can account for the similarities in job ?ows and di?erences in unemployment between Europe
and the US. Although this paper will not examine the political economy of the origin of the EAS,
one of the chief objectives of the EAS has been to reduce the volatility of employment.
As wage compression can be considered as a precondition for ?ring restrictions, some labor
market institutions, namely labor adjustment costs and wage rigidities, are likely preconditions for
the EAS, since the subsidy will not be used if labor adjustment is costless or if wages can absorb
shocks. Although there are few quantitative studies that estimate the cost of ?ring workers in
Japan, there is some legal evidence that suggests that ?ring workers in Japan is generally very
di?cult, more similar to the European than the US case.
4
Moreover, the post-war tradition of
life-time employment has encouraged ?rms to invest in building ?rm speci?c human capital.
5
This
evidence indicates that adjusting employment has been quite costly in Japan. Accordingly, the
EAS was designed in order to “assist ?rms in their e?orts to maintain employment in times of
temporary unfavorable business conditions owing to economic recession or changes in the indus-
trial structure of the Japanese economy, as well as to promote employment stability and prevent
4
Takashi Araki (2000) discusses the legal evidence of stringent ?ring restrictions in Japan from the perspective
of corporate governance.
5
A detailed discussion of the relationship between intensive human capital investment and the low turnover rate
in Japan is provided by Mincer and Higuchi (1988).
49
unemployment.”
6
While there has not been a formal empirical study on the e?ect of the subsidy program,
primarily due to the unavailability of data, some have attempted to examine if the EAS distorts
employment behavior. For instance, Hashimoto (1993) uses monthly aggregate manufacturing
data and concludes that employment became less sensitive, while working hours became more
sensitive, to demand shocks after the subsidy program was enacted in 1975.
7
However, the results
in the previous chapter demonstrated that the impact of the subsidy is hard to detect in the
manufacturing sector during the 1990s in which subsidy take-up peaked. On the other hand, the
results from the Iron and Steel industry indicated that the subsidy kept employment relatively
unresponsive to demand shocks even during the period of higher volatility in the shock processes,
while increasing the intensity of the adjustment through work hours.
8
Another related yet unexplored empirical issue is that the presence of subsidized workers
reduces measured productivity, since hoarded workers are not properly taken into account in
employment statistics. This paper will attempt to estimate the number of unutilized workers
through the subsidy program in the Iron and Steel industry, as well as the reduction in productivity
that can be accounted for by the inclusion of subsidized workers in employment statistics. Then
these estimates will be used for the calibration of the model. The model developed here o?ers
insights beyond the direct e?ect of labor hoarding on productivity. The indirect e?ects of the EAS
on the cyclical dynamics of output and employment generate a wide set of empirical predictions,
testable in future research as more data becomes available.
The model exploits the theoretical framework of Hopenhayn (1992) and Hopenhayn and
6
Japanese Ministry of Health, Labor and Welfare. “Guidebook for Employment Adjustment Subsidy,” 2002.
7
He also points out that the treatment of temporarily laid o? workers in Japanese statistics as ‘employed’ explains
part of the di?erences in unemployment rates between Japan and the US.
8
On the contrary, the unemployment insurance (UI) system in the US encourages temporary layo?s instead of
temporary business closures. Feldstein (1976, 1978) and Anderson and Meyer (1993) discuss the incentive for ?rms
to increase temporary layo?s when the experience rating of ?rms’ unemployment insurance is imperfect. Feldstein
(1976) explains why employment instead of hours is reduced in response to negative demand shocks under the UI
system in the US.
50
Rogerson (1993). The main advantage is that, as previously mentioned, this model allows for a
heterogeneity across establishments and therefore allows us to evaluate the impact of the subsidy
program on industry dynamics by explicitly modeling the equilibrium response of heterogeneous
establishments. Unlike Hopenhayn and Rogerson, however, the consideration of labor supply
decisions and thus the households’ problem will be omitted to focus on the impact of the subsidy
on establishment-level dynamics. Hence the analysis will be a partial equilibrium estimate of
the change in overall industry dynamics caused by the subsidy program. Moreover, two-state
aggregate uncertainty is added to the model, a feature that was not present in Hopenhayn and
Rogerson (1993). Since the wage remains constant in the model, the aggregate uncertainty should
be best interpreted as re?ecting the partial equilibrium real impact of shocks net of their impact
on wages.
In interpreting the impact of the subsidy on average labor productivity, a word of caution
is in order: while ?rms are heterogeneous in the model, workers are homogeneous in the sense
that productivity does not increase with tenure. The subsidy could increase average productivity
if this feature were added to the model. This was not done in this paper because of the high
concentration of the subsidy in sectors where the value of workers’ skills seems to be depreciating
faster in comparison to other sectors.
9
In my model, the di?erence between old and new workers
is solely re?ected in the hiring cost, which reduces output during the ?rst period; the productivity
of new and old workers is equalized afterwards.
I show that the subsidy program reduces steady-state average productivity primarily by in-
creasing the number of unutilized workers (labor hoarding e?ect). Roughly speaking, the reduction
in average productivity is more or less proportional to the fraction of subsidized workers: when
the fraction of subsidized workers is about 1%, average productivity also falls by about 1%. At
the same time, average ?rm-level employment increases and the job turnover rate falls with the
subsidy. When the cost of the subsidy and the gains of reduced adjustment costs are included in
9
For example, the subsidy seemed to have concentrated in those sectors with comparative disadvantage in the
international market. The government often cites as reason for industry selection into the EAS as “unfavorable
business conditions arising from the competition with cheaper imports from China” etc.
51
the calculation of average productivity, productivity is further reduced for reasonably sized labor
adjustment costs, as the cost of the subsidy exceeds the savings on labor adjustment costs.
10
The estimated direct impact of the subsidy on productivity is small, as the (estimated)
average fraction of subsidized workers in the Iron and Steel sector between 1990 and 2002 is about
2.1%. However, the second moment features generated by my simulation exercises reveal that
with realistic parameters, the subsidy program has a disproportionately large impact on output
and employment dynamics over the business cycle. In particular, output volatility can increase
by 3.5% even when the steady-state fraction of subsidized workers is around 1.6%. The intuitive
reason for this result is that the subsidy increases the sensitivity of output to aggregate shocks
symmetrically: following unfavorable shocks, the subsidy allows ?rms to reduce production without
laying o? workers, while following favorable shocks, ?rms are able to increase output without hiring
new workers.
On the other hand, the subsidy reduces employment volatility. In some cases, the drop in
employment volatility can be substantial, even when the fraction of subsidized workers is small.
Below, I show that hiring and ?ring costs set equal to the annual wage of workers can reduce the
volatility of employment by about 12% even if the fraction of subsidized workers is less than 2%.
The reduction in employment volatility is achieved by the reduced sensitivity of job creation and
destruction to aggregate shocks over the business cycle. The EAS also increases the average size
of the ?rm while reducing average ?rm level output at the steady-state. Finally, the steady-state
exit/entry rate as well as the steady-state job creation/destruction rate drop with the subsidy.
This chapter proceeds as follows: section (3.2) provides a brief background of the EAS as
well as an overview of the employment and output trends obtained from the aggregate Iron and
Steel industry data. I then calculate the direct impact of the EAS on TFP induced by labor
hoarding, which later will be used for the calibration of the model. Section (3.3) lays out the
theoretical framework of the industry model and provides analytical results. Section (3.4) shows
results from solving a stochastic version of the model through numerical dynamic programming. I
10
However, with high enough labor adjustment costs, it is possible that the savings on adjustment costs could
exceed the cost of the subsidy.
52
present key statistical features from the stationary distribution of the model, as well as simulation
exercises that compare the subsidy case with the benchmark case that sets the subsidy to zero.
Section (3.5) o?ers my conclusions.
3.2 Background
3.2.1 Summary of the EAS
The Employment Adjustment Subsidy program was initiated in 1975 as a preemptive mea-
sure against unemployment. More speci?cally, it was initiated in response to policymakers’ concern
that the unemployment rate would rise following the ?rst oil shock and the resulting changes in
the industrial structure of the Japanese economy.
11
In principle, the subsidy was intended to help
sustain employment during temporary unfavorable business conditions without incurring the loss
associated with labor adjustment costs. This was mainly achieved by reimbursing a fraction of
wages for establishments closing part or all of its operations, or a fraction of the cost of sending
workers to other (unrelated) establishments. The subsidy was expected to lower unemployment
as well as the cost of unemployment insurance by reducing the unemployment rate.
Prior to 2001, the government selected eligible industries, either entire four-digit sectors
or subsectors, based on recent trends in industrial output and employment, or changes in the
industrial structure, such as rising competition from foreign imports. The o?cial selection criteria
in terms of output and employment were: i) the average of the past three months’ industrial
production dropped more than 5% compared to the same months of the previous year, and ii) the
average of the past three months’ employment had not increased compared to the same months of
the previous year.
12
Furthermore, additional special selection criteria were set in 1995 for more
11
The Japanese Ministry of Labor reports that the EAS was originally designed in response to a recommendation
by the OECD that the Japanese government prepare for higher unemployment arising from the transition from a
growing to a mature economy. [Japanese Ministry of Labor, Employment Security Bureau (1999), p.14.] Another
justi?cation often provided was to assist ?rms, which had been the primary provider of job security often in the
form of life-time employment, to sustain employment during di?cult times.
12
As for the employment criteria, it became ‘a drop of 5% or more’ between March 2000 and October 2001.
53
generous subsidy coverage: “as a result of an appreciation of the yen or economic globalization, the
monthly average of the past six months’ industrial production and employment fell or is predicted
to fall more than 10% compared to the same season in one of the three previous years.” The
selection was not completely deterministic as explained by the government: the “selection is not
solely based on ?gures but also determined in accordance with our objective of the prevention
of unemployment.”
13
The Japanese government abolished industry selection criteria in October
2001, replacing them with tougher establishment-level eligibility criteria.
Under the standard selection rules, industries were selected for one year with the possibility
of an extension for an extra year if needed. Once selected, industries could be re-selected after
a six-month break. For the special selection rules between 1995 and 2001, the selection period
was set to two years with the possibility of an extension. Between 1990 and 2001, the unweighted
average length of eligibility for a selected industry was 2.6 years with a maximum of 7 years.
During the same period, about 96% of the selected four-digit industries or subcategories belonged
to the manufacturing sector, of which about 14% belonged to Ceramic and Clay Products, 13%
to General Machinery, 10% to Metal Products, 10% to Textiles and 9% to the Iron and Steel
industry.
Once an industry was selected, establishments in this industry, as well as their upstream
suppliers, could take up the subsidy if the average of their last three months’ production (em-
ployment) was less (equal or less) than the monthly average for the same season a year before.
Small- and medium-size establishments meeting these criteria could receive 2/3 of their labor costs
(3/4 under special selection) and large establishments could receive 1/2 of their labor costs (2/3
under special selection) while they implemented temporary closures of their business operations.
14
13
Japanese Ministry Labor, Employment Security Bureau (1999), p.191.
14
Note that establishments do not have to pay full wages while they implement temporary business closures.
Moreover, the maximum coverage for the establishments in an industry selected under standard selection criteria
(shitei-gyosyu) was 100 days × the total number of employees, and the maximum coverage for ?rms in a industry
selected under the special selection criteria (tokutei koyo chosei gyosyu) was 200 days × the total number of
employees. Between July 1995 and October 2000, about 44% of the targeted establishments could apply under the
special selection criteria.
54
0
10
20
30
40
50
60
76 78 80 82 84 86 88 90 92 94 96 98 00
Temporary business closures
Temp. business closures w/ training
Sending workers to other establishments
Figure 3.1: Annual total subsidy bill (in billions of yen) by three types of activities for 1975?2001.
Data source: the Employment Security Bureau of Japanese Ministry of Health, Labor and Welfare.
Additional allowances of three thousand yen per worker per day were given if establishments pro-
vided job training to workers while they temporarily closed their businesses.
15
Instead of business
closures, establishments could also send workers to other unrelated establishments for more than
three months. In this case, the receiving establishment was required to pay for the labor service
provided by the subsidized workers, and the sending establishment paid the di?erence between the
workers’ original wage and the amount paid by the receiving establishment. The subsidy covered
a fraction of the cost borne by sending establishments.
Although the subsidy program started in 1975, its e?ect was probably largest during the
1990s, the decade of sluggish growth. Figure (3.1) shows the subsidy bill for each of the three
options available to establishments. The total subsidy bill dramatically increased after 1992.
Furthermore, among the three options, temporary business closure had the highest share of the
total subsidy bill, especially during the 1990s. Subsequently, the analysis of this chapter focuses
15
In October 2001, however, the allowance for training was reduced to 1200 yen.
55
on the 1990s for the following reasons: i) more establishments were made eligible during the 1990s,
ii) the subsidy rules stabilized by 1990, and iii) data on the subsidy bill by two-digit sector is
available only after 1990. In the theoretical section, I will model the policy using the criteria prior
to the October 2001 revision.
Table 3.1: Share of subsidy bill by industries for 1990?2002.
Total Bill Annual Average
Manufacturing Total 93.96% 93.45%
Food 0.09% 0.13%
Beverage, Feed and Tobacco 0.04% 0.03%
Textiles 5.31% 4.93%
Apparel and Other Textiles 1.74% 1.53%
Lumber and Wood Products 0.63% 0.59%
Furniture and Fixtures 0.64% 0.59%
Pulp and Paper Products 0.44% 0.26%
Printing and Publishing 0.03% 0.03%
Chemical and Allied Products 1.54% 1.28%
Petroleum and Coal Products 0.15% 0.15%
Plastics 0.54% 0.38%
Rubber Products 1.40% 1.13%
Leather, Tanning, Fur Products 0.19% 0.17%
Ceramic, Stone and Clay Products 3.98% 3.52%
Iron and Steel 40.70% 47.03%
Non-ferrous Metals 1.61% 1.42%
Fabricated Metals 3.36% 2.78%
General Machinery 12.75% 10.49%
Electrical Machinery 6.24% 7.21%
Transportation Equipment 10.69% 8.15%
Precision Instruments 1.06% 0.96%
Ordinance 0.03% 0.02%
Other Manufacturing 0.80% 0.67%
Other Sector Total 6.04% 6.55%
The share of the total subsidy bill between 1990 and 2002 as well as the annual average
share by two-digit sector is provided in Table (3.1).
16
The Iron and Steel industry has the
16
This data was made available upon request from the Employment Stability Bureau of the Ministry of Health,
Labor and Welfare. Unfortunately, the data prior to 1990 is not currently available.
56
largest annual average share (47.03%), followed by General Machinery (10.49%), Transportation
Equipment (8.15%), and Textiles (4.93%).
17
As mentioned previously, the high concentration
in the Iron and Steel industry motivates my modeling the e?ects of the subsidy program on this
industry.
18
3.2.2 Overview of the Iron and Steel Industry
This section provides an overview of output, employment and productivity behavior in the
Iron and Steel industry between 1973 and 2001. The data set used to study output is the Japan
Industry Productivity Database (JIP database).
19
This data set was compiled as a part of the
Japanese government’s project to calculate annual TFP for 84 sectors in Japan between 1973 and
1998.
20
Since the database is based on the 1968 SNA (System of National Account), currently
data is available only through 1998. Figure (3.2) shows real gross output between 1973 and
1998. There is a considerable increase in output in the late 1980s and early 1990s, followed by
a large drop in the mid- and late-1990s. Figure (3.3) shows the employment trend, taken from
the Employment Trend Survey, which includes both permanent and temporary workers for all
establishments with more than ?ve employees.
21
Except in the mid-1980s, employment exhibits
a steady decline since 1973. This, combined with the positive trend in real gross output implies
increased capital intensity or TFP during this period.
If subsidized workers are included in employment, then standard productivity measures will
17
The share calculated is in terms of annual average. The results for the total subsidy bill between 1990 and
2002 are similar.
18
A strong union presence, which generates wage rigidity and high labor adjustment costs, may be one of the
reasons why the Iron and Steel industry has a high take-up rate. However, since eligible industries are given by
four-digit industries or subcategories within four-digit industries while the estimated number of subsidized workers
are available by two-digit industries, the investigation of the take-up rates across sectors requires the size of eligible
workers to be estimated by two-digit industries. This was not done in this paper, and remains an area for future
research.
19
The JIP database is made available in English by Kyoji Fukao on his website: http://www.ier.hit-
u.ac.jp/˜fukao/english/data/index.html.
20
See Fukao et al. (2003) for the TFP analysis of the 84 sectors from 1973 to 1998 using the JIP database.
21
The beginning-of-year (January 1st) ?gure was used to represent the employment of the previous year.
57
19000
20000
21000
22000
23000
24000
25000
26000
27000
28000
72 74 76 78 80 82 84 86 88 90 92 94 96 98
Real gross output
Figure 3.2: Annual real gross output in the Iron and Steel industry (in billions of yen). Data
source: JIP database.
240
280
320
360
400
440
480
520
72 74 76 78 80 82 84 86 88 90 92 94 96 98
Employment
Figure 3.3: Annual employment in the Iron and Steel industry (in thousands), which include both
permanent and temporary workers for all establishments with more than ?ve employees. Data
source: Employment Trend Survey.
58
be distorted since labor input will be systematically overstated.
22
The data provides the annual
subsidy bill by two-digit sector between 1990 and 2002, but does not provide the total number of
subsidized work days in each sector. Consequently, we need to estimate the number of unutilized
workers for each year using the annual subsidy bill. This was accomplished as follows: ?rst, the
average subsidy cost per work-day (i.e. per worker per day) was calculated by dividing the total
subsidy bill covering the entire economy by the total number of subsidized work days covered each
year.
23
Then the annual subsidy bill for the Iron and Steel industry was divided by the annual
average subsidy cost per work-day in order to calculate the total number of subsidized days in this
industry. Finally, this number was divided by the annual average work days for workers in the
Iron and Steel industry to get an estimate of the number of subsidized workers for each year.
24
Figure (3.4) shows the result of this calculation. On average, 2.1% of Iron and Steel workers were
subsidized during this period. In 1995, the highest take-up year, 4.6% of Iron and Steel workers
were subsidized.
25
Since the JIP dataset ends in 1998, an alternative source of output data must be used to
calculate productivity between 1990 and 2001. I use measures of real value added as well as capital
stock, both based on the 1993 SNA standard, from the Annual Report on National Account.
26
An
22
Note that average work hours may capture part of labor hoarding through the EAS, but it is unlikely to
entirely capture the total number of subsidized workers. For the discussion of variable factor utilization in a?ecting
cyclicality of productivity, see Basu and Kimball (1997), Basu and Fernald (2000) and Basu, Fernald and Shapiro
(2001).
23
Since there are three subsidy options (i.e. temporary closures, temporary closures with training, and sending
workers to other establishments), the weighted average of these three was taken to estimate the average cost per
work-day. Since the work-day cost for sending workers to other establishments cannot be estimated, this was
replaced by the work-day cost of temporary closures.
24
The average work days for workers in the Iron and Steel industry was taken from Monthly Labor Statistics by
the Japanese Ministry of Health, Labor and Welfare. Since the ?gure provided here is the monthly average, it was
multiplied by 12 to get an approximate annual ?gure. The data is available at the following website in Japanese:
http://stat.jil.go.jp.
25
However, since the subsidy bill includes the third option, namely ‘sending workers to other establishments,’ if
we focus only on temporary business closures given by the ?rst two options, the estimated fraction of workers should
be somewhat smaller than 2.1%.
26
Capital stock is at completion basis. The data can be found at the following website in Japanese:
59
0
2000
4000
6000
8000
10000
12000
14000
90 91 92 93 94 95 96 97 98 99 00 01 02
Estimated number of hoarded workers via EAS
Figure 3.4: Estimated annual number of workers who are unutilized for production via EAS in the
Iron and Steel industry. Data source: the information on subsidy was provided by the Employment
Security Bureau of the Japanese Ministry of Health, Labor and Welfare. Other data used for the
estimation is provided in the text.
annual growth accounting exercise, as in Hayashi and Prescott (2000), was performed to estimate
the level as well as the growth rate of TFP both before and after adjusting labor inputs for the
number of subsidized workers. More speci?cally, I adopt the following Cobb-Douglas speci?cation:
Y = AK
?
(h · (E ?S))
1??
, (3.1)
where Y is real value added, A is the measure of TFP, K is the real capital stock, h is average work
hours, E is employment and S is the number of subsidized workers.
27
The cost share of capital
? is set equal to 0.464, which corresponds to the average cost share of capital excluding material
inputs between 1973 and 1998 given by the JIP database.
28
http://www.esri.cao.go.jp/jp/sna/toukei.html.
27
The average work hours was taken from Monthly Labor Statistics by the Japanese Ministry of Health, Labor
and Welfare, and employment data is taken from the Employment Trend Survey. Note that the employment ?gure
is based on establishments with more than 5 employees, while the work hour ?gure is based on establishments with
more than 30 employees, due to the lack of series since 1975.
28
In aggregating the cost share at the two-digit level with the JIP dataset, nominal gross output was used as a
weight because the dataset does not provide the total cost for each sector.
60
.035
.036
.037
.038
.039
.040
.041
.042
.043
.044
90 91 92 93 94 95 96 97 98 99 00 01 02
TFP TFP (with subsidy adjustment)
Figure 3.5: TFP (1990?2001) in the Iron and Steel industry. Data source: Annual Report on
National Account for the output and capital stock, Employment Trend Survey for annual employ-
ment, and Monthly Labor Statistics for average work hours. See the text for the estimated annual
number of subsidized workers.
Figure (3.5) shows the level of TFP in the Iron and Steel industry with and without ad-
justments for the subsidy, using the National Accounts data. The level of TFP is higher when
employment is adjusted for the subsidy for obvious reasons. The adjustment is particularly large
during the mid-1990s, and on average, adjusted TFP is higher than unadjusted TFP by 1.16%
between 1990 and 2001. Figure (3.6) demonstrates the level of TFP using the JIP database.
Since the subsidy bill by industry is not available before 1990, the number of subsidized workers
prior to 1990 is estimated by applying Iron and Steel’s average annual share of 47% between 1990
and 2002 to the total subsidy bill. Except during the 1990s, the two measures of TFP are almost
identical.
In the JIP database, the correlation between the log of TFP and the log of real gross output
falls from 0.7916 to 0.7843 when the subsidy adjustment is made, and the correlation between the
log of TFP and the log of real value added falls from 0.9921 to 0.9906. The correlation between
the log of real gross output and the log subsidy bill is ?0.645. The result is consistent with the
argument that labor hoarding via EAS increases the procyclicality of productivity, although only
61
.01
.02
.03
.04
.05
.06
.07
72 74 76 78 80 82 84 86 88 90 92 94 96 98
TFP TFP (with subsidy adjustment)
Figure 3.6: TFP (1973?1998) in the Iron and Steel industry. Data source: the JIP database for the
output and capital stock, Employment Trend Survey for annual employment, and Monthly Labor
Statistics for average work hours. See the text for the estimated annual number of subsidized
workers.
a small part is accounted for by the subsidy.
29
The exercise in this section reveals that the subsidy, due to the small fraction of subsidized
workers, has a trivial impact on the level and procyclicality of TFP. The calibrated model in the
next section will attempt to match these moments to investigate the impact of the subsidy program.
I will show later that even when the direct impact is small, the EAS can have a signi?cant impact
on output and employment volatility.
29
In terms of growth rate, the correlation between the TFP growth rate and the growth rate of value added falls
from 0.9929 to 0.9879. The same exercise using National Accounts data shows that the correlation between the
log of TFP and the log of real value added falls from 0.435 to 0.396, and the correlation between the log of real
value added and the log of subsidy bill is ?0.244. However with this data, signi?cance levels are low due to a small
number of observations.
62
3.3 An Industry Model
In this section, I build a simple industry model to capture the e?ect of the employment
subsidy. Let n
t
denote the total number of employees in the ?rm and e
t
? n
t
the number of
workers who are utilized for production at period t. The ?rm needs to pay a wage equal to w
to each of the e
t
workers who actually work and produce, and a fraction ? of w to the n
t
? e
t
workers who are unutilized for production. Firms are eligible for the subsidy with probability ?.
If eligible, they can receive payments for their n
t
?e
t
unutilized workers. Let s denote the fraction
of the labor cost of unutilized workers that the government subsidizes. That is, for each unutilized
worker, the government pays a fraction s of the discounted wage ?w that unutilized workers receive,
and the remaining (1 ? s)?w is paid by the ?rm. Hence, the total subsidy received by a ?rm at
time t when subsidized is given by (n
t
?e
t
)?ws.
30
Total employment n
t
will be the state variable
that ?rms carry to the next period, unless they decide to exit the market.
Firms have a stochastic production function f(e
t
, ?
t
), use labor as the only input of pro-
duction and receive a pro?tability shock, denoted as ?
t
, that has an idiosyncratic component as
well as an aggregate component common to all ?rms. The production function is assumed to be
strictly concave in labor and satis?es f
e
> 0 and f
ee
< 0. Moreover, the wage and price are both
assumed to be exogenously determined and invariant over time. For a given price p, the expected
pro?ts for a ?rm that employs n
t
workers, utilizes e
t
workers for production, takes up the subsidy
if available, and receives a shock ?
t
at period t are as follows:
pf(e
t
, ?
t
) ?we
t
??w(n
t
?e
t
) +?
t
(n
t
?e
t
)?ws ?pc
f
??(n
t
, n
t?1
) ??(n
t
, n
t?1
). (3.2)
The ?rst term is revenue from output. The second and third represent wage payments to utilized
and unutilized workers respectively. The fourth captures the subsidy receipts. Here, ?
t
is a
random variable that takes a value of 1 with probability ? and 0 with probability 1??. The term
pc
f
re?ects the ?xed costs of production each period and can be interpreted as the opportunity
cost of the entrepreneur. This ?xed cost provides ?rms incentives to exit the market when their
30
Note that the government provides a guideline on ?, but the consent of the workers is required (typically through
an agreement with their labor union) for them to miss work at a discounted wage ?w.
63
prospects look su?ciently unfavorable, instead of simply waiting for their future prospects to turn
around. As described in Hopenhayn and Rogerson (1993), this term is necessary for some positive
amount of exit to exist in equilibrium. In what follows, p will be set as a numeraire so that it will
be omitted from the analysis.
The terms ?(n
t,
n
t?1
) and ?(n
t
, n
t?1
) represent linear hiring and ?ring costs respectively,
and are speci?ed as:
?(n
t
, n
t?1
) = ?
h
· max(0, n
t
?n
t?1
) (3.3)
?(n
t
, n
t?1
) = ?
f
· max(0, n
t?1
?n
t
) (3.4)
where ?
h
and ?
f
are the ?xed costs of hiring and ?ring a worker. Either ?
h
or ?
f
must be positive
in order to provide ?rms incentives to take up the subsidy, since without labor adjustment costs,
labor adjustment is always instantaneous and there is no need to keep excess workers when ?rms
receive unfavorable shocks.
The timing of decisions is given as follows. An incumbent starts t with previous period’s
shock ?
t?1
and previous period’s employment n
t?1
. Before observing its current pro?tability
shock and subsidy eligibility, a ?rm must decide whether to shut down or stay in business based
on its expected pro?tability. If the ?rm decides to exit its business, the workers will be dismissed
entirely and the ?rm must pay the ?ring cost to each of its workers, while avoiding the ?xed cost of
operation c
f
.
31
It then receives zero pro?ts in all future periods. If the ?rm decides to stay, the
incumbent ?rm observes current pro?tability ?
t
and subsidy eligibility ?
t
, and it decides whether
to take up the subsidy or not if ?
t
= 1. It then chooses employment n
t
and the number of utilized
workers e
t
, and produces with e
t
< n
t
with the subsidy or e
t
? n
t
without the subsidy, before
moving to the next period with n
t
. Here, I do not impose the constraint e
t
= n
t
when ?rms
are not subsidized, although this equality will hold at an optimum for the set of parameter values
provided in the next section.
31
Alternatively, this implies that at the beginning of the period when the current state is revealed to the ?rm, it
decides whether or not it exits from the market at the end of the period.
64
The value function for ?rms under this policy scheme is given by the following equation:
V (n
t?1
, ?
t
, ?
t
) = max
e
t
?n
t
,n
t
{f(e
t
, ?
t
) ?we
t
??w(n
t
?e
t
) +?
t
(n
t
?e
t
)?ws ?c
f
??(n
t
, n
t?1
) ??(n
t
, n
t?1
) +?{ max
stay, exit
[EV (n
t
, ?
t+1
, ?
t+1
), ??(0, n
t
)]}},
(3.5)
where e
t
= n
t
if the ?rm fully utilizes all its workers. The ?rst order conditions of the value
function with respect to e
t
and n
t
imply that the optimal level of e
t
is driven by the current shock
?
t
and parameters such as s, w, and ?, while the optimal n
t
is a?ected by w, s, ?
h
, ?
f
and the
expected marginal future bene?t of the extra worker. This implies that the decision to take up
the subsidy will depend not only on the size of the subsidy and labor adjustment costs, but also
on how unfavorable today’s shock looks relative to future prospects.
For a given set of parameter values, the state variables n
t?1
, ?
t
and ?
t
a?ect ?rms’ decisions
regarding employment (production) and subsidy decisions. First, I will provide a graphical expla-
nation of the state spaces over n
t?1
and ?
t
for which subsidy take-up takes place given eligibility.
Then using the ?rst order conditions, I will show the marginal change that eligibility generates by
comparing the behavior of eligible and non-eligible ?rms facing the same pro?tability shock and
the same level of previous employment, assuming that the eligible ?rm ?nds it optimal to take up
the subsidy.
Two intuitive implications of the subsidy program are the following. The ?rst is that an
increase in the volatility of aggregate and/or idiosyncratic shocks, as well as a reduction in the
persistence of shocks, increases subsidy take-up by reducing optimal utilization beneath the optimal
level of employment when a ?rm receives a temporary unfavorable shock. A numerical experiment
to examine the impact of increased volatility on the subsidy take-up decision is provided in the
appendix. The second is that an eligible ?rm keeps the level of employment higher, and output
lower, in comparison with a non-eligible ?rm with the same previous level of employment and
current pro?tability conditions.
Regarding the optimal choice of n
t
, notice that it features a region of inaction owing to the
presence of labor adjustment costs. Figure (3.7) illustrates the optimal employment decision rule
for a given pro?tability shock. The dotted diagonal line represents the points where n
t
= n
t?1
.
65
0 5 10 15
0
5
10
15
optimal n
n
t
nt?1
nt
nt=nt?1
Figure 3.7: Employment decision rule. It shows the optimal choice of employment given the
previous level of employment. The diagonal line represents the circumstance in which employment
remains the same.
The ?rm expands in employment size when n
t?1
is such that the optimal n
t
lays above the dotted
line, and it contracts if n
t
lays below the dotted line. Where the two lines overlap, the ?gure
shows the region of inaction.
On the other hand, the optimal choice of e
t
is independent of the state variable n
t?1
. Now,
ignoring the constraint e
t
? n
t
, consider a case in which a ?rm receives a temporary favorable
shock. In this case, the e
t
dictated by the optimal current production decision will be higher
than n
t
driven by the future prospect of pro?tability. Therefore, we have an infeasible situation
in which e
t
is higher than n
t
, as illustrated by ?gure (3.8). Obviously, no ?rm can take up the
subsidy under this scenario.
Next consider a case in which a ?rm experiences a temporary unfavorable shock. Figure
(3.9) presents a situation in which e
t
lays below n
t
for some region of n
t?1
. Note that if ?rms are
small and they wish to expand, they will not take up the subsidy regardless of how unfavorable
the shock is. As mentioned before, this is because labor hoarding is costly even when ?rms receive
66
0 5 10 15
0
5
10
15
optimal n vs. optimal e for an unsubsidized firm
n
t
,

e
t
nt?1
nt
et
nt=nt?1
Figure 3.8: Employment and production decision rule for an unsubsidized ?rm. Since e
t
is
constrained to be less than n
t
, this represents the circumstance in which the subsidy take-up does
not take place.
0 5 10 15
0
5
10
15
optimal n vs. optimal e for a subsidized firm
n
t
,

e
t
nt?1
nt
et
nt=nt?1
Figure 3.9: Employment and production decision rule for a subsidized ?rm. Firms apply when
the optimally chosen e
t
is strictly below n
t
.
67
0 5 10 15
0
5
10
15
optimal subsidy coverage
n
t
?
e
t
nt?1
Figure 3.10: Optimal subsidy coverage. This graph shows the distance between n
t
and e
t
in ?gure
(3.9) for n
t
strictly greater than e
t
.
a subsidy. Therefore, no subsidy take-up takes place when the state variable n
t?1
is such that
the optimal n
t
lays above the dotted diagonal line. The optimal subsidy coverage in this case is
the di?erence between n
t
and e
t
for n
t
< n
t?1
. This is presented by ?gure (3.10). As we can
see, the subsidy coverage increases with the state space n
t?1
within the region of inaction, but
stays constant above the region. The distance between the optimal n
t
and e
t
will increase as the
current pro?tability shock either becomes more unfavorable relative to future prospects, or the
current shock becomes highly transitory.
Now, I will illustrate two cases contrasting di?erences in the behavior of eligible and non-
eligible ?rms in the same values for state variables. As mentioned previously, the purpose of
this comparison is to study the marginal change in ?rm behavior that subsidy eligibility induces.
Accordingly, I restrict attention to the portion of the state space of the pro?tability shocks and
the level of employment such that subsidy take-up is optimal contingent on eligibility.
32
The
32
Subsidy take-up often takes place over the pro?tability and employment state space in which downsizing is a
preferred option for the ?rms. This does not mean that all downsizing ?rms take up the subsidy. For example,
68
behaviors of expanding ?rms are not discussed since they optimally never take up the subsidy
regardless of eligibility. Neither will I discuss the situation where the ?rm is optimally in a region
of inaction regarding employment. Furthermore, I will not focus on the reallocative implications
of the subsidy program for the sake of simplicity, and therefore exit decisions are omitted from
the analysis for now. Lastly, note that this exercise is not intended to compare behavior with the
subsidy program to behavior without the subsidy program. That comparison will be performed
using simulations from numerical dynamic programming in the next section.
Case 3.1 Firms are eligible for the subsidy
The program requires that a ?rm not increase employment when receiving a subsidy. This
constraint is not binding in equilibrium since expanding ?rms are unwilling to bear the labor costs
of underutilizing workers.
33
Therefore, subsidized ?rms naturally have n
t?1
? n
t
> e
t
. Ignoring
the region of inaction, the ?rst order conditions of equation 3.5 with respect to n
t
and e
t
for
downsizing ?rms are:
(1 ?s)?w = ?EV
n
(n
t
, ?
t+1
, ?
t+1
) +?
f
(3.6)
and
w ?(1 ?s)?w = f
e
(e
t
, ?
t
), (3.7)
where EV
n
(n
t
, ?
t+1
, ?
t+1
) is the derivative of EV (n
t
, ?
t+1
, ?
t+1
) with respect to n
t
.
34
Equation (3.6) shows that the unsubsidized portion of the labor cost of keeping an extra
worker, given by the left side of the equation, must be equated with the marginal future bene?t of
keeping the worker as well as the bene?t from avoiding the ?ring cost today. This provides the
optimal condition for n
t
. Similarly, equation (3.7) shows that the cost of utilizing a worker, given
?rms are less likely to apply, the more persistent the sequence of pro?tability shocks becomes. These cases are not
examined as they are irrelevant for the study of the marginal change in ?rm’s behavior with eligibility.
33
This result may not hold if labor adjustment costs are nonlinear in the number of workers, thereby creating a
smoothing incentive for labor adjustment, or if adjustment costs are stochastic.
34
More speci?cally, let ?
1
and ?
2
be the Lagrange multipliers of constraints n
t?1
? n
t
and n
t
> e
t
, respectively.
By complementary slackness, ?
2
must be zero for ?rms receiving the subsidy. Similarly, ?
1
must also be zero as
we are considering downsizing ?rms.
69
by the di?erence between the wage of a production worker and the cost a ?rm bears to sustain
a worker unutilized, must be equated with the marginal revenue product. This characterizes the
optimal condition for e
t
.
Note that the concavity of EV implies that EV
n
is declining in n
t
.
35
Hence, holding
everything else constant, optimal n
t
will increase as s approaches one or as ? approaches zero. In
addition, decreases in ? and increases in s or in the probability of being eligible ? increase EV
in the presence of labor adjustment costs. This implies further increases in the optimal n
t
. On
the other hand, the concavity of f implies that the optimal e
t
will decrease with s and increase
with ?. Therefore, a higher s or lower ?, by reducing the costs of unutilized workers, increases
the distance between the optimal n
t
and e
t
, thereby resulting in higher subsidy coverage.
36
Equation (3.6) also implies that, holding EV constant, a higher ?ring cost ?
f
increases n
t
.
However, this e?ect is muted since an increase in ?
f
indirectly reduces optimal n
t
by reducing EV .
Hiring costs do not a?ect n
t
directly, as hiring costs already paid are sunk for non-expanding ?rms.
But hiring costs reduce the optimal n
t
indirectly by lowering EV . This is the intuition given by
Hopenhayn and Rogerson (1993): while high ?ring costs may directly prevent ?ring, equilibrium
employment can still be smaller if high labor adjustment costs substantially reduce pro?ts.
Finally, combining equation (3.6) and equation (3.7), we obtain the following:
w ??
f
= ?EV
n
(n
t
, ?
t+1
, ?
t+1
) +f
e
(e
t
, ?
t
). (3.8)
This implies that when ?rms are downsizing, they set the expected marginal future bene?t of
an employed worker, combined with the marginal revenue product of a utilized worker, equal to
35
Once exit decisions are included in the problem, EV is not always concave in n
t
. However, EV is still concave
over the range of n
t
for which ?rms decide to stay in business.
36
More formally, consider the case for a downsizing ?rm (i.e. ?
1
= 0). The implicit di?erentiation of equation
(3.6) with respect to n
t
and s gives ?n
t
/?s = ?[?w + ?(?EV
n
/?s)]/?EV
nn
> 0 due to the concavity of EV and
?EV
n
/?s > 0, while the implicit di?erentiation of equation (3.7) with respect to e
t
and s yields ?e
t
/?s = ?w/f
ee
< 0
due to the concavity of f. Similarly, the implicit di?erentiation of equation (3.6) with respect to n
t
and ? gives
?n
t
/?? = [(1 ?s)w ??(?EV
n
/??)]/?EV
nn
< 0 due to the concavity of EV and ?EV
n
/?? < 0, while the implicit
di?erentiation of equation (3.7) with respect to e
t
and ? yields ?e
t
/?? = ?(1 ? s)w/f
ee
> 0 due to the concavity
of f.
70
the di?erence between the wage and ?ring cost. The ?ring cost is subtracted from wage as it
represents the bene?t from avoiding a payment that would otherwise be due to the marginal ?red
worker.
37
Case 3.2 Firms are not eligible for the subsidy
Next, we will investigate the case for a downsizing ?rm that is not eligible for the subsidy.
As mentioned previously, we still allow for the possibility of not utilizing some of their workers
when ?rms are not eligible, but ?rms are not required to underutilize their workers. Hence, we
have n
t?1
? n
t
? e
t
. We maintain the assumption that these constraints do not bind, as we are
considering ?rms that would optimally take up the subsidy if eligible.
38
The ?rst order conditions
for this case is given simply by setting s = 0 for equations (3.6) and equation (3.7):
?w = ?EV
n
(n
t
, ?
t+1
, ?
t+1
) +?
f
(3.10)
and
w ??w = f
e
(e
t
, ?
t
). (3.11)
Similarly to equation (3.6), equation (3.10) shows that the labor cost of keeping an extra worker
unutilized must be equated with the marginal future bene?t of keeping the worker in addition to
the ?ring cost. Moreover, equation (3.7) shows that the cost of utilizing an unutilized worker, given
by the di?erence between the wage and labor hoarding cost, must be equated with the marginal
revenue product. Now with the absence of s, we can see that the distance between n
t
and e
t
shrinks faster as ? gets closer to one. Hence, higher ? reduces the likelihood of a ?rm idling some
37
On the other hand, the ?rst order condition for an expanding ?rm is:
w + ?
h
= ?EV
n
(n
t
, ?
t+1
, ?
t+1
) + f
e
(n
t
, ?
t+1
). (3.9)
In this case, hiring costs show up as a cost of having an extra worker. Moreover, n
t
= e
t
holds at an optimum for
expanding ?rms.
38
As shown later, ?rms under the described setting choose not to underutilize workers when the subsidy is not
available so that n
t
= e
t
holds at an optimum for non-eligible ?rms. However, since the value of the Lagrange
multiplier (i.e. ?
2
for n
t
> e
t
) when the constraint binds is expected to be small, as only downsizing ?rms are
considered, it is ignored for the sake of simplicity.
71
of its workers in the absence of a subsidy, provided that ?
f
is low enough.
39
Again, combining
equations (3.10) and (3.11) yields equation (3.8), with e
t
replaced by n
t
when all workers are
utilized.
Comparison between (3.6) and (3.10) reveals n
t
given by equation (3.6) (hereafter denoted
by n
s
t
) is strictly higher than the n
t
given by equation (3.10) (denoted simply by n
t
) due to the
concavity of EV . In addition, e
t
given by equation (3.7) (hereafter denoted by e
s
t
) is strictly
smaller than the e
t
given by equation (3.11) (denoted simply by e
t
) due to the concavity of f.
Hence, for a given pro?tability shock ?
t
, the following condition holds for a downsizing ?rm that
applies for a subsidy when eligible:
40
n
s
t
> n
t
? e
t
> e
s
t
. (3.12)
Hence, an eligible ?rm keeps the level of employment higher, and output lower, in comparison with
a non-eligible ?rm.
Next, we will study the conditions for positive subsidy take-up with the eligibility, for any
given pro?tability shock. Accordingly, we study the nonstochastic version so that ?
t
will be
omitted, and ?
t
is set equal to 1 and will be omitted as well. Now, let V
s
(n
t?1
) denote the value
function satisfying ?rst order conditions given by equations (3.6) and (3.7) (i.e. n
s
t
and e
s
t
) and
V (n
t?1
) denote the value function with the ?rst order conditions given by equations (3.10) and
(3.11) (i.e. n
t
and e
t
). Given eligibility, ?rms will take up the subsidy when V
s
(n
t?1
) > V (n
t?1
).
39
This is not to say that there is no labor hoarding without subsidy. The change in the intensity of the labor
inputs’ use is a common practice, but this feature is not modeled in this paper for a simpler exposition of the e?ects
of the policy.
40
Keep in mind that the condition given by equation (3.12) characterizes the employment and production behavior
of subsidized and unsubsidized ?rms under the same subsidy program with the same s and ?. If we wish to compare
the behavior of a ?rm without the subsidy program (s = 0) and a ?rm with the subsidy program (s > 0, ? > 0), we
also need to take into account the change in EV . In this case, the optimal n
t
will be even higher with the subsidy
while the optimal e
t
remains the same.
72
That is, the following condition must hold for a subsidy take-up to take place:
(n
s
t
?e
s
t
)s?w
total subsidy receipt
+ ?
f
(n
s
t
?n
t
)
savings on ?ring costs
+{?[EV (n
s
t
) ?EV (n
t
)]}
change in future value
+ (1 ??)w(e
t
?e
s
t
)
reduced wage payments
> {f(e
t
) ?f(e
s
t
)}
reduction in revenue
+ ?w(n
s
t
?n
t
)
increased employment costs
.
(3.13)
The ?rst term on the left side represents the total subsidy received by the ?rm, the second
term shows savings on ?ring costs with the subsidy, while the third term captures the change in
the expected marginal future bene?t arising from the di?erent choices of n
t
, and the fourth term
represents the savings on labor costs arising from increasing the number of unutilized workers
(i.e. ?rms pay ?w instead of w so that the reduction in payment is w ? ?w or (1 ? ?)w for each
unutilized worker). In contrast, the ?rst term on the right side represents the reduction in revenue
associated with reduced production and the second term represents the increase in the cost to the
?rm for sustaining excess workers through the subsidy program. Notice that with the subsidy,
?rms bene?t from the reduced wage payments at the production worker margin, while ?rms lose
from higher labor costs at the employment margin. Consequently, ?rms apply when the total
bene?t exceeds the cost.
As we have previously seen, the ?rst term on the left is only positive for downsizing ?rms.
Next, the second term on the left hand-side and the last term on the right-hand side both involve
n
s
t
?n
t
, a term which is positive when a ?rm applies for the subsidy, according to equation (3.12).
Combining these two, the bene?t of applying rises relative to the cost as the size of the ?ring cost,
?
f
, increases relative to the cost of sustaining a worker, ?w, and vice versa. Here, I call this a
direct e?ect of ?
f
. The relative sizes of ?
f
and ?w also indirectly a?ects the bene?t of the subsidy
through the third term on the left side. Equation (3.6) and equation (3.10) show that if (1?s)?w
> ?
f
, then EV
n
> 0 for both equations, and in particular, EV (n
s
t
) > EV (n
t
). On the contrary, if
?w < ?
f
, then EV
n
< 0 for both equations and EV (n
s
t
) < EV (n
t
).
41
That is, when ?ring costs are
very high, the optimal level of n
t
is already so high that increasing n
t
through the subsidy reduces
the expected future value. In the later exercise, we will see that higher ?ring costs in general
41
Furthermore, the slope of EV given by equation (3.6) is positive and the slope given by equation (3.10) is
negative if ?w > ?
f
> (1 ?s)?w. In this case EV (n
s
t
) ?EV (n
t
) can be either positive or negative.
73
increase subsidy take-up even when ?w < ?
f
, suggesting that the direct e?ect dominates.
42
We now investigate the exit decisions of ?rms. Firms will decide to exit from the market
when the expected loss of staying in the market is greater than the cost of ?ring its entire workforce
(i.e. EV (n
t
, ?
t+1
, ?
t+1
) is smaller than ??(0, n
t
)). Since EV (n
t
, ?
t+1
, ?
t+1
) considered here is
concave and ??(0, n
t
) is linearly declining in n
t
, the threshold level of the exit decision will be
given by the intersection of EV (n
t
, ?
t+1
, ?
t+1
) and ??(0, n
t
) when they are plotted against n
t
while
holding everything else constant. That is, the intersection gives the upper bound of n
t
below which
?rms decide to exit for a given ?
t
. EV and ?ring costs are plotted against n
t
in ?gure (3.11).
Here, EV (2) corresponds to a higher level of pro?tability shock compared to EV (1). As the ?gure
shows, no ?rms with a pro?tability shock corresponding to EV (2) will exit from the market, while
some small ?rms with a pro?tability shock corresponding to EV (1) will exit. The subsidy shifts
EV up slightly for all n
t?1
, thereby reducing the upper bound of n
t?1
for exiting. This, combined
with the higher employment induced by the subsidy program, reduces the equilibrium amount of
exit at the steady-state.
The following strategy was used in order to simplify the numerical dynamic optimization
problem given by equation (3.5). We know from equation (3.7) that the unconstrained optimal
e
t
is static. Accordingly, by using this ?rst order condition, the value function can be reduced
to one that involves one choice variable, n
t
, even when some workers are not utilized. We obtain
?rm’s decision rules regarding the subsidy take-up, Z(n
t?1
, ?
t
, ?
t
), where Z = 1 corresponds to
applying for a subsidy and Z = 0 corresponds to not applying, by comparing V
s
(n
t?1
, ?
t
| ?
t
= 1)
with V (n
t?1
, ?
t
| ?
t
= 1) as explained above.
We also obtain the following decision rules by solving the dynamic optimization problem:
X(n
t?1
, ?
t
, ?
t
), where X = 1 corresponds to exiting from the market and X = 0 corresponds to
staying; N(n
t?1
, ?
t
, ?
t
), which gives the optimal choice of employment; and E(n
t?1
, ?
t
, ?
t
), which
provides the optimally chosen level of production at time t. Furthermore, whenever Z = 1, a
fraction ? of ?rms follow the decision rules obtained from solving the value function with subsidy
42
The size of hiring costs ?
h
, on the other hand, only has an indirect e?ect through the third term on the left by
a?ecting EV .
74
0 5 10 15
?12
?10
?8
?6
?4
?2
0
2
4
E
V

a
n
d

F
i
r
i
n
g

C
o
s
t
s
n
EV (1)
EV (2)
? firing costs
Figure 3.11: EV vs. ?ring costs. Firms decide to exit from the market when the expected loss of
staying in the market is greater than the cost of ?ring its entire workforce. EV (2) corresponds to
a higher level of pro?tability shock compared to EV (1).
while the remaining fraction 1 ?? of ?rms follow the decision rules implied by the value function
without subsidy. On the other hand, when Z = 0, all ?rms follow the decision rules obtained from
solving the value function for ?
t
= 0. The decision rule regarding the optimal number of utilized
workers, E(n
t?1
, ?
t
, ?
t
), is obtained according to the ?rm’s subsidy take-up decisions. Here again,
a fraction 1 ?? of ?rms follow the decision rules given by the value function without subsidy even
when they wish to apply.
From the solutions above, we obtain a stationary distribution over the employment and
pro?tability shock pairs for a given level of entry M. This in turn will provide us the rates
of entry, exit, job reallocation, average employment, average output and average productivity in
a stationary equilibrium. Furthermore, a mass of size M new entrants are added each period
in obtaining a stationary distribution through contraction mapping. Following Hopenhayn and
Rogerson (1993), the starting level of pro?tability shock (or put di?erently, initial luck of the draw)
for an entrant is taken from the uniform distribution, and all entrants start at zero employment.
75
The boundaries of this uniform distribution are set by the condition of the discretization of the
AR(1) idiosyncratic pro?tability shock process explained in the following section.
43
After the
initial pro?tability shock, entrants evolve just as incumbents. Furthermore, entering ?rms are
assumed not to receive a subsidy with their ?rst production, and they must produce at least once
before exiting from the market.
Denoting ?
t
as a vector which describes the distribution over the entire set of employment
levels and pro?tability shocks at period t, and T(?
t
, M) as the transition matrix that maps the
state at time t to the next state period given ?rms’ decision rules, the state transition equation is
given by ?
t+1
= T(?
t
, M). Accordingly, the time stationary distribution is described as a vector
´
? such that
´
? = T(
´
?, M). This distribution provides us with steady-state average employment in
the economy. Moreover, the stationary distribution over production-pro?tability shock pair can
be constructed from
´
?, by moving the corresponding fraction of ?rms to the optimally chosen level
of production given by the ?rst order condition of e, obtained from equation (3.7) for each level of
shock, whenever their optimal employment exceeds the optimal number of utilized workers. This
distribution, in turn, provides us with the steady-state level of average production in the economy.
Because the growth rate of the industry is held constant in equilibrium, the number of the
?rms that exit the market must be o?set by the number of ?rms that enter the market M. Hence,
the analysis is one in which there is no net entry, as exit and entry rates are identical in the steady-
state. This simpli?cation also follows Hopenhayn and Rogerson (1993). Since total employment
is held constant in equilibrium, the number of jobs destroyed by incumbents and exiting ?rms have
to be matched by the amount of jobs created by the incumbents and entering ?rms.
Finally, the operator T is homogeneous of degree one in
´
? and M. Consequently, the rate
of entry (and therefore the rate of exit) remains constant regardless of the size of M, as doubling
M also doubles the total number of ?rms in a stationary equilibrium. Accordingly, choosing a
43
As explained in the next section, the upper bound and the lower bound are set at three standard deviations
away from the mean, and the state space of idiosyncratic pro?tability shock is discretized into forty states. The use
of an uniform distribution was preferred over that of a stationary or normal distribution, since these distributions
would reduce the steady state rate of exit (and therefore entry) by reducing the number of ?rms that start o? poorly.
76
particular level of M corresponds to choosing a particular measure of ?rms and the total amount
of employment in a stationary equilibrium, while statistics such as average employment, average
output and productivity and the rates of job creation and destruction are una?ected by the choice
of M. Although a positive subsidy can potentially a?ect the total number of ?rms through M by
raising the expected value of starting a business, M has not yet been endogenized in this model.
In the following section, the equilibrium amount of entry M is simply set so that the total number
of ?rms in equilibrium are the same for the subsidy case with s > 0 and the benchmark case with
s = 0.
3.4 Results
3.4.1 Basic Setup and Calibration
To ?nd an equilibrium via numerical dynamic programming, I begin by specifying the pro-
duction function as:
f(e
t
, ?
t
) = ?
t
· e
?
t
where 0 < ? < 1. (3.14)
The path for the pro?tability shocks ?
t
is given as follows:
?
t
= ?
t
+u
t
, (3.15)
and
?
t
=
_
¸
¸
¸
¸
¸
¸
¸
¸
¸
¸
_
¸
¸
¸
¸
¸
¸
¸
¸
¸
¸
_
?
g
with prob. ? if ?
t?1
= ?
g
?
b
with prob. 1 ?? if ?
t?1
= ?
g
?
g
with prob. 1 ?? if ?
t?1
= ?
b
?
b
with prob. ? if ?
t?1
= ?
b
_
¸
¸
¸
¸
¸
¸
¸
¸
¸
¸
_
¸
¸
¸
¸
¸
¸
¸
¸
¸
¸
_
where ?
g
> ?
b
> 0 (3.16)
and
u
t
= ?u
t?1
+v
t
where 0 < ? < 1 and v
t
? i.i.d. with E[v
t
] = 0. (3.17)
Here, ?
t
represents the aggregate state. It follows a two-state Markov process with symmetric
transition probability ?. Although actual business cycles arguably display asymmetric transition
probabilities with the good state being longer than the bad state, a symmetric probability was
77
used to re?ect the longer than usual downturn experienced by the Japanese economy during the
1990s.
44
Meanwhile, u
t
captures the idiosyncratic pro?tability shock, which follows an AR(1)
process. The parameter ? is the persistence of idiosyncratic shocks that ?rms receive each period,
and v
t
is a Gaussian white noise process with the standard deviation ?
v
. For a given level of
persistence ? and the standard deviation ?
v
, a corresponding forty-state Markov transition matrix
and state vector for idiosyncratic shocks were created to approximate the AR(1) process for each
level of ?. Further, for each aggregate state, the upper and lower bounds of the shock are set
at three standard deviations of u
t
away from ?
g
and ?
b
. Note that forty idiosyncratic states
combined with two aggregate states yields a total of eighty pro?tability states.
The pro?tability shocks can be interpreted as technology shocks or as demand shocks since
?
t
will be multiplied by the price level p which is normalized to one. Here, we do not consider
the distinction between supply and demand shocks, and simply regard ?
t
as pro?tability shocks.
Furthermore, note that the steady state statistics in section (3.4.2), computed analytically by the
stationary distributions, refer to the average ?gures of both aggregate states. Alternatively, the
steady state statistics for a good aggregate state and a bad state can be computed separately.
However, the average statistics were used in order to measure the long-run impact of the subsidy.
The second moment properties of the subsidy in terms of the volatility of employment, productivity
and output (i.e. ?uctuation around the long-run mean) are examined via simulation in section
(3.4.3), instead of using an analytical computation.
Key parameters used to solve the model are summarized in Table (3.2). Since subsidy data
is only available annually, the time interval is set to one year. Moreover, the focus of the exercise
will be the 1990s, during which the subsidy bill increased and data by two-digit sector is available.
The wage is normalized to one, and both hiring and ?ring costs are set equal to 80% of the annual
wage.
45
Later, we will examine the impact of higher adjustment costs by setting both hiring and
44
The asymmetric transition probability reduces the steady-state fraction of subsidized workers and makes it more
di?cult to match with the description of the data during the 1990s.
45
Although the price is also normalized to one in the model, it is allowed to ?uctuate relative to the wage as it is
multiplied by a pro?tability shock.
78
Table 3.2: Parameter values used to obtain stationary distributions with annual frequency.
w = 1 wage
?
h
= 0.8 hiring costs
?
f
= 0.8 ?ring costs
c
f
= 2 ?xed cost of operation
r = 0.04 interest rate
? = (1/(1 +r)) = 0.96 discount rate
? = 0.8 fraction of wage paid to unutilized workers
? = 0.5 prob. of being eligible for the subsidy
s = 2/3 subsidy coverage
? = 0.55 labor share of total cost
? = 0.75 persistence of idiosyncratic shocks
?
v
= 0.5 standard deviation of v
t
?
g
= 3.13 mean pro?tability of good state
?
b
= 2.27 mean pro?tability of bad state
? = 0.6 aggregate state transition probability
?ring costs equal to the annual wage. The ?xed cost of operation (or entrepreneur’s opportunity
cost) is set to twice the wage. The annual interest rate is set equal to 4%. This ?gure corresponds
to the government ?nancial institutions’ key lending rate to small- and medium- size enterprizes
averaged in the 1990s.
46
The EAS provides a guideline on the fraction of wages that ?rms should pay to subsidized
workers, and it does not require that subsidized workers be paid the full amount. Accordingly,
payment to unutilized workers is set equal to 80% of the wage. This number was estimated by
combining three ?gures: the annual salary of manufacturing workers, taken from the Basic Survey
on Wage Structure; the average work-days of the manufacturing sector, provided by the Monthly
Labor Statistics; and the average subsidy cost per worker per day as described in section (3.2.2).
47
The estimated subsidy cost per person per day is about 42% of the average basic wage between
46
The interest rate data is available at the Bank of Japan’s website in Japanese:
http://www.boj.or.jp/stat/dlong f.htm.
47
Both the Basic Survey on Wage Structure and the Monthly Labor Statistics are published by the Ministry of
Labor (current Ministry of Health, Labor and Welfare). The data used in the paper is posted on the website of
the Japan Institute of Labor Policy and Training in Japanese: http://stat.jil.go.jp.
79
1985 and 2001. This implies that if s = 1/2, ? = 0.94 (or ? = 0.84 if instead of the basic wage,
the actual wage which includes overtime is used) and if s = 2/3, ? = 0.71 (or ? = 0.63 if the actual
wage is used).
48
The parameter value is set around the mid-point at ? = 0.8.
The probability of being eligible for the subsidy program each year is set equal to 50%. This
seems reasonable given the high concentration of subsidies in the Iron and Steel industry during
the 1990s.
49
The subsidy coverage is set equal to 2/3 of the wage paid to unutilized workers. The
parameter ?, which equals the labor’s share of total cost, is set to 0.55; this ?gure corresponds to
the average cost share of labor (excluding intermediate inputs) between 1973 and 1998 given by
the JIP database.
The persistence of the shock is set equal to 0.75, and the standard deviation of v
t
is set
equal to 0.5.
50
The mean pro?tability shock in the bad state (?
b
) is set at 2.27, so that the lowest
shock in a bad state takes a positive value, and the distance between ?
g
and ?
b
is set slightly
above one standard deviation of idiosyncratic shocks.
51
Here, ?
g
is set at 3.13. The probability
that the aggregate state persists (?) is equal to 0.6. These parameter values are assigned to
generate realistic statistical properties of key variables such as the fraction of subsidized workers,
job creation and destruction rates, and entry and exit rates. Employment was discretized in 301
grid points ranging from zero to ?fteen; the upper bound was set to guarantee that it exceeds
equilibrium employment with the highest value of the pro?tability shock.
Average productivity is de?ned as total output divided by total employment. More speci?-
cally, using
´
?(n
i
, ?
j
) and
´
?(e
i
, ?
j
) to represent the proportion of ?rms over each (n
i
, ?
j
) and (e
i
, ?
j
)
48
Since the estimated subsidy cost per work-day is not available by two-digit sectors, these estimates are for the
entire manufacturing sector.
49
Unfortunately, information on the fraction of ?rms covered by the subsidy is not currently available.
50
These two combined implies that the standard deviation of the idiosyncratic shock is about 0.756 since ?
u
=

?
2
v
/(1 ??
2
).
51
With ?
b
= 2.27, the lowest value of ?
t
is 0.002.
80
pairs in a stationary equilibrium, the average productivity is de?ned as:
Average productivity =
Total Output
Total Employment
=

?
j

e
i

n
i
_
n
i
·
´
?(n
i
, ?
j
)

?
j

n
i
n
i
·
´
?(n
i
, ?
j
)
_
_
f(n
i
, ?
j
)
n
i
_
· ?,
where ? =
_
´
?(e
i
, ?
j
) · f(e
i
, ?
j
)
´
?(n
i
, ?
j
) · f(n
i
, ?
j
)
_
. (3.18)
The term in the ?rst bracket shows the relative share of employment in each (n
i,
?
j
) pair of the
stationary distribution, and the second term re?ects output per worker when n
i
workers are used
for production. ? is the ratio of the actual output to the output which would have been realized
if n
i
workers were used instead of e
i
. This ratio is strictly less than one when some workers are
unutilized. The products of these terms are summed over the entire range of employment and
shocks to obtain average productivity. Notice that this de?nition includes subsidized workers,
who produce zero output, in calculating the productivity.
I also present a productivity measure adjusted for hiring and ?ring costs and the subsidy cost
per worker. This measure controls for the gain associated with having to spend less resources in
hiring and ?ring with the subsidy, as well as the associated loss in the form of a higher government
de?cit and/or higher tax. The calculation is done simply by subtracting the hiring and ?ring
costs per worker as well as the cost of the subsidy per worker from average productivity as de?ned
by equation (3.18). However, this should not be interpreted as a welfare measure, as we have
not modeled the utility bene?t of the subsidy for workers nor the gains associated with sustaining
better job-worker matches for experienced workers.
Average productivity is alternatively de?ned as total output divided by the total number of
utilized workers:
Average productivity
(based on utilized workers)
=
Total Output
Total Number of Utilized Workers
=

?
j

e
i
_
e
i
·
´
?(e
i
, ?
j
)

?
j

e
i
e
i
·
´
?(e
i
, ?
j
)
_
_
f(e
i
, ?
j
)
e
i
_
. (3.19)
Obviously, this de?nition excludes unutilized workers. Hence, comparing equation (3.18) and
equation (3.19) for the same level of subsidy coverage s captures the direct e?ect of hoarding
81
on average productivity. More speci?cally, the ratio of productivity based on employment to
productivity based on utilized workers (both when s = 2/3) shows a reduction in productivity as
a direct result of labor hoarding (i.e. the ratio of productivity calculated using equation (3.18) to
that given by equation (3.19)). Since this ?gure is equivalent to the ratio of the total number
of utilized workers to total employment, one minus this ratio matches the fraction of subsidized
workers.
Finally, the steady-state rate of job turnover is the ratio of the total number of jobs destroyed
by incumbents and exiting ?rms to total employment at the steady-state. Since total employment
stays constant in a stationary equilibrium, this ?gure obviously equals the steady-state rate of
job creation, which is the ratio of the jobs created by both incumbents and entrants to total
employment at the steady-state. These measures allow us to evaluate the magnitude of total job
reallocation occurring in the economy.
3.4.2 Stationary Distribution
This section examines the properties of stationary distribution. In order to examine the
e?ects of subsidies on productivity, the benchmark model sets s = 0 while the subsidy case sets
s = 2/3. First, I investigate a case without volatility in aggregate shocks. The value of ? in this
exercise is set equal to 2.7. Then I will add volatility in ?, while preserving the mean, as speci?ed
in the previous section. Finally, I will increase the hiring and ?ring costs from 80% of the wage to
100% to investigate the impact of this change. As mentioned previously, the pro?tability shocks
are parameterized to generate realistic values for the fraction of subsidized workers, the rates of
entry and exit, and the rates of job creation and destruction.
Although studies on annual rates of entry, exit, job creation, and destruction in Japan
are not extensive, due to a lack of data comparable to the LRD for American manufacturing
establishments, Motonishi and Tachibanaki (1999) attempt to estimate these ?gures by using the
establishment level data for 1988, 1990 and 1993 from Census of Manufacturers compiled by the
Japanese Ministry of Economy, Trade and Industry. The rate of entry (exit) on an annualized
82
basis is 8.74% (7.91%) for the Iron and Steel industry for 1988?1990, and 5.68% (8.15%) for
1990?1993.
52
Motonishi and Tachibanaki also provide the rate of job creation and destruction
(adjusted on an annualized basis) during these periods.
53
The rate of job creation (destruction)
on an annualized basis provided by this study is 4.55% (4.81%) for the Iron and Steel industry for
1988?1990, and 2.91% (4.83%) for 1990?1993.
In this exercise, the number of entrants M is set so that the total number of ?rms is equal
to one in both cases. As mentioned before, increasing M increases the total number of ?rms,
and therefore total employment and output proportionally, but average size as well as average
?rm output remains the same. Here, I assume that the impact of the subsidy on M is trivial.
Moreover, the values for the average size of ?rms (or total employment), average output by ?rm
(or total output) and average productivity obtained for the subsidy case are normalized by the
corresponding benchmark values to facilitate comparison, and for this reason these benchmark
values are set equal to one.
The key statistics given by the stationary distributions without aggregate volatility are
summarized in Table (3.3). Overall the changes are small. The fraction of subsidized workers
generated by the stationary distribution is 0.36%. The exit rate drops from 4.96% to 4.86% with
the subsidy, while the job turnover rate falls from 3.83% to 3.78%. Average ?rm size is 0.14%
higher and average ?rm level output is 0.15% lower. The reduction in output in spite of higher
employment is caused by the presence of unutilized workers.
Average productivity falls by about 0.29% with the subsidy program. When average pro-
52
While this data includes all manufacturing establishments with more than 4 employees, it does not include ?rms
that have entered and exited between census years. As a result, the ?gures on entry and exit rates presented in
this study (which are adjusted on an annualized basis) may underestimate the true magnitude of entry and exit.
53
Again, the annual rates of job ?ows may be underestimated since ?rms that enter and exit between the census
years are not included. Furthermore, employment volatility during the census years could potentially generate
smaller ?gures for both job creation and destruction rates when calculated on an annualized basis than the actual
annual job creation and destruction rates (i.e. if a ?rm hires 100 new employees in 1990 and ?res 100 in 1993, this
?rm’s employment stays constant over the 1990 and 1993 census). GDP growth rates ?uctuate slightly between
1988?1990, but follow a steady decline for 1990?1993, so that the underestimation arising from employment
volatility is potentially less for the latter interval.
83
Table 3.3: Summary statistics of stationary distributions without aggregate volatility: ? = 2.7.
s = 0 s = 2/3
Fraction of workers covered by the subsidy 0.0000 0.0036
Exit rate 0.0496 0.0486
Job turnover rate 0.0383 0.0378
Total number of ?rms 1.0000 1.0000
Average ?rm level employment 1.0000 1.0014
Average ?rm level output 1.0000 0.9985
Average productivity based on employment 1.0000 0.9971
— adjusted for hiring and ?ring costs 1.0000 0.9974
— adjusted for hiring, ?ring and subsidy costs 1.0000 0.9961
Average productivity based on utilized workers 1.0000 1.0007
ductivity is calculated based on utilized workers, it increases slightly by 0.07%. This gain is
generated by the increased ?exibility of production decisions via the subsidy program: under the
benchmark case without subsidy, ?rms hold some excess workers who are used for production due
to the presence of labor adjustment costs. While ?rms hold even more excess workers with the
subsidy program, these workers are not used for production, thereby increasing productivity when
calculated only in terms of utilized workers.
Here, the drop in productivity due to labor hoarding, which corresponds to the size of sub-
sidized workers, is 0.36%. In addition, when average productivity is adjusted for labor adjustment
costs, the negative impact of the subsidy on productivity shrinks, re?ecting the fact that the sub-
sidy helps ?rms avoid labor adjustment costs. However, when we further control for the cost of
the subsidy, average productivity falls slightly further in comparison with the benchmark value,
indicating that the cost of the subsidy is higher than savings on labor adjustment costs.
Now we add aggregate volatility without changing the mean ?, while keeping hiring and
?ring costs at 0.8. The results are presented in Table (3.4). The fraction of subsidized workers
generated by the stationary distribution now increases to 1.28%. As expected, this implies that
volatility increases subsidy take-up. Since the estimated annual average fraction of subsidized
84
workers in the Iron and Steel industry is 2.1%, the model does not exaggerate the extent of
subsidy coverage. The model’s exit rate is 4.89% when the subsidy is set equal to zero, and it
drops to 4.73% when the subsidy is set equal to two-thirds of payments to unutilized workers. The
job turnover rate falls from 4.05% to 3.91% when the subsidy program is in place. Compared
with the “no aggregate volatility” case, the drop in both the exit rate and the job turnover rate
is slightly bigger with volatility. This may be due to the fact that the subsidy’s bene?t increases
with higher aggregate volatility, thereby raising EV .
Table 3.4: Summary statistics of stationary distributions with aggregate volatility: ?
g
= 3.13,
?
b
= 2.27.
Low adj. costs High adj. costs
?
h
= 1 = ?
f
= 0.8 ?
h
= 1 = ?
f
= 1
s = 0 s = 2/3 s = 0 s = 2/3
Fraction of workers covered by the subsidy 0.0000 0.0128 0.0000 0.0157
Exit rate 0.0489 0.0473 0.0508 0.0484
Job turnover rate 0.0405 0.0391 0.0369 0.0343
Total number of ?rms 1.0000 1.0000 1.0000 1.0000
Average ?rm level employment 1.0000 1.0096 1.0000 1.0187
Average ?rm level output 1.0000 0.9982 1.0000 1.0015
Average productivity based on employment 1.0000 0.9887 1.0000 0.9831
— adjusted for hiring and ?ring costs 1.0000 0.9895 1.0000 0.9851
— adjusted for hiring, ?ring and subsidy costs 1.0000 0.9850 1.0000 0.9796
Average productivity based on utilized workers 1.0000 1.0016 1.0000 0.9988
Similar to the “no aggregate volatility” case, average ?rm level employment goes up with
the subsidy while average ?rm level output drops. Again, higher average employment does not
lead to higher average output at the ?rm level, due to the presence of subsidized workers. Average
productivity based on employment, given by equation (3.18), falls about 1.13% with the subsidy.
As before, average productivity based on utilized workers goes up by 0.16% due to the ?exibility of
production decisions with the subsidy. The sum of these two measures approximately corresponds
to the drop in productivity as a direct result of labor hoarding. Again, average productivity falls
85
0 0.5 1 1.5 2 2.5 3 3.5 4
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
n (s = 0)
n (s = 2/3)
e (s = 2/3)
Figure 3.12: Cumulative distribution functions of three stationary distributions. The solid line
shows the cdf of ?rm level employment when the subsidy is set equal to zero. The dashed line
shows the cdf of employment when the subsidy is set equal to 2/3 of wage. The dotted line shows
the stationary distribution in terms of utilized workers when subsidy is set equal to 2/3 of wage.
even further after controlling for labor adjustment and subsidy costs.
The drop in productivity due to labor hoarding generated by this model is quite successful
in approximating the impact of labor hoarding in the data as described in section (3.2.2). Namely,
the adjusted TFP (i.e. average productivity based on utilized workers) is higher than unadjusted
TFP (average productivity based on employment) by about 1.2% in the data between 1990 and
2001. However, in the growth accounting exercise, the drop in TFP is smaller than the fraction
of subsidized workers, as only the labor share of total cost applies to the overall reduction in
productivity.
54
Figure (3.12) provides cumulative distribution functions of three stationary distributions: a
stationary distribution over employment for all levels of idiosyncratic and aggregate shocks when
54
Although the Iron and Steel sector went through a process of substitution from labor towards capital over the
last couple of decades, the intensity of capital usage and labor are likely to be complementary over a much shorter
horizon (i.e. a year or less). This short-run complementarity assures that the correlation between capital usage
and labor is high at the high frequency, and therefore, introducing capital should not undermine the result given
by the model.
86
s = 0; a stationary distribution over employment for all levels of idiosyncratic and aggregate
shocks when s = 2/3; and ?nally a stationary distribution over utilized workers for all levels of
idiosyncratic and aggregate shocks when s = 2/3. Note that the distributions are bumpy since
the state spaces (employment and pro?tability) are discontinuous. The ?gure con?rms that the
average ?rm level employment is higher when the subsidy program is in place, while we cannot
tell whether or not the average ?rm level production is larger with the subsidy program.
55
The ?nal case investigates the impact of higher adjustment costs. Here, hiring and ?ring
costs are set equivalent to the annual wage. The results are also provided by Table (3.4). The
fraction of subsidized workers rises further to 1.57%. The rate of reallocation in terms of exit
and job turnover falls again with the subsidy: the exit rate drops from 5.08% to 4.84%, while the
job turnover rate falls from 3.69% to 3.43%. A comparison with the “low adjustment costs” case
reveals that the exit rate rises while the job turnover rate drops with the increase in adjustment
costs. Note that high labor adjustment costs have two competing e?ects on exit behavior: while
high ?ring costs increase the cost of exiting and therefore prevent exit, high labor adjustment costs
(both hiring and ?ring) reduce the expected value and encourage exit. In our example, the exit
rate rises with higher adjustment costs, indicating that the “encouragement” e?ect of high ?ring
costs outweighs the “prevention” e?ect of high ?ring costs. However, higher adjustment costs
still seem to reduce the job turnover rate. Furthermore, the impact on the average size of ?rms
is greater with higher adjustment costs, as average employment rises by 1.87% compared to the
benchmark.
Average productivity based on employment falls by 1.7%, while unlike the ?rst two cases,
average productivity based on utilized workers falls by 0.12%. The drop in the second productivity
measure implies that the distortion that the subsidy generates in the reallocation measures is
greater with the “higher adjustment costs,” and this o?sets the productivity gain generated by
the ?exible production adjustment provided by the subsidy. When productivity is adjusted for
hiring/?ring costs, the drop in productivity is not as severe, as a result of the gains accrued
55
This is because the cdf for e(s = 2/3) and the cdf for e(s = 2/3) intersect (around the employment level equals
to 2.3).
87
from smaller adjustment costs. However, productivity falls again below the baseline employment
productivity, by 2.04%, when it is adjusted for both labor adjustment and subsidy costs.
Even though the direct e?ect of the subsidy on productivity observed in this section are
small in all three cases, the indirect e?ect of the subsidy over the business cycle can be substantially
larger. We will examine these results in the next section.
3.4.3 Simulation Results
In the previous section, we saw that the direct e?ect of the subsidy on steady-state produc-
tivity is more or less proportional to the number of subsidized workers. However, the simulation
exercises reveal that even when the productivity e?ect is small, the e?ects of the subsidy on output
and employment dynamics over business cycles are quite striking. Accordingly, in this section,
cyclical implications of the subsidy program are highlighted via simulation.
For each simulation, a sequence of pro?tability shocks is generated for 150 periods from the
Markov-process described above for 5000 ?rms. The idiosyncratic component of the pro?tability
shock varies across ?rms, while the aggregate component is shared by all ?rms. Furthermore,
each time a ?rm exits, a new ?rm enters to replace the old ?rm so that the total number of ?rms
remains constant using the steady-state condition.
56
When a new ?rm enters, a new sequence of
the idiosyncratic component of pro?tability shocks is drawn from the distribution, and the ?rm
starts with zero employment.
In addition to pro?tability shocks, a sequence of eligibility is also generated for all ?rms
based on the unconditional probability ?. After generating employment, output, entry and exit
behavior for 5000 ?rms for 150 periods, the ?rst 50 periods are deleted in order to eliminate the
56
Although exits would likely exceed entries during downturns, this simulation abstracts from the variations in
net entries over the business cycle. As long as the e?ect of the subsidy program on the variations in net entries is
small, normalization with the benchmark case insures that this simpli?cation does not pose a signi?cant problem in
assessing the policy impact. If the reduced variation in net entries is incorporated, both employment and output
should be less volatile than suggested by the results here. This implies that the employment volatility results will
be enhanced, while the output volatility results will be mitigated.
88
e?ects of the initial distribution. This entire exercise, in turn, was repeated 100 times to obtain
the mean and the standard deviation of each statistic. Note that given the procedure described
above, ‘total output’ and ‘total employment’ in this exercise refer to the total sample of 5000
?rms.
Table 3.5: Summary statistics obtained from simulation exercises with low adjustment costs: ?
h
=
0.8, ?
f
= 0.8.
s = 0 s = 2/3 Ratio
Correlations between
— total output and average productivity 0.9870 0.9895 1.0025
(0.0007) (0.0006)
— total output and average productivity (e) 0.9891
(0.0006)
Standard deviations of
— total output 0.1670 0.1717 1.0284
(0.0006) (0.0006)
— total employment 0.0424 0.0399 0.9409
(0.0007) (0.0007)
— average productivity 0.1320 0.1387 1.0512
(0.0003) (0.0003)
— job creation rate 0.0205 0.0198 0.9680
(0.0003) (0.0002)
— job destruction rate 0.0200 0.0186 0.9304
(0.0002) (0.0002)
First we examine the “low adjustment costs” case that sets both hiring and ?ring costs
to 80% of the annual wage. Then, we investigate the “high adjustment costs” case where both
hiring and ?ring costs are increased to 100% of the annual wage to investigate its impact. Table
(3.5) reports statistics obtained from simulating the “low adjustment costs” case. It provides
statistics for s = 0 and s = 2/3, as well as their ratio, with the benchmark ?gure set as a
denominator. Standard deviations of each statistics are reported in parentheses. Note that
output, employment and productivity are now in measured in natural logarithms. As the ‘ratio’
column shows, the correlation between total output and average productivity rises by 0.25% with
the subsidy indicating that the procyclicality of productivity is stronger with the subsidy program.
89
However, the predicted increase is very small.
The JIP database presented in section (3.2.2) showed that the correlation between TFP
and real gross output falls from 0.7916 to 0.7843 when the subsidy adjustment is made, and the
correlation between TFP and real value added falls from 0.9921 to 0.9906. In this theoretical
exercise, the correlation between total output and average productivity falls slightly, from 0.9895
to 0.9891, when subsidized workers are taken into account in calculating average productivity (i.e.
when I use equation (3.19) instead of (3.18)).
Perhaps the most signi?cant ?nding of this exercise is that the standard deviation of output
increases on average by 2.84% when s = 2/3 compared to when s = 0. This is a substantial
increase in volatility given that the fraction of subsidized workers is only 1.3% of total employment
at the steady-state. Intuitively, this results from a symmetric increase in output sensitivity to
aggregate shocks: when the bad aggregate shock hits the economy, total output is lower than
otherwise as the subsidy allows for a reduction in output while sustaining employment. When
the good aggregate shock hits the economy, total output is higher with the subsidy program as
?rms spend less on hiring. Since the subsidy program keeps average employment higher, ?rms
can more readily raise production in times of favorable shocks. This generates more volatility in
total output.
On the contrary, the volatility of employment falls by about 6% with the subsidy program
in place. This matches the objective of the government to reduce undesired ?uctuation in employ-
ment due to business cycles. The reduction comes from reduced job destruction during unfavorable
aggregate conditions as well as stunted job creation during favorable times. The standard devi-
ation of job creation falls by about 3.2% with the subsidy, whereas the standard deviation of job
destruction falls by about 7%. Finally, the standard deviation of average productivity rises by
5.12%.
57
57
Since labor productivity is now expressed in logs (i.e. ln(Y/N)), the following formula applies:
var(ln(Y/N)) = var(ln Y ) + var(ln N) ?2cov(ln Y, ln N). (3.20)
Note that since the variance of output is much larger than the variance of employment, the increase in the variance
of output results in the higher variance of productivity, even with the reduction in the variance of employment.
90
Table 3.6: Summary statistics obtained from simulation exercises with high adjustment costs:
?
h
= 1, ?
f
= 1.
s = 0 s = 2/3 Ratio
Correlations between
— total output and average productivity 0.9896 0.9927 1.0032
(0.0007) (0.0007)
— total output and average productivity (e) 0.9921
(0.0007)
Standard deviations of
— total output 0.1630 0.1687 1.0348
(0.0007) (0.0007)
— total employment 0.0373 0.0327 0.8759
(0.0008) (0.0009)
— average productivity 0.1322 0.1418 1.0722
(0.0003) (0.0004)
— job creation rate 0.0177 0.0159 0.9008
(0.0002) (0.0003)
— job destruction rate 0.0182 0.0149 0.8225
(0.0002) (0.0002)
Table (3.6) highlights the results of the “high adjustment costs” case. The fraction of
subsidized workers given by the stationary distribution in this case is 1.59%. The results for
correlations are similar to the “low adjustment costs” case except that the correlations are slightly
higher due to higher adjustment costs. The volatility of output increases by about 3.5%, but the
volatility of employment falls substantially by about 12%. This result is generated by a reduction
in the volatility of job creation by 10% and job destruction by 18%. In addition, the standard
deviation of average productivity rises by 7.2%.
The comparison between the “high adjustment costs” and “low adjustment costs” cases
reveals that even when the e?ect of the subsidy on the steady-state employment and job reallocation
rate is trivial, the e?ect on the volatility of employment over the business cycle is substantial.
This result is mainly driven by the reduced sensitivity of job creation and destruction to aggregate
Furthermore, the covariance between output and employment falls with the subsidy as expected, thereby further
increasing the variance of productivity under the subsidy case relative to the benchmark case.
91
shocks. Hence, the policy leads to a substantial reduction in the volatility of job churning over
the business cycles. Finally, although it is not reported in this paper, the volatility of output
increases by 4.2% and the volatility of employment falls by 10% when the size of adjustment costs
are further increased to ?
h
= ?
f
= 1.5, for the fraction of subsidized workers equal to 2%.
58
3.5 Conclusion
This chapter examined the e?ects of the EAS, Japan’s major employment insurance pro-
gram, on average productivity, employment, and the volatility of output and employment over the
business cycle, through the examination of the Iron and Steel industry. The partial equilibrium
model described in this chapter shows that the subsidy reduces average productivity primarily by
increasing the number of unutilized workers, although the direct impact of the subsidy on produc-
tivity is predicted to be small, given that the fraction of subsidized workers is small. However,
simulation exercises reveal that the subsidy may have a substantial impact on the volatility of
output and employment. In particular, when hiring and ?ring costs are set equal to 80% of
the annual wage, output volatility increases by 2.8% over the business cycles with the subsidy,
while employment volatility drops by 6%, even when the fraction of subsidized workers is about
1.3%. When hiring and ?ring costs are increased equivalent to the annual wage, the volatility of
employment drops by 12% while the volatility of output increases by 3.5%.
While measures such as productivity, employment and output volatility are often used to
evaluate welfare, I do not intend to draw a normative conclusion on the welfare e?ect of the subsidy
program. However, I believe that the implications highlighted in this theoretical exercise are
important ones, providing policymakers a better understanding of the program, thereby allowing
them to more successfully target their policy objectives. Here, I raise a couple of issues for a more
complete welfare assessment. First, the paper predicts that the subsidy increases output volatility
while reducing employment volatility. Hence, an assessment of the policy requires an analysis of
58
Note that higher adjustment costs do not always enhance the e?ectiveness of the subsidy in reducing employment
volatility as we see in the case where ?
h
= ?
f
= 1.5. This is because high adjustment costs of this magnitude are
already associated with very low employment volatility. This reduces the e?ect of the subsidy.
92
the cost of output volatility and the bene?ts of employment stability.
59
Second, although some
labor market imperfections are assumed for subsidy take-up to take place (i.e. ?ring restrictions
and rigid wage), I have not investigated how the subsidy program may enhance or reduce labor
market imperfections.
60
Neither have I conducted a hypothetical comparison with a benchmark
without labor market imperfections.
The analysis presented here raises several additional issues for further investigation. First,
since the quantitative impact of the subsidy on the volatility of output and employment is sensitive
to the magnitude of labor adjustment costs, it will be important to quantify these costs accurately
to evaluate the potential impact of the subsidy program. Second, the analysis treated the Iron
and Steel industry as an independent economy with no interaction with other industries. New
policy implications may arise if inter-industry interactions between high productivity sectors and
low productivity sectors are present in the model.
61
Third, it seems worthwhile to investigate
why the subsidy was so highly concentrated in the Iron and Steel sector. Finally, employment
volatility during the severe recession of the 1990s was surprisingly mild in Japan compared to other
industrial nations, despite the fact that EAS coverage was highly concentrated in certain sectors
of the economy.
62
It would be interesting to empirically investigate what factors contributed to
the stabilization of employment.
59
For example, the subsidy program could bring a substantial bene?t by promoting long-term employment if the
skill/productivity of workers increases with tenure.
60
For example, the subsidy could potentially enhance the downward rigidity of wage. Similarly, it may create
less incentive to legislate reductions to ?ring restrictions and promote labor mobility.
61
The subsidy program may have an inter-industry reallocation e?ect as some industries are more heavily sub-
sidized than others. This feature could potentially add another dimension to the analysis of overall productivity
dynamics.
62
According to Labor Force Survey, the unemployment rate during the 1990s followed a steady increase rather
than being cyclical. The unemployment rate at the trough from 1998-1999 was still below 5%.
93
Appendix A
Construction of Variables using the Nikkei Financial Dataset
‘Total sales revenue’ (var90) is used as a measure of gross output. Nominal value of sales in
turn are de?ated into a constant year 2000 value, using the annual averages of monthly corporate
good price indices (CGPI) provided at the Bank of Japan’s website in Japanese.
1
Note that CGPI
is available only for the manufacturing sector at the two-digit industry level. Also, since CGPI for
‘rubber’ (Nikkei industry code # 13) was not available, it was omitted from the analysis. Moreover,
CGPI for ‘nonferrous metals’ are used for ‘nonferrous metals and metal products’ (Nikkei industry
code #19).
‘Number of employed workers’ (var158) is used as the measure of labor input in the pro-
ductivity decomposition analysis. Note that the same series were used for the job reallocation
exercises. ‘Total material cost’ (var292) is used as a measure of material input. Nominal value is
converted into a real value using CGPI. The material cost share was calculated by dividing var292
by the ‘total cost’ (var306) and the labor cost share was calculated by dividing the ‘total labor
cost’ (var293) by the ‘total cost’ (var306).
The measure of capital stock is constructed using the ‘total tangible assets’ (var21) of
the Nikkei dataset. Var21 is the sum of buildings (var23), machineries (var24), transportation
equipment (var25), other equipment (var26), land (var27) and others (var28). According to var260
which explains the method of depreciation of tangible assets, 84% of all observations use a constant
rate of depreciation, 14% use a combination of the constant rate and the constant value, and the
rest use a combination of constant rate, constant value, and the rate of depreciation proportional
to output. These ?gures in turn are converted to a constant 1995 value using the annual average
of the monthly wholesale price index (WPI) provided by the Bank of Japan for machinery and
equipment. The WPI is available at the Bank of Japan’s website.
1
http://www.boj.or.jp/stat/dlong f.htm.
94
Appendix B
Examination of the Impact of Higher Volatility of Shocks on Subsidy Applications
In this section, I discuss the implications of higher volatility of (industry level) aggregate
shock processes on subsidy application decisions using the theoretical framework developed in
Chapter 3. In particular, a numerical experiment is conducted to examine the impact of higher
volatility on subsidy application decisions. The same framework used previously applies, except
that the frequency is changed from annual to monthly in order to be consistent with the empirical
analysis given in Chapter 2. Table (B.1) gives the parameter values for this particular experiment.
Table B.1: Parameter values used to obtain stationary distributions with monthly frequency.
w = 1 wage
?
h
= 3 hiring costs
?
f
= 3 ?ring costs
c
f
= 2 ?xed cost of operation
r = 0.0033 interest rate
? = (1/(1 +r)) = 0.9967 discount rate
? = 0.8 fraction of wage paid to unutilized workers
? = 0.7 prob. of being eligible for the subsidy
s = 2/3 subsidy coverage
? = 0.55 labor share of total cost
? = 0.85 persistence of idiosyncratic shocks
?
v
= 0.3 standard deviation of v
t
? = 0.6 aggregate state transition probability
To examine the impact of higher volatility, the distance between ?
g
and ?
b
is gradually
increased by the increments of 0.05 while the mean is held constant. More speci?cally, I ?rst set
both ?
g
and ?
b
equal to 2.7, then I increased (decreased) the size of the good (bad) state by 0.025
each time, until the good shock reaches 3.3 and the bad shock reaches 2.1 at which the lowest
idiosyncratic shock becomes closest to the boundary of zero.
1
Note that the symmetric aggre-
1
As before, the lowest boundary is set at the three standard deviations of idiosyncratic shocks away from the
95
0
5
10
15
20
25
30
35
40
0
5
10
15
20
25
0
1
2
3
4
5
6
7
8
9
10
idiosyncratic profitability shock
volatility measure
c
u
t
o
f
f

l
e
v
e
l

o
f

e
m
p
l
o
y
m
e
n
t
Figure B.1: Subsidy application decision rules with volatility for the good aggregate state. The
higher number of volatility measures indicates higher volatility and the higher number of idiosyn-
cratic shocks represents more favorable conditions.
gate transition probabilities preserves the mean while the distance between ?
g
and ?
b
increases.
Therefore, it allows us to focus on the impact of increased aggregate volatility. Employment
was discretized in 201 grid points ranging from zero to ten. Again, the upper bound was set to
guarantee that the highest optimal employment does not bind.
Figure (B.1) shows the subsidy application decision rules for the good aggregate state. The
decision rule shows the cuto? level of employment above which subsidy applications take place,
for a given level of volatility measure and idiosyncratic pro?tability shock. Here, volatility goes
up as the measure increases from 1 to 25, and the idiosyncratic pro?tability shock improves as the
measure increases from 1 to 40. When there are no ?rms applying at any given combination of
idiosyncratic shock and the volatility measure, the cuto? level of employment is at its maximum
level which here is set equal to 10. In general, the lower measure of idiosyncratic shocks should
be associated with an increased chance of subsidy applications, as expanding ?rms do not apply.
At the very low level of idiosyncratic shocks, however, ?rms decide to exit from the market and
therefore, they do not apply for the subsidy. In the good aggregate state, subsidy applications
mean.
96
0
5
10
15
20
25
30
35
40
0
5
10
15
20
25
0
1
2
3
4
5
6
7
8
9
10
idiosyncratic profitability shock
volatility measure
c
u
t
o
f
f

l
e
v
e
l

o
f

e
m
p
l
o
y
m
e
n
t
Figure B.2: Subsidy application decision rules with volatility for the bad aggregate state. The
higher number of volatility measures indicates higher volatility and the higher number of idiosyn-
cratic shocks represents more favorable conditions.
fall as the volatility measure increases, since the mean pro?tability shock captured by ?
g
increases
with a rise in volatility
On the other hand, the subsidy applications increase as the volatility measure goes up in
the bad aggregate state, and this rise is larger than the reduction in subsidy applications in the
good aggregate state. Therefore, overall subsidy applications increase with volatility. Figure
(B.2) shows the subsidy application decision rules for the bad aggregate state. Here we can see
that the area for subsidy applications continues to expand as the degree of volatility increases.
Finally, a stationary distribution with low volatility was compared with a stationary distri-
bution with high volatility in Table (B.2). Here, the benchmark case is the low volatility case.
Moreover, I use an asymmetric probability matrix this time in which the probability of a good
state continuing is 0.7 and the probability of bad state continuing is 0.3, as the equilibrium level of
subsidized workers turned out to be too large with the previous symmetric transition probability
and the other parameters given by table (B.1). The low volatility case sets ?
g
= 2.8 and ?
b
= 2.45
while the high volatility case sets ?
g
= 2.94 and ?
b
= 2.12. The unconditional expected mean for
97
both is approximately 2.695.
Table B.2: Summary statistics of stationary distributions with low and high aggregate volatility.
Low Volatility High Volatility
?
g
= 2.80 ?
g
= 2.94
?
b
= 2.45 ?
b
= 2.12
Fraction of workers covered by the subsidy 0.0074 0.0226
Exit rate 0.0174 0.0160
Job turnover rate 0.0181 0.0167
Total number of ?rms 1.0000 0.9999
Average ?rm level employment 1.0000 1.0049
Average ?rm level output 1.0000 0.9937
Average productivity based on employment 1.0000 0.9888
— adjusted for hiring and ?ring costs 1.0000 0.9927
— adjusted for hiring, ?ring and subsidy costs 1.0000 0.9868
Average productivity based on utilized workers 1.0000 1.0045
The table shows that the steady-state fraction of subsidized workers with low volatility is
0.74%, and it increases to 2.26% with high volatility. The exit rate falls with volatility from
1.74% to 1.6%, as more ?rms with low pro?tability shock decide to stay in the market by taking
advantage of the subsidy. Similarly, the job turnover rate falls from 1.81% to 1.67% since the
subsidy reduces both job creation and job destruction at the steady-state. Other results are based
on the same intuitions we’ve seen in the previous sections.
98
Appendix C
Industry Correspondence used for the Construction of the Demand Instrument
Table (C.1) shows the concordance of the industry classi?cations for the manufacturing
sector for the following three data sources: the JIP database, Indices of Industrial Production
published by the Japanese Ministry of Economy, Trade and Industry (METI), and Corporate Good
Price Indices (CGPI) constructed by the Bank of Japan.
This matching was employed for the construction of a demand instrument, which was con-
structed to investigate the output responses to demand shocks in the Iron and Steel industry. I
used the input-output table of the JIP database to create the annual weight which captures the
annual share of consumption of the Iron and Steel industry’s shipments among downstream in-
dustries. Then the original monthly series of shipment index of the downstream industries, taken
from the Indices of Industrial Production, were de?ated by CGPI, and the real growth rate was cal-
culated by taking the log di?erence. Finally, the weighted average growth rate of the downstream
industries was calculated by using the weights described above.
Although the classi?cation with smaller industrial units is available for Indices of Industrial
Production, it does not easily correspond with the classi?cations from the JIP database. Fur-
thermore, CGPI is not available for smaller industrial units. Therefore, the JIP industries were
aggregated to match with a broader classi?cation of the Indices of Industrial Production.
99
Table C.1: Concordance of industry classi?cations between JIP dataset, Indices of Industrial
Production (METI), and CGPI.
METI
JIP (last 3-
code JIP industry name digit) CGPI
7 Coal, lignite mining 132 Minerals
8 Metal mining
9 Crude oil, natural gas exploration
10 Quarry, gravel extraction, other mining
11 Livestock products 110 Processed foodstu?s
12 Processed marine products
13 Rice polishing, ?our milling
14 Other foods
15 Beverages
16 Tobacco
17 Silk 103 Textile products
18 Spinning
19 Fabrics and other textile products
20 Apparel and accessories
21 Lumber and wood products 127 Lumber and wood products
22 Furniture 124 Other manufacturing
23 Pulp, paper, paper products 98 Pulp, paper and related products
24 Publishing and printing
25 Leather and leather products 123 Other manufacturing
26 Rubber products 122 Other manufacturing
27 Basic chemicals 77 Chemicals and related products
28 Chemical ?bers
29 Other chemicals
30 Petroleum products 94 Petroleum and coal products
31 Coal products
32 Stone, clay and glass products 72 Ceramic, stone and clay products
33 Steel manufacturing 3 Iron and steel
34 Other steel
35 Non-ferrous metals 11 Nonferrous metals
36 Metal products 16 Metal products
37 General machinery equipment 21 General machinery and equipment
38 Electrical machinery 405 Electrical machinery and equipment
39 Equipment and supplies for household use
40 Other electrical machinery
41 Motor vehicles 57 Transportation equipment
42 Ships
43 Other transportation equipment
44 Precision machinery and equipment 68 Precision instruments
45 Other manufacturing 128 Other manufacturing
100
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