Description
A stable value fund is a type of investment available in 401(k) plans and other defined contribution plans as well as some 529 or tuition assistance plans.
ABSTRACT
Title of Document: STABLE FIRMS AND UNSTABLE WAGES.
Ana Luisa Gouvea Abras, PhD, 2010
Directed By: Professor John Haltiwanger, Department of
Economics
In this work I study recent developments in firm employment and earnings instability
in the US economy over the last 30 years. Despite the decline in aggregate and firm
level volatility, earnings instability has increased steadily for job stayers since the late
seventies. I measure and model these phenomena as a result of a decline in labor
market institutions that compress wage volatility, and an increase in the incidence of
compensation schemes that attach wages to worker performance.
STABLE FIRMS AND UNSTABLE WAGES
By
Ana Luisa Gouvea Abras
Dissertation submitted to the Faculty of the Graduate School of the
University of Maryland, College Park, in partial fulfillment
of the requirements for the degree of
Doctor of Philosophy
2010
Advisory Committee:
Professor John Haltiwanger ,Chair
Professor John Shea
Professor Katharine Abraham
Assistant Professor Pablo D.Erasmo
Assistant Professor Sanjay Chugh
© Copyright by
Ana Luisa Gouvea Abras
2010
ii
Acknowledgements
I thank my dissertation committee: John Haltiwanger, John Shea, and Katharine
Abraham. This work would not have been possible without their help. For every-
thing they taught me, I thank the professors in the macro sequence, Borang
Aruoba, Sanjay Chugh, and Pablo D’Erasmo. My greatest intellectual indebt-
edness though is to my advisor, John Haltiwanger. Countless people helped me
along in graduate school. I also thank my sister Leticia Abras, and Abby Alpert for
their support.
Contents
List of Tables v
List of Figures vi
Chapter 1. Trends in Employment and Wage Instability 1
1.1. Introduction 1
1.2. New evidence from the March CPS 16
Chapter 2. Stable Firms and Unstable Wages 29
2.1. An island model of the labor market 30
2.2. Simulation results 48
Chapter 3. Uncertainty in Employment Relationships and the Business
Cycle 57
3.1. Model 62
iii
3.2. Calibration and Simulation 72
3.3. Last Remarks 82
1. Figures and Tables 83
2. Data Appendix 106
3. Derivation of equilibrium in performance pay markets
111
Appendix. References 124
iv
List of Tables
Table 1 95
Table 2 96
Table 3 97
Table 4 98
Table 5 99
Table 6 100
Table 7 100
Table 8 101
Table 9 102
Table 10 103
Table 11 103
Table 12 104
Table 13 105
Table 14 106
v
List of Figures
Figure 1 83
Figure 2 84
Figure 3 85
Figure 4 86
Figure 5 87
Figure 6 88
Figure 7 89
Figure 8 90
Figure 9 91
Figure 10 92
Figure 11 93
Figure 12 94
vi
CHAPTER 1
Trends in Employment and Wage Instability
1.1. Introduction
The purpose of this dissertation is twofold. In the …rst two chapters I study
the rise of earnings instability in light of recent changes in volatility both at the
macroeconomic and the …rm level. Despite the moderation in the variance of
macroeconomic and …rm outcomes from 1979 to 2007, earnings instability for job
stayers increased over the same sample period. I present both theory and evidence
on these apparently contradictory phenomena. I …nd that earnings instability
for job stayers increased over the same sample period using the Matched March
CPS. I also measure earnings instability using the PSID from 1976 to 1996. I
…nd that jobs that received some form of bonus or commission have higher wage
volatility than jobs with wages subject to collective bargaining. I use my empirical
…ndings in order to guide construction and simulation of a model of the labor
market that explains increased wage volatility by combining a decline in labor
market institutions that compress wage volatility and an increase in the use of pay
schemes attached to worker performance. I calibrate the model to match standard
1
2
moments of the US labor market such as unemployment and job turnover, but
also values of size, standard deviation of bonus pay, and incidence of performance
related payment in the PSID. Simulations results suggest that moving the economy
from unionized markets to performance pay arrangements explain the bulk of the
decline in …rm volatility, and 29% of the increase in wage instability present in the
data in the last 30 years.
In the third chapter I turn to the analysis of a model of business cycle with
performance pay contracts. Extensive empirical evidence documents that worker
and job ‡ows are high and variable even for narrowly de…ned industries. Gross
reallocation rates are large both in booms and recessions, suggesting a constant
reshu-ing of resources taking place in the economy (Davis, Haltiwanger and Schuh,
1996). I extend a standard search model to include performance pay contracts and
analyze whether the uncertainty in employment relationships brought by contracts
help explain high frequency moments of compensation schemes, vacancies, and
unemployment in the US economy. I use a non-standard set of moments to calibrate
the model: values of size, incidence, and cyclicality of bonus payment in the PSID.
I …nd that a model that targets the moments of compensation schemes can explain
at least half of the high frequency variation in unemployment and vacancies in
the economy. I develop in the model bundled shocks. Besides the standard labor
productivity variation, I include in the model uncertainty shocks, represented by
3
time varying private information at the employment level. Uncertainty a¤ects the
value of employment by changing incentives and e¤ort in contracts, and decreases
the value of a job by making it harder to assess outcomes. Economic downturns
correspond to periods with increasing noise in the principal-agent problem in the
economy. To that extent, I develop a theory of recessions based on uncertainty
in employment relationships. Simulation results suggest that uncertainty shocks
are capable of generating high frequency variation in unemployment and vacancies
without resorting to high variance in labor productivity shocks, overcoming a well
known problem of labor search models (Shimer, 2003).
1.1.1. Empirical Evidence on Firm and Earnings Instability
Macroeconomic outcomes in the US and other major developed countries became
less volatile in the mid-1980’s and volatility remained low through 2006. This
widely discussed phenomenon, known as the Great Moderation, is re‡ected in the
decline in the variance of GDP, in‡ation and other aggregate series. This trend in
macroeconomic outcomes has been accompanied by a decline in business growth
rate volatility. In this work, I focus on an aspect of the economy that has not been
touched by increasing stability : labor market earnings. Evidence from a variety
of sources over the last 25 years shows a rise in the variance of household earnings
4
in the US. Greater heterogeneity in job outcomes manifests itself in di¤erent ways
besides variability of wages. Lower average tenure, higher occupational mobility,
and a greater job loss rate in previously secure high-skilled positions all suggest a
more ‡uid labor market. I search in this work for ways to reconcile evidence that
earnings volatility has increased while …rm volatility has decreased over the last
two decades.
My work provides an extended empirical analysis using Matched March CPS
data from 1980 to 2008. In a sample of job stayers in private non-farm jobs, I
…nd that volatility in both hourly earnings and total earnings displays an upward
trend. The increase in hourly earnings instability for job stayers over this period
is 35%. I also measure earnings instability using the PSID from 1976 to 1996. I
…nd that jobs that receive some form or bonus or commission have higher volatility
than jobs with wages subject to collective bargaining.
To attempt to understand these patterns in the data, I develop a general equi-
librium model of the labor market with worker and …rm heterogeneity. I extend the
frictional labor market model of Lucas and Prescott (1974). My extensions involve
the inclusion of di¤erent pay setting mechanisms in di¤erent sectors or islands in
the labor market. The way the model works is as follows. Due to search frictions,
wages and employment are heterogeneous in separated local labor markets. In
5
some markets, wages are awarded according to performance, while in other mar-
kets institutional arrangements prevent wages from being equal to the marginal
product of labor in all states of the world. The institutions that I emphasize are
unions and wage norms, both of which tend to compress the wage distribution and
decrease wage instability. These institutions were prevalent in the early eighties,
but have declined in importance since.
I postulate that the driving force of this change in labor market arrangements
is a decrease in the cost of monitoring workers. Improvements in information
technology have allowed for better evaluation of worker performance and make it
easier to o¤er wages aligned to productivity. New IT diminishes the asymmetry
of information between …rms and workers and raises the gains from operating un-
der performance pay arrangements. Since compensation becomes more responsive
to idiosyncratic conditions under performance pay, the cross section dispersion
of wage growth increases. This mechanism is consistent with the empirical evi-
dence discussed below that reports an increase over the last 30 years in the use of
compensation arrangements attached to worker performance.
Theory and measurement are linked since the model is used to illustrate how
technological change a¤ects employment and wage instability. I calibrate the model
to match standard moments from the labor market in the 2000’s. The main goal of
6
the simulation exercise is to evaluate the ability of changes in labor market institu-
tions to explain the path of wage volatility. I perform this exercise by keeping the
underlying idiosyncratic shock process constant and changing only the technology
of compensation in the economy. Simulation results suggest that a model with new
compensation technologies that attach wages to worker performance works quali-
tatively in the right direction of explaining the diverging trends in …rm and wage
instability, and appears to account for a substantial fraction of the quantitative
change observed in the data.
There are a number of recent papers that motivate my consideration of alterna-
tive pay arrangements. The …rst paper is Lemieux, MacLeod and Parent (2009a,
henceforth LMP). The authors test the e¤ect of performance pay on wages in the
PSID and ask whether returns to worker and job characteristics di¤er according
to pay schemes. They …nd that compensation in performance pay jobs is more
closely tied to both observed (by the econometrician) and unobserved productive
characteristics of workers. The increase in the incidence of performance pay over
time provides an important channel through which technological changes in the
cost of monitoring and in returns to skill a¤ect wage inequality. Performance pay
is closely linked to the idea that wages are tied to e¤ort and productivity of the
7
worker. A shift to paying wages that equal performance outcomes means poten-
tially more ‡exible wages and a departure from norms and rigidity that could
regulate behavior in the labor market.
A change in the technology of compensation is central to the explanation I
advance for the increase in earnings instability. The second set of papers relevant
to my hypothesis include Hubbard (2000) and MacLeod and Parent (1999). Hub-
bard argues that the use of on-board computers in the trucking industry provided
managers with a better way to monitor production processes. IT in monitoring
is productivity enhancing and potentially capable of explaining changing wage
incentives. MacLeod and Parent use several data sources to document the re-
lationship between type of job and compensation. The authors …nd that jobs
with high power incentives (piece or commission rates) tend to be associated with
more worker autonomy and that tight labor market conditions increase the use of
bonuses and promotions. Moreover, the authors report anecdotal evidence that
shows an increasing use of software for evaluating worker performance and a boom
of services for monitoring workers. Lemieux, MacLeod and Parent (2009b) argue
that performance pay jobs seem to be associated with higher wage ‡exibility, and
that wages respond more to conditions in their local labor markets. Based on the
evidence from those papers and evidence below, I allow di¤erent wage schemes in
8
my model and show how declining costs of monitoring can move the economy from
"rigid" compensation schemes to an increased use of pay-for-performance.
1.1.2. Evidence on macroeconomic and …rm-level instability
The variances of GDP, investment, and aggregate income began declining in the
mid-eighties. Stock and Watson (2003) report that the standard deviation of four-
quarter GDP per capita growth in the US declined about forty percent comparing
the 20-year-windows before 1984 and after 1984. Several papers document and dis-
cuss the causes of the increased aggregate stability that followed the eighties (Kim
and Nelson, 1999, Stock and Watson, 2005, Blanchard and Simon, 2001). More
interesting for our purposes are the trends in job turnover and business volatility
for the same period. Turnover rates, as measured by creation and destruction of
jobs, have decreased steadily in the US economy after the 1983 recession. A sim-
ilar trend is observed by Davis, Faberman and Haltiwanger (2006) for the entire
economy in the nineties using Business Employment Dynamics data. In the same
vein, Davis, Haltiwanger, Jarmin and Miranda (2006, henceforth DHJM) report an
overall decrease in the volatility of growth rates of businesses in the US beginning
in the late 70’s.
1
1
Previous work - Comin et al (2006) - focused on publicly traded …rms, which display rising
volatility in recent years. Davis, Haltiwanger, Jarmin and Miranda (2006) partially overturn the
results of Comin et al (2006) for …rm volatility with COMPUSTAT data, showing that once the
9
Figures 1 to 3 show the secular decline in business volatility and turnover
rates in the US economy over the period 1976 to 2005. I present the evidence on
…rm volatility using di¤erent measures and data sources to demonstrate that the
decline in …rm instability is a robust feature of the data. Figure 1 displays the
cross section standard deviation of the growth rate of employment, computed using
the Longitudinal Business Database (LBD), which contains annual observations on
employment and payroll for all U.S. businesses.
2
This measure of …rm volatility
is cyclical, and displays its highest level in the pre-nineties period. There is a
declining trend in volatility when we compare the periods before and after the the
early eighties.
Figure 2 shows turnover rates measured using job ‡ows data from the LBD.
Job creation and destruction rates represent the amount of job churning in the
economy. Both series display a steady decreasing trend over my sample period.
3
Figure 3 shows the quarterly excess job reallocation rate for the whole private
sector calculated using the BLS Business Employment Dynamics (BED) database.
The excess job reallocation rate provides a measure of cross sectional dispersion in
establishment growth rates. It measures the amount of turnover that exceeds what
sample is increased to include both private and publicly owned …rms, there has been an overall
decrease in …rm level volatility.
2
Source: Davis, Faberman and Haltiwanger (2006a).
3
Source: DFHJM.
10
is necessary to account for the net employment growth in the economy.
4
Note that
despite the di¤erent data source and measure, we still see a decline in business
volatility over the sample period.
Labor market outcomes are the result both of churning jobs between …rms, and
of churning workers across labor market states. There is no long, consistent time
series measuring worker ‡ows for the US economy, which makes it hard to identify
long run trends in overall accessions and separations. It is possible, however, to
document trends for the subset of worker transitions in and out of employment
using data from the Current Population Survey (CPS). Figure 4 shows quarterly
averages of unemployment in‡ows and out‡ows using the CPS from 1976 to 2008.
Worker ‡ows fell almost by half from the early 1980s to the mid 1990s and there-
after. The evidence discussed below of decreases in tenure and increases in residual
inequality and earnings volatility has not been associated with rising instability of
…rm employment, or with higher job and worker ‡ows.
4
Excess job reallocation equals the sum of gross job creation and destruction less the absolute
value of net employment growth. The excess reallocation rate is equivalent to the employment-
weighted mean absolute deviation of establishment growth rates about zero. See Davis, Halti-
wanger and Schuh (1996). I use a similar measure for change in earnings in the CPS in Section
2 in order to calculate wage instability.
11
1.1.3. Evidence on earnings instability
Since the work of Gottschalk and Mo¢tt (1994) calculating labor earnings instabil-
ity using the PSID, several papers have devoted attention to documenting recent
trends in earnings volatility in the US economy.
5
Despite di¤erences in results,
methods, and measurement, overall the evidence suggests that the labor market is
becoming more unstable; workers seem less able now to hold jobs with predictable
earnings.
Dynan, Elmendorf and Sichel (2008), using the PSID, document a steady rise
in instability of household earnings since the late 70’s. The authors …nd an in-
creasing trend in the standard deviation of percentage changes in several measures
of earnings, such as total household income, household head earnings, combined
head and spouse earnings, head annual hours and head real earnings per hour.
6
Below, I present similar evidence using Matched March CPS data from 1980 to
2008.
A related result is analyzed in Cunha and Heckman (2007). The authors sep-
arate trends in the predictable and unpredictable components of earnings at the
time agents make relevant job market decisions. They estimate that the variance
5
See Cameron and Tracy (1998), Haider (2001), and Hertz (2006) for examples.
6
Shin and Solon (2008) repeat the exercise of Dynan et al (2008) using di¤erent earnings measures
and …nd a smaller increase in wage instability.
12
in the unpredictable part of earnings at the time of schooling choice has increased
when comparing cohorts born in the sixties and late seventies.
Two additional facts about recent US labor market trends are noteworthy in
this context: …rst, occupational mobility increased up to the mid 90’s and stabilized
thereafter (Moscarini and Thomsson, 2007). Second, wage inequality increased in
overall measures prior to the early 90’s.
7
Several papers study the evidence of rising
wage inequality in the US (Katz and Autor, 1999, Acemoglu, 1999, 2002, Violante,
2002, Piketty and Saez, 2003). The empirical evidence clearly suggests that recent
earnings gains have been highest in the highest wage percentiles. Increases are
also evident in other measures of inequality including the 90/10 gap, college/high
school gap and residual inequality (accounting for age, gender, experience and
education). In this paper I focus on instability rather than inequality. Though
these two phenomena are likely to have similar origins, they do not follow the
same trend over time. Hence I treat them as separate pieces of evidence.
1.1.4. Alternative explanations for the rise in earnings instability
7
According to Autor, Katz and Kearney (2005), wage inequality kept increasing for the 90-50
wage percentiles after the mid-90s, but remained stable or decreased for some groups in the lower
half of the wage distribution.
13
Like most complex events, the recent rise in earnings instability can accommodate
several possible explanations. I discuss here several possible explanations related
to secular changes in the labor force or higher "turbulence" in the labor market.
The composition of the US labor force has changed over the last 30 years. The
population is aging even while the tenure distribution is apparently decreasing
(Farber, 2008). Also, skilled workers occupy a growing share of jobs (Autor, Katz
and Kearney, 2005). It is unlikely that these changes in labor force composition
can provide a consistent explanation of rising earnings instability, since experienced
and skilled workers should be less susceptible to wage instability than other groups.
Financial innovation has allowed households to self-insure against increasing
wage instability, according to Dynan, Elmendorf and Sichel (2008). Though the
authors argue that this link is important in explaning the Great Moderation, they
are silent about the events in the labor market that could have triggered higher
income instability. Financial innovation has a¤ected both …rms and workers, and
…nancial constraints can make employment more sensitive to shocks.
8
However, it
is unclear a priori why …nancial innovation would change compensation schemes
used in the labor market.
8
See Chugh (2009).
14
Cunha and Heckman (2007) …nd that the variance in the unpredictable part
of earnings at the time of schooling choice has increased over the last 20 years.
They speculate that this is linked to higher "turbulence" or skill depreciation after
job loss (Ljungqvist and Sargent, 2004). Earnings losses of displaced workers have
been detected by several authors in the literature (see Farber, 2005 for a summary).
Though Ljungqvist and Sargent use turbulence to explain rising European unem-
ployment, it can also explain rising earnings uncertainty if the rate of skill loss has
increased. The main drawback of this reasoning is that the rate of involuntary job
loss, the type most likely to lead to declines in earnings, has if anything decreased
since the early eighties (Davis, 2008). It would take a large increase in the loss in
skills following job loss to o¤set that trend.
Another plausible source of higher volatility is discussed in Violante (2002).
The author uses a model with search frictions that links new vintage speci…c skills
to workers matched to di¤erent machines. He shows that in such a model an
increase in the pace of technological change spreads the wage distribution of similar
workers. Workers face losses from separation since they have to learn new vintage
abilities, and uncertainty in outcomes increases with turnover.
As discussed by Comin, Groshen and Rabin (2006), several models imply that
higher turbulence for …rms will lead to more turbulent wages. Coincident …rm and
worker trends can be explained as resulting from "bad luck" - larger idiosyncratic
15
…rm shocks translate into unstable wages. Since the …rm evidence discussed in
the previous section does not suggest higher idiosyncratic …rm shocks, however,
a story based on changes in the size and variance of the shock process a¤ecting
…rms is unlikely to explain simultaneous occurrence of rising wage instability and
declining …rm instability. Models in which shocks to occupations, jobs or vintages
accelerated generally imply that both worker and …rm instability should have gone
in the same direction. The literature has yet to come to grips with the con‡ict
between trends in labor market and in …rm outcomes.
9
The evidence highlighted above is discussed in Davis and Kahn (2008). Despite
the ongoing volume of research on the Great Moderation and its relationship to
…rm behavior, little attention has been given to reconciling the evidence of macro-
economic and …rm moderation with evidence of growing earnings instability. Davis
and Kahn suggest an explanation based on employment relationships having be-
come more ‡exible. They argue that employers are increasingly capable of using
wages as a margin of adjustment. Less unionization, weakening restrictions on
9
I do not consider the problem of consumption volatility and its response to income shocks.
As argued in Krueger and Perri (2009), consumption response to income shocks is higher for
individuals who do not own real state or business. This suggests that …nancial constraints matter
for the transmission of earnings volatility to consumption and wealth volatility. Whether the
increase in earnings instability is related to changes in the trends of consumption volatility for
the US economy is an open question. To the extent the …nancial innovation has increased since
the early eighties, the connection between the two volatility outcomes is likely to have decreased
with better access to …nancial markets.
16
minimum wages, and more ‡exible pay schemes are consistent with fewer job ‡ows
and more earnings volatility. Davis and Kahn suggest this explanation without
explicitly modeling it. If wage institutions are the key to explaining the puzzle,
we need to model the underlying factors that have lead to the adoption of pay
schemes under which workers face more variability.
1.2. New evidence from the March CPS
The ideal data to study the relationship between the volatilities in …rm and
earnings outcomes is matched longitudinal data on …rms and their employees. To
the best of my knowledge, Comin, Groshen and Rabin (2006) is the only work in
this vein. They use the Federal Reserve Bank of Cleveland’s Community Salary
Survey (wages and employment for speci…c occupations for identi…ed …rms) to link
higher …rm volatility and the rising variance of wages. The result is in line with
their previous work with …rm volatility in the COMPUSTAT data. However, as
mentioned above, DHJM …nd that …rm volatility has declined over time in a more
representative sample of …rms.
I adopt a route that is more roundabout but that does not require as much
information. I use matched March CPS data to construct measures of earnings
growth for short panels. The cross sectional variation in the earnings growth
data allows me to answer questions such as: Are trends for job stayers and job
17
movers di¤erent? Do labor market conditions like the unemployment rate matter
for volatility? I use answers to such questions to guide my model construction.
The data I use are the March CPS …les from 1980 to 2008. The CPS was
not designed for longitudinal analysis. Groups are interviewed for 4 consecutive
months, dropped from the sample for 8 months, then reinterviewed for another 4
months. Given this structure, around half of the sample in each month will appear
again a year later and can potentially be matched. I match rotation groups from
March to March in order to construct short panels that give earnings growth for
a relatively large sample. Mandrian and Lefgren (1999) develop an algorithm to
match observations and evaluate the quality of the match results from 1980-98,
which I extend up to 2008. I link individuals based on their CPS identi…cation
codes. Since there is some level of mismatch, I further restrict observations to
matches that have the same sex and race across the two observations.
There are some advantages in using the CPS instead of other data previously
analyzed for similar questions, such as the PSID. The CPS is used to study both
standard micro labor topics and aggregate ‡ows in and out of employment. It
collects earnings information not only from heads and spouses, as in the PSID,
but from all members of the household. The sample size is also larger and more
18
representative of the labor force. Hence, using the CPS allows me to address
competing explanations that rely on compositional changes in the labor market.
These advantages come at a cost. Matched CPS data only provide information
for one-year changes. None of the intertemporal structure discussed in the work
that initiated the study of variance in transitory and permanent components of
earnings (Gottschalk and Mo¢tt, 1994) can be captured with the CPS. I am forced
to focus only on short-term changes.
Amore worrisome problemis that the CPS does not provide tenure information.
The tenure distribution has likely changed over my sample period. Farber (2008)
presents evidence on tenure using CPS Tenure Supplements from1973 to 2006. The
results are puzzling - job tenure is decreasing while the job loss trend as measured
with the Displaced Worker Survey (DWS) is not increasing. Farber argues that
the DWS might not be capturing all instances of separations. This explanation is
unlikely to capture the entire story since other measures also point to lower job
loss in the last 20 years (Davis, 2008).
The lack of information on tenure makes it harder to evaluate competing ex-
planations of earnings instability that rely on increased mobility. There is evidence
that job-to-job and occupational mobility have increased since the late 70’s (see
Moscarini and Thomsson, 2007, and Fallick and Fleishman, 2004, for evidence with
19
monthly CPS, and Kambourov and Manouskii, 2007, for evidence with the PSID).
Nevertheless, mobility trends are more cyclical than the results I present later for
earnings instability for job stayers. While earnings instability increased steadily
over my sample period, Bjelland et al (2008) report that the pace of employer-to-
employer ‡ows as a fraction of employment and separations has remained low in
the post-2001 period following the recession.
One should worry whether the matched sample is representative of the overall
labor force for which I want to measure the trend in volatility. The probability
of being matched in two consecutive March interviews depends on observables
such as marital status, age, employment, etc. I correct for such selection in the
following exercises by using propensity score weights in all weighted measures. See
the Appendix on sample selection for details on this method.
10
The variables used in the analysis are total annual wage and salary earnings,
hourly earnings and total annual hours worked. Those variables are either asked
directly in the March Supplement or can be constructed, and refer to the previous
10
Each year is matched to the following year’ survey. For instance, 1980 refers to the merge of
1980-81 and corresponds to calendar years 1979-1980. Years 1985-86 and 1995-1996 could not be
matched due to problems with the household identi…ers. The exercises reported exclude married
women from the sample for reasons discussed in Footnote 12. For more details on matching and
sample selection, see Appendix 1.
20
calendar year.
11
With the short panels, I calculate measures of the dispersion in
growth rates in earnings and hours for di¤erent groups. Assume we have earnings c
for person i in periods t and t+1. The growth rate of c is given by G
cit
=
c
ti+1
c
it
.5(c
ti+1
+c
it
)
.
The …rst exercise is similar to Davis and Kahn (2008).
12
I measure instability
as the cross-section weighted average of absolute growth rates. This measure is
analogous to the excess job reallocation rate calculated at the …rm level.
(1.1) o
t
= \ciq/tcd_¹·c:cqc([G
cit
[)
Figure 5 shows this measure of hourly earnings instability and total hours
instability for the sample of private non-farm workers (excluding married women
13
)
11
Total household income, Total earnings, Hours worked in the previous year and Weeks worked
in the previous year are asked directly. From these I construct Total hours worked= Hours
worked per weekX Weeks worked, and Hourly earnings=Total earnings/ Total hours worked.
12
Davis and Kahn (2008) measure consumption volatility using quarterly data from the interview
segment of the Consumer Expenditure Survey. The authors compute the absolute value of the
log change in consumption expenditures for each household and then average over households.
This average value for the magnitude of household-level consumption changes is their measure
of consumption volatility. In results not reported I calculate two other dispersion measures: the
weighted average of individual growpth rates demeaned by the year average growth rate, and
the cross section standard deviation of growth rates. All measures display similar results for the
trend in earnings instability.
13
I exclude married women from the sample. The trend for total hours instability in the sample
including married women shows a decline in hours volatility. This is likely due to the increase in
labor force attachment for this group over the sample period. The exclusion of married women
from the sample does not change results for earnings volatility substantially and has the advantage
of not confounding long term changes in the composition of the labor force with changes in the
stability of earnings within employment relationships.
21
from 1980 to 2007. There is no notable trend in total hours instability, but hourly
earnings instability displays an increasing trend.
Figures 6 and 7 separate workers between job stayers and job movers/losers.
Job stayers are de…ned as workers who report in both March interviews being em-
ployed and having worked full time full year in the previous year without changing
employers.
14
As of March of their second interview, stayers have at least two years
of job tenure. Job movers/losers are workers who report experiencing unemploy-
ment or job change prior to one of the March interviews.
15
Figure 6 shows an
increase in total earnings instability for job stayers. Figure 7 shows no increase
14
March CPS data are retrospective, and I infer worker ‡ows from 3 variables: 1) "For how many
employers did ...work in 20..? If more than one at same time, only count it as one employer". 2)
"Weeks was ... looking for work or on layo¤ from a job? ". 3) "Were the weeks ... was looking
for work (or on layo¤) all in one stretch?". For full time full year workers with one employer
in each period, the problem is immaterial, since these workers stay in the same job. A more
comprehensive measure of job stayers includes part time part year workers with no more than
one employer in each period and no weeks looking for a job or on layo¤. Those might not be
stayers in case they exited the labor force at the end of period t and reentered in t+1 with a
di¤erent employer. Results with the comprehensive measure of stayers are virtually the same as
with full time full year workers. The fraction of job stayers does not display a trend over time in
my sample. Job movers/losers are workers that report unemployment or more than one employer
in the previous year in one or two March interviews. There might be some stayers in this group
if they are in the beginning of their job tenure in the beginning of t or the end of their tenure
in the end t+1. The fraction of those workers is no more than 5% of the overall sample in each
year, and also displays no trend over time. The comprehensive measure of job stayers and the
job movers/losers constitute two mutually exclusive groups.
15
Note that I am not separating job movers into those that experience unemployment and those
that transit directly between di¤erent employers. The consequences for wage instability are po-
tentially di¤erent since displaced workers are more likely to experience earnings losses (Jacobson
et al, 1993).
22
in total earnings instability for job movers/losers. Hourly earnings instability in-
creased for both groups of workers. The lack of trend in total earnings instability
for job movers/losers is probably due to two opposing e¤ects: higher hourly earn-
ings instability and smaller worker and job ‡ows.
In order to compute the long-run change in instability over the entire period
I estimate linear trends using individual o
it
as the dependent variable. Tables
1 and 2 give coe¢cients for the linear trend and implied cumulative growth of
instability.
16
Table 1 reports results for the entire sample of private non-farm
workers, job stayers and job movers/losers. Total earnings and hourly earnings
instability increased for both the full sample and job stayers. Job movers display
rising instability in hourly earnings but a decrease in total earnings and total hours
instability.
In table 2, I examine job stayers with high school or less education and
job stayers who are less than 45 years old. The increase in earnings instability for
the samples of younger and less educated job stayers is higher than the increase in
instability for the overall sample of stayers. Younger and less educated workers are
16
I calculate the total increase in instability using the value of the coe¢cient, ,, of the time
trend in a linear regression. For instance, the increase in instability for total earnings for the full
sample over 28 years is given by 28 +
´
, = .029, where
´
, is the estimated coe¢cient on the time
trend for total earnings instability.
23
a declining fraction of the population over the sample period. This decline along
with their higher and increasing instability dampens the overall instability trend
for job stayers.
My last exercise looks at di¤erences between performance pay and non-performance
pay jobs. The March CPS does not provide detailed information about the type
of pay, which prevents the identi…cation of performance pay jobs. I replicate to
the extent possible the CPS instability measures by calculating one-year percent
changes in hourly earnings in the PSID from 1976 to 1996 for job stayers.
17
Following the literature, I de…ne performance pay jobs as those receiving some
pay in the form of a commission, bonus or piece-rate over the duration of the
17
I thank Daniel Parent for providing the data from LMP. The sample consists of male heads of
the household aged 18 to 65 with average hourly earnings between $1.00 and $100.00 (in $79)
Due to the longitudinal feature of the PSID, I can de…ne job stayers as workers that remain in
the same job match. I construct one-year changes in hourly earnings for job stayers using worker
that remained in the same job match. Note that in the case that the job match is observed for
more than one year, I have the growth rate for the same individual in more than one time period.
In the CPS I only observe the growth rate of an individual once, when she is matched accross
two consecutive interviews. See appendix for details on the CPS and PSID samples.
24
worker-…rm match.
1819
I also look at unionized jobs, de…ned as jobs with wages
subject to collective bargaining. I separate jobs into four mutually exclusive groups:
workers in performance pay with no collective barganing, workers with collective
bargaining and no performance pay, workers not in performance pay or collective
bargaining, and workers in both collective bargaining and performance pay.
20
Table
3 presents mean hourly earnings instability for those four groups over the sample
period. Table 3 also presents t-statistics for di¤erences in mean instability between
18
As in the literature, I de…ne performance-pay jobs as employment relationships in which part
of the worker’s total compensation includes a variable pay component (bonus, a commission,
piece-rate) at least once during the course of the relationship.
The issue of measuring incidence of performance-pay in the beginning and end of the sample
arises. The classi…cation of jobs according to pay understates the fraction of performance pay
in the two end points of the sample. Conditional on job duration, a job is observed fewer times
at the two ends, thus it is less likely to display positive bonus, commission, or piece-rate. One
solution to this problem is to rebalance the sample using regression methods. As indicated in
Lemieux at al (2009), reweighting the sample does not a¤ect substantially incidence graphs or
regression results using performance pay dummies.
19
Tips are not included in the de…nition of performance pay jobs. Though they constitute a
form of incentive pay (done by the consumer and not the employer), the questions about form of
pay change over time in the PSID. For interview years 1976-1992, the question about pay refers
speci…cally to any amounts earned from bonuses, overtime, or commissions in addition to wages
and salaries earned. Starting with interview year 1993, there are separate questions about the
amounts earned in bonuses, commissions, tips, and overtime for the previous calendar year. For
the sake of comparability, overtime and tips are excluded from the de…nition of performance pay.
This procedure is likely to understate the incidence of performance pay jobs, and causes a bias
if the fraction of workers receiving tips is changing over time. Using the data starting in 1993, I
compare incidence of performance pay and size of incentive in terms of total wages between the
full sample and the sample without jobs reporting positive tips. I …nd no signi…cant change in
results.
20
The sample size is too small to calculate separate time trends for these subgroups. I choose to
pool all observations. I compute 'ca
[q
I|
[) using growth rates in hourly earnings for each job
group. Results use PSID sampling weights.
25
groups.The results indicate that earnings instability is signi…cantly higher for non-
union performance pay jobs than for union non-performance pay jobs. For non-
union jobs there is no signi…cant di¤erence in instability between performance and
non-performance pay jobs. Union jobs display less variability than non-union jobs
regardless of whether performance pay is observed.
Mean di¤erences in wage instability can obscure the e¤ect of performance pay
and unions on volatility if performance pay or union status are correlated with
other factors that are potentially associated with instability. I use the following
regression exercise to net out the e¤ect of worker and job match characteristics as
well as conditions in the local labor market. I regress individual [q
it
[ on a dummy
for performance pay jobs and a dummy for collective bargaining. The control
variables used are worker …xed e¤ects, tenure, experience, year e¤ects, 1-digit oc-
cupation and industry dummies, unemployment at the county level and a measure
of 1-digit industry-level …rm instability.
21
The coe¢cients for the performance pay
dummy and union dummy are presented in Table 4. Column 1 presents results
without worker …xed e¤ects and characteristics. The dummy for unionized job is
negative and statistically di¤erent from zero. Colums 2 presents results including
worker …xed e¤ects and characteristics. Regression results in Column 2 indicate
21
Standard errors are clustered at the job match level. The data for …rm-level instability come
from DJHM (2006). See their paper for de…nitions of volatility and dispersion in …rm outcomes
and data construction.
26
that the e¤ect of performance pay on wage instability is positive when control
variables are included (column 2), but not when control variables are excluded
(column 1). The e¤ect of the union dummy is not statistically di¤erent from zero
once I include controls in the regression. This suggests that job stayers in perfor-
mance pay jobs have characteristics such as higher educational level and tenure
that decreases their wage instability. Nevertheless, the e¤ect of bonus or comission
on instability is positive.
Figure 8 displays the incidence of performance pay jobs in the PSID over time
for my sample period. It also shows the fraction of jobs that received a bonus,
commission or piece-rate in a given year, and the fraction of unionized jobs.
22
One
can see a clear rise in the incidence of performance pay jobs, which is accompanied
by a decline in unionization. A simple back-of-the-envelope calculation using the
average instability for each group over the period, and the change in incidence of
wage setting institutions from 1976 to 1996, gives an increase of 1.27% in hourly
eanings instability.
23
22
Note that not all performance pay jobs receive a bonus in a particular year. Performance pay
jobs are de…ned as jobs that get a bonus sometime during the job match.
23
In the back-of-the-envelope calculation I take the average value of wage instability in each
group, and weight each group by their fraction in the PSID sample in 1976 and 1996. The
di¤erence between the instability in the two time periods measures the portion of the increase in
wage instability due to a change in composition of wage schemes. I also estimate the time trend
coe¢cient for the regression on wage instability with the sample of job stayers in the PSID. The
total increase in wage instability the estimated time trend is 7.2%.
27
To summarize our results, the main message we take is that rising wage insta-
bility reached several segments of the labor market. This phenomenon is unlikely
to represent a …gment of the data, since the results are robust to di¤erent data
sources and methods. Nevertheless, aggregate measures mask large degrees of
heterogeneity between groups.
The change I report is more related to the behavior of earnings than hours.
While earnings instability is cyclical, especially for job movers/losers, the long-
term rising trend in instability cannot be due to increased transitions in and out
of unemployment. As discussed in the previous section, worker and job ‡ows seem
to be decreasing over the same period.
The most important result concerns job stayers in the March CPS. Those work-
ers do not report any major job transitions and are thus by de…nition in a "stable"
employment relationship. The fact that dispersion for this group displays a sub-
stantial trend increase gives more con…dence that the phenomenon of rising insta-
bility a¤ects ongoing employment relationships. Secular changes in mobility, skill
loss after displacement and demographic characteristics of the labor force could
still matter for instability. Nevertheless, given that the rise in hourly earnings
instability is large for job stayers, I choose to focus on the latter group for the
remainder of this paper.
28
Lastly, the exercise with the PSID indicates that jobs with some form of bonus
pay have higher wage instability than other jobs. This suggests that the formof pay
matters for wage instability outcomes. Based on that, I argue in the next section
that main mechanism driving the increase in earnings instability is an institutional
change in wage determination. The model is built upon this conjecture.
The dissertation proceeds as follows. The remainder of Chapter 1 discusses the
evidence on …rm and wage instability. Chapter 2 presents a model of performance
pay and unionized markets in order to tackle the diverging long run trends in
employment and wage instability. Chapter 3 presents a business cycle model of
performance pay with uncertainty shocks.
CHAPTER 2
Stable Firms and Unstable Wages
What I refer to as an institutional change in wage setting is a shorthand for a
series of events in the labor market that have happened in the past three decades:
less unionization, fewer restrictions on minimum wages, and more ‡exible pay
schemes attached to …rm and worker performance. Institutional changes have
been proposed as an explanation for the rise in wage inequality in the US. I argue
below that the same changes might help to explain increased earnings instability
of job stayers.
My conjecture is that there are two equilibria in wage setting institutions. The
…rst prevailed during the eighties, when monitoring worker productivity was too
costly and the wage had to be tied to job characteristics. The second is the current
labor market in which information technology has allowed for performance based
pay schemes. Some institutions naturally belong to the eighties steady-state, such
as minimum wages and unions. Performance pay is more related to recent events,
so can be identi…ed with the 2000’s model.
29
30
2.1. An island model of the labor market
I move below to a structural general equilibrium model of the labor market.
I start with an indirect search version of the Lucas and Prescott (1974) model of
frictional labor markets. That set up is used in several wage inequality and unem-
ployment studies (Jovanovic, 1987, Alvarez and Veracierto, 1999, Veracierto, 2008,
Kambourov and Manovskii, 2007). I choose to build on Alvarez and Veracierto
(1999).
I describe …rst the features of the environment that hold in all sectors of the
economy, regardeless of their choice of pay scheme. Then I proceed to discuss the
speci…c elements that apply to …rms that use performance pay contracts versus
those that use union/norm wage setting.
Environment:
There is a continuum of local labor markets dubbed islands that are separated
geographically. Islands are constantly hit by idiosyncratic productivity shocks and
movement of workers between islands requires one period of search.
Islands have an idiosyncratic productivity process, . that follows a Markov
process that can take values
1
<
2
< ... <
n
and has transition matrix Q(.
0
).
At the beginning of every period, each island is characterized by a pair (r
t
.
t
) where
r is the labor force and the current productivity shock. Accordingly, feasibility
31
in the market implies that q(r. ) _ r, where q(r. ) is employment, and the labor
force in the island evolves with the arrival of new agents from unemployment, l.
joining those that worked in the previous period, such that r
0
= l + q(r. ). The
employment rule and the Markov process for idiosyncratic productivity generate
an invariant distribution of islands over labor force and productivity given by
(A
0
.
0
) =
_
f(a,.):l+j(a,.)2A
0
g
Q(.
0
)(dr d).
There is a measure one of potential workers with linear preferences over con-
sumption, c
t
. I assume complete markets. The timing is such that after ob-
serving (r. ) and total compensation, n(q(r. ). ), workers decide on whether
to stay or leave their local labor market. Search is indirect, hence workers who
leave their market face one period of searching and arrive randomly next period
to a new island. Those who stay work at the given wage rate. I denote the
expected value of unemployment as c, and the expected value of employment
as ·(r. ). The agents problem is described by ·(r. ) = max¦c. n(q(r. ). ) +
,1
_
·(l + q(r. ).
0
)Q(. d
0
)¦, where agents take q(r. ) and the wage determi-
nation as given.
Each island has a continuum of producers that share a common island-speci…c
productivity shock. The production technology uses labor, q. e¤ort, c, and has
decreasing returns to scale, c, where 0 _ c _ 1 indexes the elasticity of output
32
with respect to q. Output is given by 1(q. ) = q
c
.I assume there are two types
of productive arrangments. In performance pay jobs the worker exerts positive
e¤ort and output is given by 1(q. ) = (1 + .c)q
c
, where c stands for worker
e¤ort and . is the marginal contribution of e¤ort to output. The performance pay
job uses monitoring and sets up a contract to de…ne compensation. In unionized
jobs e¤ort is zero and output is given by 1(q. ) = q
c
, which is equivalent to
setting . equal to zero.
1
Unions are the case when no monitoring technology is
used. We can interpret the productive arrangement in the unionized case as if the
worker exerts an "ordinary" level of e¤ort, which I normalize to zero. I denote the
marginal product of labor by ,(q. ) = (1 + .c)cq
c1
.
In equilibrium, employment in the island has to be consistent with individual
decisions. If ·(r. ) o, all individuals in the market are strictly better staying
than leaving, and q(r. ) = r. If ·(r. ) = o, agents are indi¤erent between staying
and leaving, and q(r. ) = q(), where q() solves c = n(q(). ) + ,1
_
·(l +
q().
0
)Q(. d
0
). Using q(r. ) = r if ·(r. ) o, and q(r. ) = q() if ·(r. ) = o,
in the agents problem we obtain the functional equation ·(r. ) = max¦c. n(r. )+
,1
_
·(l+q(r. ).
0
)Q(. d
0
)¦. The employment rule for this problem is such that
q(r. ) = min¦r. q()¦.
2
1
We can interpret the productive arrangement in the unionized case as the case that the worker
exerts an "ordinary" level of e¤ort, which I normalize to zero.
2
See Alvarez and Veracierto (1999) for a complete derivation of the problem.
33
I model below two types of labor markets according to their wage setting insti-
tutions: markets with only performance pay jobs and markets with only unionized
jobs. Both market types are in the same framework, but di¤er on how total com-
pensation or the wage rate is determined.
Wage setting in performance pay markets: The performance pay model I use
is based on Baker, Gibbons and Murphy (1994). I extend the baseline set up in
the island model in order to include an e¤ect of worker choice of e¤ort on output
outcomes. Assume that the marginal contribution of worker e¤ort to …rm output
is given by :. Wage contracts between …rms and workers cannot be written on :,
since it is too complex to be objectively assessed. However, there is a veri…able
performance measure, 1, which is an imperfect measure of :. In order to simplify
notation, assume that : can only take values of .q
c
or 0, and 1 can take values
of .q
c
or 0. The …rm observes 1 and :, but only 1 is contractible.
At each period, the worker can choose an action that stochastically determines
both output and performance. The relationship between worker e¤ort, c, and
the …rm’s outcome is such that Pr o/
= .q
c
[ c) = c, where c is between 0
and 1. The probability of observing a positive performance measure is given by
Pr o/(1 = .q
c
[ c) = jc, where j is a random variable with mean 1(j) and
variance ·c: (j), bounded above so that Pr o/(1 = .q
c
[ c) _ 1. We can think of
j as the di¤erence between the e¤ect of e¤ort on performance and output. There
34
are states of world when j is large and high e¤ort contributes more to performance
measures than to the value of the …rm. When j is small, we have the opposite
case, and high e¤ort would likely generate large value for the …rm, but would not
increase performance measures. I assume that …rms do not know j, while workers
observe j after deciding whether to stay on the island, but prior to choosing e¤ort.
From the viewpoint of the …rm and the worker, e¤ort and bonus are stochastic
prior to the realization of j. The problem of the …rm is to o¤er a compensation
package prior to the realization of j that aligns e¤ort to productivity, and the
problem of the worker is to choose the optimal level of e¤ort once j is realized.
The sequence of events is such that …rms and workers start the period knowing
the state of the economy (r. ). and the variance and mean of j. At the island
level there is a spot market for binding wage contracts. The assumption of binding
contracts is common in the literature, since revelation of j to the worker and worker
e¤ort can be thought of as occurring simultaneously. The contracts estipulate a
base pay, and a bonus paid in case a positive performance measure is observed.
More speci…cally, the pay scheme o¤ers a base pay, n(r. ), and a bonus, 1, paid
if 1 = .q
c
.
The …rm takes the base pay as given and decides on the size of the bonus
and employment. The worker then decides whether to take the contract or not.
After hiring takes place, the worker observes j and chooses e¤ort. The worker is
35
privately informed about j, hence the …rm has to o¤er a compensation scheme
based on the expected value of j and the schedule for the worker’s optimal choice
of e¤ort. Before observing j, the expected value of the bonus for the worker is
given by 1
j
[jc
1]. Exerting e¤ort is costly for the worker. I assume that the
disutility caused by the e¤ort level c equals ¸c
2
. I also assume that j is iid and
that the …rm and the worker are atomistic, taking the base pay as given.
Worker problem:
The Bellman equation for the worker is given by:
(2.1)
·
j
(r. ) = max¦c. 1
j
[max
o
n(r. )+jc1÷¸c
2
+,1
_
·
j
(l
j
+q(r. ).
0
)Q(. d
0
)]¦
The choice of e¤ort and bonus is then equivalent to a one period game between
the worker and the …rm. Optimal e¤ort maximizes the current return from working
and is equal to c
=
j1
2¸
.
The worker accepts the performance pay job only if it gives an expected value
higher than searching. The worker choice of taking the job or searching gives the
minimum base pay that clears the local market:
36
(2.2) 1
j
[max
o
n(r. ) + jc1 ÷¸c
2
+ ,1
_
·
j
(l
j
+ q(r. ).
0
)Q(. d
0
)]¦ _ c
(2.3) n(r. ) _ 1
j
[c ÷(jc
1 ÷¸c
2
+ ,1
_
·
j
(l + q(r. ).
0
)Q(. d
0
))]
Firm problem:
The technology is such that 1
j
[1(q. )] = 1
j
[(1 +.c)q
c
]. On average, worker
e¤ort increases output by 1
j
[.cq
c
]. The …rm problem is to choose 1 and q to
maximize pro…ts taking into account the incentive constraint for the worker:
: = max
1,j
1
j
[(1 + .c
)q
c
÷nq ÷jc
1q] (2.4)
s.t. c
=
j1
2¸
(2.5)
The …rst order conditions are as follows:
(2.6) 1 : 1
j
[.
j
2¸
q
c
÷
j
2
1
¸
q] = 0
37
(2.7) q : 1
j
[(1 + .
j1
2¸
)cq
c1
÷n ÷
j
2
1
2
2¸
] = 0
The …rst order conditions imply:
(2.8) 1
=
.
2
1
j
[jq
c
]
1
j
[j
2
q]
(2.9) n = 1
j
[(1 + .
j1
2¸
)cq
c1
÷
j
2
1
2
2¸
]
From (10), …rms pay the expected bene…t of e¤ort upfront in the form of base
pay, .
j1
2¸
cq
c1
÷
j
2
1
2
2¸
. After the worker observes j, she chooses optimal e¤ort.
Equilibrium employment:
The base pay that clears the market depends on supply and demand for labor.
3
Using (4) and (10), we have:
3
See appendix for the derivation of performance pay market equilibrium conditions.
38
(2.10)
n = 1
j
[(1+.
j1
2¸
)cq
c1
÷
j
2
1
2
2¸
] _ 1
j
[c÷(jc
1
÷¸c
2
+,1
_
·
j
(l+q(r. ).
0
)Q(. d
0
))]
which can be rearranged as follows:
(2.11) 1
j
[cq
c1
+ (c
.cq
c1
÷¸c
2
) + ,1
_
·
j
(l + q.
0
)Q(. d
0
)] _ c
In (12), the expected net bene…t of e¤ort is given by the second term in paren-
theses, c
.cq
c1
÷ ¸c
2
. The …rst best would be for the worker to exert e¤ort
until the marginal cost equals marginal bene…t, or c
11
=
¸.cj
1
2¸
, independently of
j. Because the worker is privately informed on e¤ort and j, this outcome cannot
be achieved, and e¤ort is given by c
=
j1
2¸
.
4
4
Note that the expected bene…t of e¤ort is quadratic in e¤ort. The …rm and the worker achieve
the maximum bene…t in the a
J1
case. The two extreme cases are when e¤ort is zero, and there is
no probability of positive performance or value; and when a=
o¸¸
1
~
, and the worker is exerting
too much e¤ort in order to increase the chances of receiving a bonus. Note that the existence of a
perfect performance measure allows for the implementation of the …rst best. Assume without loss
of generality that ·ar(j) = 0, c = 1,2, and j = 1, but output is not contractible. The worker
chooses e¤ort to maximize the current return n + a/ ÷ ¸a
2
. Using the fact that in this case
n = (1+¸a)c-q
o1
÷a/, we have that a
=
¸o:¸
1
2~
, which implies a
= a
J1
. This is a standard
result in contract theory. Given the preference assumptions, whenever there is a performance
measure that responds to e¤ort in the same way that output respondes to e¤ort, the …rst best
can be implemented (see Baker, 1992).
39
Next consider the optimal bonus choice and the base pay. Since the size of
the bonus and employment are decided before the realization of j. the …rm can
treat j as independent of q. so that the optimal bonus can be simpli…ed as 1
=
1[¸
2
.j
]
1[
2
j]
=
¸
2
1[j].j
1
[1[j]
2
+·ov(j)]
. When idiosyncratic productivity is high or the labor
force in the island is low, it pays for both sides of the market to increase the bonus
and e¤ort. The bonus is thus sensitive to local labor market conditions. In a
similar fashion, for high values of the marginal contribution of e¤ort to output
., performance pay is a more productive arrangement, and the bonus increases.
Also, the higher the variance of the objective measure of performance, the smaller
the optimal bonus and the smaller the e¤ect of productivity on pay. When j
has higher variance, the performance measure is a noisier signal of the actual
worker contribution to output and the …rm has to settle for weak incentives. Weak
incentives then induce a smaller e¤ort choice by the worker. The converse is true
when the variance of j is low. In this case, the …rm can provide a strong incentive
using the bonus.
The variance of j has a similar e¤ect on base pay. Substituting the optimal
bonus into the …rm …rst order condition in equation (10) yields:
(2.12) n = cq
c1
+
1
4¸
1
j
[j]
2
(.q
c1
)
2
(1
j
[j]
2
+ ·cj))
_
c ÷
1
2
_
40
The use of incentive pay based on performance a¤ects the marginal product
of labor and the base pay. The base pay is decreasing in ·cj) if c
1
2
.
5
The
intuition is the same as in the case of the optimal bonus. When 1 is a noisy
signal of the contribution of e¤ort to outcomes, the optimal level of e¤ort and
the marginal value of labor are low, which decreases not only the odds of having
a positive realization of 1 but the base pay that clears the market. Note that,
neglecting the participation constraint, pro…ts are quadratic in bonus. Optimal
bonus level is given by 1
=
¸
2c
1[j].cj
1
1[j
2
]
=
1
2c
1[j]
1[j
2
]
1
11
, where 11 denotes …rst
best. The coe…cient
1
2c
1[j]
1[j
2
]
is the distortion brought by the performance measure.
For the case that c = 1,2, the …rms does not need to compensate the worker in
the base pay with the expected marginal return to e¤ort. The …rm can o¤er a base
pay cq
c1
, and a bonus
1[j]
1[j
2
]
1
11
with probability jc. This case is equivalent
to o¤ering a piece rate on a performance measure scaled to the expected marginal
vale of e¤ort in the marginal revenue. As the performance measure becomes a
5
Note that the expected bene…t of e¤ort is quadratic in e¤ort. The …rm and the worker achieve
the maximum bene…t in the a
J1
case. The two extreme cases are when e¤ort is zero, and there is
no probability of positive performance or value; and when a=
o¸¸
1
~
, and the worker is exerting
too much e¤ort in order to increase the chances of receiving a bonus. Note that the existence of a
perfect performance measure allows for the implementation of the …rst best. Assume without loss
of generality that ·ar(j) = 0, c = 1,2, and j = 1, but output is not contractible. The worker
chooses e¤ort to maximize the current return n + a/ ÷ ¸a
2
. Using the fact that in this case
n = (1+¸a)c-q
o1
÷a/, we have that a
=
¸o:¸
1
2~
, which implies a
= a
J1
. This is a standard
result in contract theory. Given the preference assumptions, whenever there is a performance
measure that responds to e¤ort in the same way that output respondes to e¤ort, the …rst best
can be implemented (see Baker, 1992).
41
perfect signal of the e¤ect of e¤ort on output (1
j
[j] ÷ 1 and 1
j
[j
2
] ÷ 1), we
approach the …rst best, which is o¤ering a piece rate of one. For c 1,2, e¤ort is
very productive. In order to induce e¤ort variation the worker receives more than
cq
c1
in the base pay. The …rm then sinks 1
j
[.ccq
c1
÷jc1] in the base pay
and o¤ers a piece rate smaller than one on the scaled performance measure.
The cuto¤ rule for the level of employment that clears the local market in each
island depends on the expected payo¤ of working under a performance pay regime.
If ·
j
(r. ) c, all workers stay and q = r. Otherwise we have that employment
at the island level solves:
(2.13) 1
j
[cq
c1
+ (c
.cq
c1
÷¸c
2
) + ,1
_
·
j
(l + q.
0
)Q(. d
0
)] = c
which can be rearranged as follows:
cq
c1
+
.
2
4¸
1
j
[j]
2
(q
c1
)
2
(1
j
[j]
2
+ ·cj))
_
c ÷
1
4
_
+ ,1
_
·
j
(l + q
.
0
)Q(. d
0
) = c
Whenever c
1
4
, the expected value of working is decreasing in the variance
of the performance measure. The less noisy the performance measure, the easier
42
it is to align e¤ort to idiosyncratic conditions in the market. Moreover, an in-
crease in the return to e¤ort, ., leads to a higher expected value of working under
performance pay.
Note that an improvement in monitoring technology represented by either a
smaller ·cj) or a higher ., raises welfare in the economy. The current return to
working in a performance pay job is given by 1
j
[n + c1j ÷¸c
2
] . Substituting the
optimal choice of e¤ort in the previous equation yields 1
j
_
n +
j1
2¸
1j ÷¸
_
j1
2¸
_
2
_
=
1
j
_
n +
j
2
1
2
2¸
÷
j
2
1
2
4¸
_
= 1
j
_
n +
j
2
1
2
4¸
_
. Since both terms inside the brackets are
decreasing in ·cj),
6
the expected value of working increases with improved tech-
nology. This e¤ect in general equilibrium raises the reservation wage of unemployed
workers and the value of non-employment, c. The value to the worker of the in-
crease in the bonus outweights the utility cost of the increase in e¤ort.
The goal of the simulation exercise presented in the next section is to evaluate
whether the improvement in the technology of compensation translates into more
wage instability. In order to build intuition on the results, let’s look in partial
equilibrium at the expected current return of working under performance pay.
Denote \
o.
the variance of the marginal product of e¤ort on output with respect
to the productivity shock, and ·c) the variance of the idiosyncratic shock. \
o.
=
6 µ
2
1
2
4~
=
µ
2
4~
2
_
¸
2
J[µ]:¸
1
(J[µ]
2
+uoµ))
_
2
=
¸
2
16~
1
µ
[j
2
]
(J[µ]:¸
1
)
2
(J[µ]
2
+uoµ))
2
=
¸
2
16~
J[µ]
2
¸
1
)
2
(J[µ]
2
+uoµ))
43
(.q
c
)
2
·c) is increasing in .. Better technology in performance pay means that
the worker has more valuable information on how her e¤ort a¤ects the output.
This is a standard result in linear performance pay contracts (Baker, 1992). More
information for the worker indicates that she can alter signi…cantly e¤ort in order
to a¤ect output. The …rm wants the worker to use that information to improve
outcomes, and gives higher incentives to generate more e¤ort variation. Since
e¤ort variation is costly, the …rm has to compensate the worker in the base pay,
n = 1
j
[(1 +.c
)cq
c1
÷j1c
]. The higher e¤ort variation induces higher wage
instability by making the base pay more responsive to idiosyncratic shocks. In
partial equilibrium, the variance of n with respect to in equation (12) increases
with improvement in technology.
7
Note that this is an optimal behavior, and the
improvement in technology raises the overall return of working under performance
pay.
Value of unemployment:
7
Assume that - follows and AR(1) with autorregressive coe¢cient j, mean zero, and variance of
the innovation o
2
. Then ·ar
= ·ar(-cq
o1
+
1
4~
J[µ]
2
(¸:¸
1
)
2
(J[µ]
2
+uoµ))
_
c ÷
1
2
_
) =
_
cq
o1
_
2
·ar(-) +
2
_
1
4~
J[µ]
2
(¸¸
1
)
2
(J[µ]
2
+uoµ))
_
c ÷
1
2
_
c
2
1¡
2
_
. In partial equilibrium, the variance of wages with respect to
the idiosyncratic shock increases with improvement in the technology of performance pay. The
variance of wages captures the increase in e¤ort variation for higher ¸ or lower ·ar(j). Note that
the variance of wages is increasing in the variance of the innovation to -. There are two ways that
the variance of wages can increase: either the shock process is more volatile, or the parameters
¸ and ·ar(j) change such that there is an improvement in performance pay technology.
44
In the case that only one type of pay scheme exists, the value of unemployment
is such that workers who leave their market receive the expected value of arriving
anywhere in the invariant distribution,
j
(dr d), of performance pay markets.
(2.14) c = ,
_
·(r. )
j
j
(dr d)¦
Equilibrium of the model with performance pay. The competitive equilibrium
is a set of prices (1, n), allocations q, functions ·
j
(r. ), e¤ort level c, numbers
c. and l. and invariant distributions,
j
(dr. d) such that:
1) c and 1 satisfy the …rm and worker problem:
(2.15) c
=
j1
2¸
(2.16) 1
=
.
2
1
j
[jq
c
]
1
j
[j
2
q]
=
.
2
1
j
[j]q
c1
[1
j
[j]
2
+ ·cj)]
2) ·
j
(r. ) is given by:
(2.17)
·
j
(r. ) = max¦c. 1
j
[max
o
n(r. ) +jc1÷¸c
2
+,1
_
·
j
(l +q(r. ).
0
)Q(. d
0
)]¦
45
3) In performance pay markets, q(r. ) satis…es
q : 1
j
[(1 + .
j1
2¸
)cq
c1
÷n ÷
j
2
1
2
2¸
] = 0
and n satis…es
n = cq
c1
+
1
4¸
1
j
[j]
2
(.q
c1
)
2
(1
j
[j]
2
+ ·cj))
_
c ÷
1
2
_
Employment at the island level satis…es feasibility 0 _ q _ r, and is consistent
with individual decisions. Two cases can occur:
i) if 1
j
[n(r. ) + jc
1
÷ ¸c
2
+ ,1
_
·
j
(l + q(r. ).
0
)Q(. d
0
)] c, then
q = r and wages are given by the FOC of the …rm:
n = 1
j
[(1 + .
j1
2¸
)cr
c1
÷
j
2
1
2
2¸
]
ii) if 1
j
[n(r. ) + jc
1
÷¸c
2
+ ,1
_
·
j
(l
j
+ q(r. ).
0
)Q(. d
0
)] = c, then
wages are given by the FOC of the …rm:
n = 1
j
[(1 + .
j1
2¸
)cq
c1
÷
j
2
1
2
2¸
]
where q satis…es:
46
cq
c1
+
.
2
4¸
1
j
[j]
2
(q
c1
)
2
(1
j
[j]
2
+ ·cj))
_
c ÷
1
4
_
+ ,1
_
·
j
(l + q.
0
)Q(. d
0
) = c
The numbers c and l, and the invariant distribution
j
satisfy:
c = ,
_
\
j
j(dr. d)
l = 1 ÷
_
q(r. )
j
(dr d)
j
(1
0
.
0
) =
_
f(a,.):l+j(a,.)2A
0
g
Q(.
0
)
j
(dr d)
The de…nition of competitive equilibrium for the unionized sector is analogous.
Wage setting in unionized markets. The union can be thought of working in the
following fashion: for each level of idiosyncratic productivity, a minimum level of
pay, n(), is established for workers that stay in unionized islands.
8
The contract
is such that in unionized jobs the level of e¤ort is constant, which I normalize
to zero, and output is given by q
c
. Wages equal the marginal product of labor,
n = cq
c1
. When the minimum pay binds, employment is such that n() =
8
See Alvarez and Shimer, 2008, for a model in which the union chooses the minimum pay to
maximize the present discounted value of unionized workers. I assume that the minimum is
exogenous and calibrate it to reproduce plausible levels of the union wage premium.
47
,(q(). ), where q() is the maximum level of employment for idiosyncratic shock
level , given the minimum wage and …rm optimization.
In the case that r < q(), the minimum pay constraint does not bind and
workers decide between receiving spot wages in their market or searching.
(2.18) ·
&
(r. ) = max¦n + ,
_
·
&
(l + q.
0
)Q(. d
0
). c¦
In the case that q() < r. either some workers leave until the point that
·
&
(r. ) = c and the minimum constraint does not bind, or the constraint binds
and a fraction of workers is forced to search, so that n() = n. A lottery assigns
workers to either searching or working in the last case. Workers that search receive
the expected value of unemployment, c
&
.
The Bellman equation when q() < r is given by:
(2.19) ·
&
(r. ) = max¦
r ÷q
r
c +
q
r
_
n() + ,
_
·
&
(l + q. ).
0
)Q(. d
0
)
_
. c¦
where q() is such that ,(q(). ) = n().
aj
a
is the probability of searching,
and
j
a
is the probability of staying.
Value of unemployment:
48
The value of unemployment under union wage setting is de…ned as the expected
value of arriving anywhere in the invariant distribution,
&
(dr d), of unionized
markets.
c = ,
_
·
&
(r. )
&
(dr d)¦
2.2. Simulation results
2.2.1. Calibration and moments to match
In this section, I address whether a model that matches the changes in wage setting
institutions observed in the US economy can generate the observed decline in job
and worker ‡ows and the observed increase in volatility in wages. Table 5 presents
parameter values and labor market moments that help discipline the calibration of
the model. The ultimate test of the model is its ability to reproduce the moments
in Table 7, namely the increase in the mean dispersion of wages and the decline in
the standard deviation of the employment growth rate, using only changes in the
technology of compensation in the economy.
9
9
The value for the increase in wage instability comes from the calculations in Table 1 for the
sample of job stayers. The value of the decrease in employment instability comes from the LBD
for the sample of continuing business.
49
As is standard in the literature, I assume that the idiosyncratic shock process
follows an ¹1(1), such that |
t+1
) =1 ÷ j) + j ln(
t
) + c
t+1
, where c
t+1
~
`(0.
2
c
). I approximate this AR(1) using a discrete Markov process with the
Tauchen (1986) method. The variance in the innovation to productivity is directly
linked to the volatility of employment and wages in the model. There is no closed
form solution relating the shock process to moments in the model. I calibrate the
parameters of the shock process so that it matches the levels of unemployment
and job reallocation in Table 6. The value of the standard deviation of labor
productivity estimated from plant-level data is around .5 (Syverson, 2003). Also,
the standard deviation of the innovation to the idiosyncratic component of …rm
pro…tability estimated in search models is around .22 (Cooper et al, 2007). The
excess job reallocation rate in the BED data is around .14 in the early 2000s. The
average unemployment rate reported by the BLS during the same period is around
5.5%. The time period in the model is equivalent to 3 months and the discount rate
corresponds to an annual interest rate of 4%. The labor share in the production
function is the value implicit in the NIPA accounts.
I calibrate the private information process and the cost and returns to e¤ort
as follows. I assume that j comes from a symmetric 1ctc(j. j)
10
distribution
10
I use j = .25 in order to match the moments of the bonus in the simulated data with values
obtained from the PSID in the late nineties. In later simulation exercises I use j in the [.05 .25]
range in order to check the sensitivity of the bonus moments to this parameter.
50
with mean 1(j) and variance \ cj). The range of j is such that for a given
draw of the private information and resulting optimal e¤ort level, we have that
j
/(1 = .q
c
[ c
)=jc
_ 1, and c
= j1
,2¸ is in the interval [0. 1]. The
payment of the bonus comes from a Bernoulli trial with probability of success jc
.
For each successful draw of the Bernoulli distribution I include the optimal bonus
in the total compensation. The size, variance, and incidence of the bonus in the
model depend on how productive the performance pay arrangement is.
11
I choose
.. ¸ and 1ctc(j. j) such that the moments of the bonus paid in the simulation are
close to their levels in the PSID for the group of performance pay jobs. As in the
literature, I calculate the bonus pay as the sum of earnings received in the form
of tips, commission, piece-rate or bonus. The size of the bonus pay is the ratio
of the bonus pay to total earnings in a given year. The incidence of bonus pay is
the number of jobs that received a bonus in a given year over the total number
of jobs classi…ed as performance pay. I calculate the size and incidence of bonus
in each year and …nd that both values present a trend increase, consistent with
11
As in the literature, I calculate the bonus pay as the sum of earnings received in the form
commission, piece-rate or bonus. The size of the bonus pay is the ratio of the bonus pay to
total earnings in a given year. The incidence of bonus pay is the number of jobs that received a
bonus in a given year over the total number of jobs classi…ed as performance pay. The standard
deviation is the cross section standard deviation of bonus. I calculate the size and incidence
of bonus in each year and …nd that both values present a trend increase, consistent with my
hyphotesis that the performance pay technology has improved over this time period. See Figure
10 for trend increase in the bonus size.
51
my hyphotesis that the performance pay technology has improved over this time
period. I present in Table 5 the incidence, variance and size of the bonus payment
estimated using PSID data from 1993 to 1998. Table 6 shows the moments to
match in the data and their values in the simulated performance pay model.
The employment and earnings instability measures are computed by simulating
a panel of islands in the economy. I compute cross section dispersion measures
across islands. The goal of the simulation exercise is to reproduce the moments in
Table 7 by changing the technology of compensation, represented by parameters
of the private information process j, and the return to e¤ort ..
In table 8, I compare the predictions of three island models: a model with
performance pay markets; a model with only unionized markets; and a "baseline"
model in which wages are equal to the marginal product of labor in all states of
the world, and in which e¤ort is normalized to zero, so that ,(. r) = q
c
and
n(. r) = cq
c1
. I keep the underlying idiosyncratic shock process constant and
calculate the same moments using the baseline, performance pay, and the "union"
model.
12
In the "union" model I set the lower bound for wages so that the average
12
The size and incidence of the bonus in the PSID in 1998 are respectively 0.057 and .1705.
Note that the model simulation produces quarterly data. I aggregate wage and bonus payments
in the simulated data in order to compare them with the annual data in the CPS and PSID.
The LBD data are also annual. In Table 8 I calculate the standard deviation of percent change
in employment considering time aggregation. Time aggregation does not a¤ect the results for
employment instability, but it makes simulated data comparable to the LBD.
52
wage in the economy reproduces the observed union wage premium when compared
to the performance pay model.
13
The unionized and performance pay models use
the wage determination described in the previous section.
The …rst thing to note is that wage instability is higher and employment in-
stability is lower under the performance pay model compared to the union model.
These results hold using either mean absolute changes or the cross section stan-
dard deviation of percent changes as the measure of dispersion. Note that the
idiosyncratic productivity process is held …xed across the three models. Moreover,
since the bonus constitutes a small fraction of total compensation, the di¤erence
in wage instability is not an artifact of introducing uncertainty with respect to the
bonus pay. The use of incentives also a¤ects the employment margin. Employment
instability is lower under performance pay, suggesting that under this wage setting
arrangement it is easier to adjust the employment margin. Intuitively, under per-
formance pay, the …rm can adjust the base wage downward when productivity is
lower, but cannot do so under unions.
Table 8 contains polar cases with the economy operating under only one type
of compensation scheme. A more realistic model would allow for unionized and
performance pay jobs to coexist. In such a model, technological advance in the
13
See Newmark and Kawaguchi (2001) for estimates of union wage premium with the March
CPS.
53
form of higher . or lower ·cj) would relocate workers to the performance pay
sector. I plan to explore such a model in future drafts.
In Table 9 I present simulation results for the case in which only performance
pay is used. I change the technology of private information and the return to e¤ort
such that the variance of j decreases and the return to e¤ort increases. Note that
Beta (1,1) is a mean preserving spread of Beta (4,4), which in turn is a mean
preserving spread of Beta (6,6). As expected, the instability of wages is higher for
Beta (6,6) and when . is equal to .25. The technology of compensation can a¤ect
the wage instability in two ways. First, through the bonus payment. Since the size
of the bonus is higher when the performance pay arrangement is more productive
with higher ., the level of e¤ort and the probability of receiving a bonus are also
higher. More productive islands will o¤er a higher likelihood of receiving bonus
pay and the cross section of wage growth outcomes will become more dispersed.
Second, as discussed in the previous section, improvement in technology makes the
base pay more responsive to the idiosyncratic shock. Better technology increases
optimal e¤ort variation, which is compensated in the base pay. The increase in
. is isomorphic to a model with a physical cost of setting up a performance pay
arrangement, and represents better monitoring technology.
14
14
See appendix for the case of positive monitoring cost.
54
Though . is a free parameter, there is some discipline in this exercise: the
natural boundary of the parameters is imposed by j/(1 = .q
c
[ c
)=jc
_ 1.
The parameters of performance pay productivity cannot be increased above the
range in which the probability of receiving a bonus is smaller than one. Also,
higher . increases the mean, variance and incidence of bonus. For the case that
. equals .25, I reproduce a empirically reasonable size and incidence of the bonus
pay in the late nineties.
We can now compare the simulation results with the …rm and wage instability
changes in the data reported in Table 7. If the economy moves from unionization
to performance pay adoption the wage instability increases by .019, and the …rm
instability decreases by 0.040 in the model simulations. These results represent
one fourth of the observed increase in wage instability and nearly all the decrease
in …rm instability in the data.
2.2.2. Last Remarks
This paper studies the relationship between recent trends in earnings and employ-
ment volatility. Evidence from a variety of sources indicates that both …rm level
instability and aggregate measures of job and worker ‡ows have declined during
55
the 1976-2007 period, while measures of earnings instability from the March CPS
rose over this period. The increase in wage instability in the March CPS is greater
for job stayers than for job movers/losers and for the overall sample of private non
farm workers. This result suggests that changes inside employment relationships
contributed to the rise in earnings volatility. I also measure wage instability for
job stayers in the PSID from 1976 to 1996. I …nd that wage instability is higher
for jobs that receive some form of bonus or commission.
I argue that technological change in compensation schemes has allowed …rms to
adjust wages more easily in response to idiosyncratic shocks, instead of hiring and
…ring workers. I illustrate this phenomenon in a general equilibrium search model
in which total compensation depends on a performance measure. A decrease in the
cost of monitoring workers is equivalent to a technological change in compensation.
The outcome of the new technology in wage setting is that wages are more aligned
to productivity, which implies higher earnings instability and lower employment
instability.
56
The exploration of more sophisticated monitoring technologies and productive
arrangements, and modelling coexistence of di¤erent pay schemes in the economy,
are left for future research.
15
15
An useful extension of theory would be to consider model with both technologies operating over
time and endogenous switching between types. Assume that workers can direct search towards a
type of market. Though they cannot choose a speci…c island to go, they can decide on whether
to move to the unionized or the performance pay sector. They bear the same cost of searching,
which is one period of forgone labor earnings.
Let’s consider the case when the two types of wage settings coexist in the economy. The problem
of the worker in a performance pay job is the same as before:
\
¡
(r, -) = max¦c, 1
µ
[max
o
n(r, -) + ja1 ÷¸a
2
+ ,1
_
·
¡
(l
¡
+ q, -
0
)Q(-, d-
0
)]¦
The problem of the worker in the unionized sector is analogous:
\
u
(r, -) = max¦c, n(r, -) + ,1
_
\
u
(l
¡
+ q, -
0
)Q(-, d-
0
)¦
The value of unemployment now takes into account that the worker can direct search to markets:
c = max¦,1
_
\
¡
(l + q, -)j
¡
(dr d-)), ,1
_
\
u
(l + q, -
0
)j
u
(dr d-)¦
When the variance of j decreases or ¸ increases, \
u
increases, which sustains a higher value
of searching. Unemployed workers increase their reservation wage and the marginal product
must increase in unionized islands. In an equilibrium with positive unemployment workers must
relocate from unionized to performance pay markets.
.
CHAPTER 3
Uncertainty in Employment Relationships and the
Business Cycle
Several recent papers have raised the question of whether uncertainty a¤ects
the business cycle. Aggregate and …rm level uncertainty have been shown em-
pirically to behave countercyclically. Bloom (2009) reports various measures of
…rm employment and stock value instability, all which vary negatively with the
cycle. On the household side, Storesletten et al (2004) present evidence with the
PSID that idiosyncratic labor income risk has a variance that increases by 75%
as the economy moves from peak to trough. Recessions are periods with higher
turnover. Figure 7 presents a measure of total earnings instability
1
for workers
in the Matched March CPS that experience some form of unemployment or job
change. Earnings instability is hump shaped during economic downturns.
2
Figure
9, from Bloom (2009), presents the Chicago Board of Exchange (CBOE) index of
1
I measure instability as the cross-section weighted average of absolute growth rates. This mea-
sure is analogous to the excess job reallocation rate calculated at the …rm level.
2
A previous literature on job ‡ows has raised the hyphotesis that ‡uctuations in the intensity
of shifts in employment opportunities across establishments a¤ects business cycle dynamics. See
Davis et al, 1990.
57
58
market volatility calculated using volatility of index option prices. One can see
a clear spike in the period corresponding to the recent credit crunch. The index
is supposed to represent market expectations of volatility in stock prices, and it
increases in all major periods of economic turmoil such as the two oil shocks, and
the Black Monday. In Table 14 I present evidence on the cyclicality of uncertainty.
The dependent variable is stock marlet volatility measured with variance of option
prices in the Chicago Board of Exchange. The …rst three regressions come from
Bloom (2009) and use as independent variables measures of cross section standard
deviation of …rm pro…t growth, …rm stock return, and industry TFP growth. The
last regression uses monthly unemployment rate from the CPS. All measures are
positively correlated with the uncertainty series from the CBOE.
In this work, I address the question of whether more information at the em-
ployment relationship level is consistent with more uncertainty in recessions, and
particularly in the current downturn. The literature so far has focused on model-
ing this evidence as re‡ecting time varying variance in productivity. Models with
time varying variance correctly produce countercyclical uncertainty. Nevertheless,
anecdotal evidence has shown that the revolution in information technology has de-
creased the level of uncertainty in employment relationships, bringing the question
of how information and uncertainty interact with the cycle. The current papers on
uncertainty and the business cycle focus on two types of e¤ects: 1) change in the
59
real option value of investment and hiring (Bloom, 2009); and, 2) uncertainty as
bad news predicting low productivity in the future (Bachmann and Bayer, 2009).
I suggest a third mechanism in which uncertainty a¤ects the value of employment
by changing incentives and e¤ort in contracts. Uncertainty decreases the value of
a job by making it harder to assess outcomes, or by increasing the noise in the
principal-agent problem in the economy. There are two types of uncertainty in
the literature. The …rst is used in Bachman and Bayer (2009) and Bloom (2009).
Uncertainty in their case is represented by changes in the cross-sectional dispersion
of …rm-speci…c Solow residual innovarions (variance in TFP). This is related to the
idea that the economy is not only hit by TFP level shocks, but the the variance of
TFP also changes stochastically over time. In terms of modeling choice, the paper
closer to my set up is den Haan and Kaltenbrunner (2005), who also use search
and matching frictions in the labor market. In deen Han and Kaltenbrunner the
amount of vacancy posting depends on expectations of futute productivity. There
is a regime switching between periods of higher and lower productivity growth.
Recessions then coincide with expectations of lower productivitity growth in the
future and a¤ect hiring in the present. I suggest a third mechanism that uses the
wage setting in performance pay markets. In those markets there is private infor-
mation in terms of the e¤ect of worker e¤ort on productivity. I model a second
moment shock as time varying variance in the private information process. When
60
futute pro…ts are expected to be higher due to relaxing the private information
problem (lower variance of the private information process), more vacancies are
posted. The private information determines e¤ort, which enters the production
function. Hence, changes in the private information process work indirectly as
changes in the total factor productivity including e¤ort as an imput. There is not
direct evidence of uncertainty in information. Nevertheless, measures of volatility
in variance of stock options and in standard deviation of GDP forecasts from the
Philadelphia Federal Reserve Bank’s biannual Livingstone survey are both counter-
cyclical. On the household side, variance of income and measures of cross-section
earnings instability covarie positively with unemployment.
I advance a theory of recessions that does not rely on the assumption of time
varying variance of productivity. I use in the model a di¤erent level of uncertainty
that relies on time varying quality of information in employment contracts. More
speci…cally, I model a type of incentive that has increased in relevance in the US
economy: performance pay contracts. Figure 2 has the fraction of jobs in the PSID
among male heads of the household that receive some form of incentive pay. The
proportional of jobs that receive bonus, commission or piece-rate has increased
steadily since the late 70’. The bene…ts of using performance pay contracts are
twofold. First, I reproduce in the model simulation moments of the data that can
discipline calibration by using the evidence on bonus pay and cyclicality in the
61
PSID as a benchmark. Second, the contract produces a direct link between uncer-
tainty in information in employment relationships and turnover. This relationship
allows for evaluating the e¤ect of uncertainty on business cycles.
The way the model works is as follows. There are search frictions in the econ-
omy. The representative …rm decides on which employment matches to retain
looking at aggregate shocks and the distribution of uncertainty shocks. The wage
rate in job matches is de…ned by a contract that establishes a base pay and a bonus
paid in case positive performance is observed. The worker has private knowledge
on how she can a¤ect both output and measured performance through e¤ort choice.
The …rm does not observe e¤ort and cannot contract on output. Hence the need
of a performance pay contract to give incentives for the worker to exert more e¤ort
in high states of the world.
The source of uncertainty is the process that gives the private information
held by the workers. I assume that the process that gives the private informa-
tion has time varying variance. Recessions are periods when the variance of the
private information process is high. Hence economic downturns are characterized
by higher di¢culty in assessing the value of employment relationships. The un-
certainty in information can function as a propagation mechanism in the model
by exacerbating the standard e¤ect of the decline in productive during recessions.
Since higher variance in private information decreases the value of employment
62
contracts, the …rm decreases hiring and we have unemployment commoving with
variance in information. In the limit, if there is no variance in the distribution of
the private information, the model reduces to a standard labor search framework
with performance pay contracts. The question then is whether the model is con-
sistent with both improvement in information technology and ampli…cation of the
business cycle through uncertainty.
3.1. Model
The model structure is based on a standard DSGE framework with labor search
frictions (see Lubik and Krause, 2003). I build on it wage contracts as in Baker,
Gibbons and Murphy (2004).
The household problem is given by:
(3.1) max
ct,occctt
,
t
[n(c
t
) ÷:
t
,(c
t
)]
st.
(3.2) c
t
+ c::ct
t
= :
t
n
t
+ (1 ÷:
t
)/ + 1
t
c::ct
t+1
63
where c is consumption, n is the wage rate, / is the unemployment bene…t, :
is the fraction of the labor force working in a given period, and 1 is the return
on assets. The labor force is normalized to one. Hence unemployment is given by
n = 1 ÷:.
First order conditions yield the discount factor :
(3.3)
1
1
t
= 1
t
_
,
n
0
(c
t+1
)
n
0
(c
t
)
_
=
The …rm problem is given by:
(3.4) max
·t,at
1(1
t
÷
t
:
t
÷··
t
)
st.
(3.5) :
t
= 1
j
(1 ÷j
t
)
t1
+ ·
t1
¡(o
t1
))
where 1 is output, is the wage bill, · is the cost of vacancy posting, and
· are vacancies. Labor market tightness is o =
·
&
. and the …ll rate for vacancies
64
¡(o
t
) comes from the matching process, taken as given by …rms and workers. At
each period a fraction j
t
of jobs is destroyed. The creation and destruction of jobs
enter the law of motion for employment. Output is subject to both aggregate .
t
,
and idiosyncratic shock . The aggregate shock follows an AR(1) process, and the
idiosyncratic shock is drawn every period from a distribution ,() with support
[0. 1].The …rm chooses at each period a fraction of jobs below the threshold ,
which are destroyed. The remaining jobs have average productivity H() that
comes from the truncated distribution H() =
_
1
.
)(.)
11(.)
d. Given the fraction of
jobs destroyed, and the exogenous separation rate j
a
, total job destruction in the
economy is equivalent to j
a
+ (1 ÷j
a
)1(). Total output for the e¤ort level equal
to zero is given by .
t
H():
t
.
First order conditions yield the job creation equation:
(3.6)
·
¡(o
t
)
= 1[1
j
(1 ÷j
t
)(
_
1 + .c
t+1
_
.
t+1
H() ÷
t+1
+
·
¡(o
t+1
)
)]
where ¸ =
_
1 + .c
t+1
_
.
t+1
H(). c
t
is optimal e¤ort by the worker, and the
parameter . gives the productivity of performance pay arrangements. Note that
the output depends on both e¤ort and ., which governs the productivity of the
performance pay contract. I assume that the marginal contribution : of worker
65
e¤ort to …rm output is given by .c
t+1
.
t+1
t+1
. Wage contracts between …rms and
workers cannot be written on the marginal contribution, since it is too complex
to be objectively assessed. However, there is a veri…able performance measure, 1,
which is an imperfect measure of :. In order to simplify notation, assume that :
can only take values of .c
t+1
.
t+1
t+1
or 0, and 1 can take values of .c
t+1
.
t+1
t+1
or 0. The …rm observes 1 and :, but only 1 is contractible.
At each period, the worker can choose an action that stochastically determines
both output and performance. The relationship between worker e¤ort, c, and the
…rm’s outcome is such that Pr o/ = .c
t+1
.
t+1
t+1
[ c) = c, where c is between
0 and 1. The probability of observing a positive performance measure is given
by Pr o/(1 = .q
c
[ c) = jc, where j is a random variable with mean 1(j). and
variance ·c: (j), bounded above so that Pr o/(1 = .c
t+1
.
t+1
t+1
[ c) _ 1. We
can think of j as the di¤erence between the e¤ect of e¤ort on performance and
output. There are states of world when j is large and high e¤ort contributes
more to performance measures than to the value of the …rm. When j is small,
we have the opposite case, and high e¤ort would likely generate large value for
the …rm, but would not increase performance measures. I assume that …rms do
not know j, while workers observe j after deciding whether to stay on the island,
but prior to choosing e¤ort. From the viewpoint of the …rm and the worker, e¤ort
and bonus are stochastic prior to the realization of j. The problem of the …rm is
66
to o¤er a compensation package prior to the realization of j that aligns e¤ort to
productivity, and the problem of the worker is to choose the optimal level of e¤ort
once j is realized. The sequence of events is such that …rms and workers start the
period knowing the state of the economy and the process for j.
The wage determination uses the ‡ow equations for the value of a job match for
the …rm J, and the value of employment \ and unemployment l for the worker.
The worker chooses the level of e¤ort according to:
(3.7) \
t
= 1
j
(max
ot
n
t
+ j
t
1
t
c
t
÷¸c
2
t
+ 1((1 ÷j
t
)\
t+1
+ j
t
l
t+1
))
First order conditions yield:
(3.8) c
t
=
j
t
1
t
2¸
where 1 is the bonus paid in case positive performance is observed and 1
j
(j
t
1
t
c
t
)
is the expected value of bonus pay.
The …rm determines bonus 1 and base pay n according to:
67
(3.9) max
1t,&t
J
t
= 1
j
(.
t
t
(1 + .c
t
) ÷n
t
÷j
t
1
t
c
t
+ 1(1 ÷j
t+1
)J
t+1
)
st.
1
j
(n
t
+ j
t
1
t
c
t
÷¸c
2
t
+ 1((1 ÷j
t
)\
t+1
+ j
t
l
t+1
)) _
/ + 1(,(o
t+1
)(1 ÷j
t+1
)\
t+1
+ (1 ÷,(o
t+1
)(1 ÷j
t+1
)l
t+1
)
c
t
=
j
t
1
t
2¸
Using the fact that the participation constraint binds and l = \, …rst order
conditions yield:
(3.10) 1
t
=
.
t
t
.1j
t
1j
2
t
(3.11) n
t
= / ÷1
j
(j
t
1
t
c
t
÷¸c
2
t
)
68
The value of a job is given by:
(3.12) J
t
= 1
j
(.
t
t
(1 + .c
t
) ÷/ + j
t
1
t
c
t
÷¸c
2
t
÷j
t
1
t
c
t
+ 1(1 ÷j
t+1
)J
t+1
)
The job destruction threshold depends on the condition that the value of the
marginal job at is zero:
.
t
(1 + .c
t
) ÷/ ÷¸c
2
t
= 0
The aggregate resource constraint is:
(3.13) 1
j
(c
t
+ ··
t
) = 1
j
(.
t
(1 + .c
t
):
t
H() + n
t
/)
The competitive equilibriumis a set of prices and numbers ¦c
t
. :
t
. ·
t
. n
t
. 1
t
. c
t
. n
t
. 1
t
.
t
. j
t
¦.
and stochastic processes for ., , and j that satisfy the equations below.
I assume that . follows an ¹1(1) process ln .
t+1
= j
:
ln .
t
+
:
t+1
, j follows
an ¹1(1) process ln j
t+1
= j
j
ln j
t
+
j
t+1
, the private information is drawn from
a symmetric 1ctc(j. j) distribution, and
t
follows an uniform distribution with
support [0. 1].
69
c
t
=
j
t
1
t
2¸
(3.14) 1
t
=
.
t
t
.1j
t
1j
2
t
(3.15) n
t
= / ÷1
j
(j
t
1
t
c
t
÷¸c
2
t
)
.
t
(1 + .c
t
) ÷/ ÷¸c
2
t
= 0
(3.16) 1
j
(c
t
+ ··
t
) = 1
j
(.
t
(1 + .c
t
):
t
H() + n
t
/)
(3.17)
1
1
t
= 1
t
_
,
n
0
(c
t+1
)
n
0
(c
t
)
_
=
70
(3.18) :
t
= 1
j
(1 ÷j
t
)
t1
+ ·
t1
¡(o
t1
))
(3.19)
·
¡(o
t
)
= 1[1
j
(1 ÷j
t
)(
_
1 + .c
t+1
_
.
t+1
H() ÷
t+1
+
·
¡(o
t+1
)
)]
(3.20) n
t
= 1 ÷·
t
(3.21) j
t
= j
a
+ (1 ÷j
a
)1().
I assume that . follows an ¹1(1) process ln .
t+1
= j
:
ln .
t
+
:
t+1
. The private
information is drawn from a symmetric 1ctc(j. j) distribution. The variance of
the private information changes over time. I assume accordingly that j follows an
¹1(1) process ln j
t+1
= j
j
ln j
t
+
j
t+1
. In periods when j is low the variance of
1ctc is high and that decreases the bonus and e¤ort. The information structure is
71
such that agents know j or the distribution of the private information when agree-
ing on the contract, but do not know the realization of j. I further assume that
draws of j are iid over time, and agents use the process of j to predict only the
variance of the private information distribution. Due to the assumption of symmet-
ric process for j, its mean is 0.5. Given the independence of j and , the average
e¤ort in the economy depends on the shocks processes given by .H()j. Note that
there is still heterogeneity in terms of e¤ort and productivity, but I assume that
it aggregates such that we can think of the economy as governed by the values
of .H()j. There are several assumptions used to obtain the simpli…cation in the
aggregation. The …rst is that all shocks are independent, j is iid and the same
for all jobs. The production function is given by (1 + .c
) .H():. Second, the
individual worker in a job does not internalize his e¤ect on total output. We can de-
compose output in two independent terms: .
t+1
H():
t
which aggregates trivially,
and
_
1 + .c
t+1
_
. E¤ort is given by c
t
=
j
t
2¸
:t.t¸1j
t
1j
2
t
. Given the assumptions on the
shock processes, we can consider
j
t
2¸
:tt¸1j
t
1j
2
t
as an aggregate term, and for all jobs
is given by
_
1
.
.)(.)
11(.)
d =
_
1
.
.
1.
d. Hence 1 =
_
1 + .
j
t
2¸
:tt¸1j
t
1j
2
t
_
1
.
.
1.
d
_
.H():.
Using the expressions for the bonus and e¤ort we have that higher variance of
the private information decreases bonus and e¤ort: 1
t
=
.t:t¸1j
t
1j
2
t
=
.t:t¸1j
t
(1+·ov(j))
, c
t
=
j
t
1t
2¸
=
j
t
2¸
.t:t¸1j
t
(1+·ov(j))
. Total compensation n
tcto|
is procyclical and given by n
tcto|
=
n + j1c = / + ¸c
2
. The net e¤ect of higher variance of the private information
72
on the value of the job is given by
0Jt
0·ov(j)
=
01(.t:t(1+¸o
t
)b¸o
2
t
+1(1j
t+1
)J
t+1
)
0·ov(j)
.
Note that the e¤ect on the current return of the job depends on the productivity
of the performance pay contract, .:
t
.
t
.
0o
t
0·ov(j)
÷¸2c
0o
t
0·ov(j)
. Hence, improvement
in monitoring represented by lower ·cj) or higher . technology increases the link
between the variance of j and job creation.
3.2. Calibration and Simulation
Since the main interest is in business-cycle dynamics - the interactions between
market structure and aggregate ‡uctuations in labor demand - I rely on local ap-
proximation as a solution method. For business cycle purposes, …rst and second-
order approximations often yield a good picture of model dynamics (Schmitt-Grohe
and Uribe, 2004, henceforth SGU). This is of course a simpli…cation of the het-
erogeneity in employment relationships. Yet, the model produces the elements
necessary to evaluate the e¤ect of uncertainty on business cycle: time varying
uncertainty, unemployment, and turnover.
Tables 10 and 11 presents the model parameters that have to be calibrated. I
take a two step approach to the calibration and simulation. First, I use standard
parameters in the labor search literature to pin down the …rst approximation of
all values in Table 1. Second, I minimize a loss function to obtain estimates of
73
the free parameters of the model. The moments used in the second stage come
directly from the PSID data for performance pay jobs.
3
There are two reasons for
choosing moments of performance pay compensation schemes in order to calibrate
the model. First, to the best of my knowledge, the PSID moments use all aggregate
data available on wage setting in contracts, helping to pin down parameters that
have no counterpart in the literature. Second, I do not assume wage rigidity,
which is usually necessary to generate empirically reasonable aggregate properties
in standard DSGE labor search models. To the extent that performance pay
schemes became pervasive in the US labor market, I use in the model a wage
setting that is both ‡exible and empirically founded.
I use as in the literature a log utility function. The model is quarterly, and
the discount rate is set at .99. The steady state vacancy, labor market tightness,
the elasticity and constant of the matching function ` = ¬n
c
·
1c
are obtained
using data estimates of average unemployment rate (6%) in the economy, the
normalization of the labor force to one, and the …ll (.7) and …nding rate (.6) of
jobs. The exogenous separation probability is .08 and total job destruction is 0.10.
In the …rst stage, I guess the remaining parameters.
3
See chapter 1 for de…nitions of PSID variables, and the appendix for a discussion of the data.
74
I calibrate the productivity and cost of performance pay, the unemployment
bene…t, the ‡ow cost of vacancy posting, and the variance to the innovation of
the uncertainty shock in order to match moments in the PSID such as the size
4
and incidence of the bonus, and the correlation of total bonus and bonus size with
unemployment at business cycle frequency, the correlation of incidence with unem-
ployment and bonus size, and the standard deviation of bonus size and incidence.
I do not target the volatility of labor market variables such as unemployment, va-
cancies, and labor market tightness. The mean of ·cj) comes from the choice of
a symmetric Beta process, with average j normalized to one.
The correlations and standard deviations are analogous to the standard busi-
ness cycle statistics but make use of the information in the PSID about compen-
sation schemes. I take the linearly detrended series of bonus, bonus size, bonus
incidence, and unemployment rate in order to calculate moments. The model
mechanism is to change future pro…ts and vacancy posting using the changes in
the incentive for e¤ort variation given by bonus. Hence, I use direct evidence on
the cyclicality of bonus pay in the data. The goal of the model is to generate labor
market volatility through uncertainty. I use the standard deviations as moments
of the compensation scheme to discipline the model since introducing excessive
4
See previous de…nitions of PSID moments in Chapter 1.
75
volatility in e¤ort and bonus could generate high levels of variance in labor market
aggregates. I also use correlations of incentive pay with unemployment since the
model implies as in the data that bonus size and its probability of positive incentive
pay in a given period depend on productivity and should decrease in recessions.
The criteria function used to decide on the calibration is given by min 1(.. /. ¸. ·) =
r
2
, where r is the di¤erence between model simulation and data moments. I
evaluate 1 over part of the parameter space around the initial guess.
5
At this stage
I weight all moments equally in the loss function. In principle one should focus on
the more reliable moments of the data, and the ones that also better describe the
model mechanisms. The solution is supposed to emulate the simulated method
of moments. Since relevant parameters of the data such as the shock process for
uncertainty and the productivity of contracts cannot be directly calculated from
the data, one has to use indirect inference with data moments in order to estimate
free parameters.
The idiosyncratic process is assumed uniform with support [0. 1]. The values
discussed so far cover all parameters in Table 10 and Table 11 except for the
aggregate productivity shock. I normalize the mean of the aggregate shock to one.
5
I also use diferent initial points in order to check for the problem of local minima in the criteria
function. This procedure is restricted by the convergence on internal loops of the simulation. All
values of the parameter space evaluated have to lead to convergence of the steady state of the
model and approximation functions.
76
The AR(1) process for . corresponds approximately to TFP in the model. I choose
the process for z such that the model without uncertainty shocks reproduces the
standard deviation output in the US economy, which is approximately 1,7%. The
model is not sensitive to the choice of autocorrelation in the shock process, so I
follow the literature and set it to .95.
As in most business cycle models, the variance of innovation to shocks governs
the bulk of the volatility of aggregate variables. In principle, any variance of
vacancy and unemployment can be obtained with the appropriate choice of shock
volatility. I discipline the calibration of the variance in the uncertainty process
by using the moments of the bonus pay in the PSID, including the variance and
ciclicality of aggregate bonus. I also conduct a sensitivity analysis of the parameters
of the shock process by looking at the moments of the bonus as I increase the
variance of j.
Table 12 presents results of the baseline model and the data moments. For a
reasonable size and cyclicality of bonus pay, the model explains more than twice the
volatility of unemployment and more than one half of the volatility of vacancies and
labor market tightness Though the model overshoots the correlation of bonus size
and incidence and the standard deviation of incidence, all remaining simulated
moments have the right sign and order of magnitude. Unlike in the standard
77
DSGE labor search model, results do not depend on a large value of the variance
of labor productivity shocks or the assumption of wage rigidity. Note that the
model is driven by two uncorrelated shocks. As we discuss below, the introduction
of uncertainty shocks is key for reproducing the ciclicality of compensation scheme
variables, since the model driven by only TFP shocks performs poorly in several
dimensions.The uncertainty shocks work indirectly as a productivity shock, since
they lead to more e¤ort variation, which enters the production function and …rm’s
expectation of future pro…ts. Below I discussion the impulse response functions
and counterfactual exercises of shutting down the e¤ort mechanism.
The Beveridge curve is not reproduced. In DSGE models with endogenous job
destruction the response of destruction to shocks is faster than creation, and the
two rates end up with a positive correlation at business cycle frequency. One can
get the right Beveridge curve with the model at the cost of assuming a constant
destruction rate. This is not a moment target by the model, hence I choose to keep
job destruction as a margin of adjustment, since empirically it seems to increase
in recessions. As discussed in the literature, the shape of the Beveridge curve is
not a priori clear. On the one hand, a shock to productivity increases pro…ts and
vacancy creation, reducing unemployment. On the other hand, higher productivity
reduces the threshold for destruction and unemployment, increasing labor market
78
tightness. Higher vacancy to unemployment ratio reduces incentives for vacancy
posting. If we shut down the endogenous job destruction margin, only the …rst
e¤ect is at work.
The ultimate test of the model is generating a propagation mechanism for
recessions that increases turnover by introducing uncertainty. Since I represent
uncertainty as time varying information process in performance pay contracts, the
metric for evaluating the model comes from the sensitivity analysis of the two main
parameters of the performance pay technology - the productivity of the contract,
., and the standard deviation of the innovation to the uncertainty shock - and its
propagation mechanism - e¤ort variation.
I conduct the following analysis. Both the incidence and size of the bonus
present a trend increase in the PSID.
6
This trend suggests that the technology of
performance pay has improved over time. Table 13 displays simulation results for
di¤erent values of free parameters. Columns 1 displays simulation results for a
low value of the variance of the innovation to j. From column 1 we can infer that
the model driven by TFP shocks performs poorly both at replicating moments
of compensation schemes and generating volatility in aggregate variables. When
we compare column 1 to column 4, it is clear that uncertainty shocks drive most
6
See Figure 8 for bonus incidence and Figure 10 for bonus size.
79
of the cycle. As we move towards column 4, the model …t improves. A model
that is driven mostly by TFP shocks (column 1) produces countercyclical bonus,
unlike in the data. The introduction of uncertainty shocks ‡ips the sign of the
correlation between bonus and unemployment. It also raises the variance of bonus
pay. As a by-product, the uncertainty shocks improve the …t of the model in terms
of replicating the volatility of aggregate and labor market variables (columns 3 and
4).
Column 3 displays results with the baseline calibration except for the higher
value of productivity in performance pay contracts. An increase in the productivity
of the contract is in line with the PSID evidence that there is a trend increase in the
size and incidence of the bonus. Results in column 3 indicate that improvement in
technology is consistent with more aggregate volatility.
7
Note that the productivity
of performance pay is relevant for model …tness. A one percent increase in ., all else
equal, helps the model explain two percent more of unemployment when compared
to the baseline calibration, without raising the volatility of the PSID moments of
compensation. This results suggest that the productivity of the contract is relevant
for model dynamics, since it a¤ects the volatility of vacancies and unemployment
outcomes.
7
Though column 3 has a lower value for the loss function criteria, it violates the assumption that
under the baseline calibration TFP shocks alone reproduce the empirical value of the output
standard deviation.
80
The last experiment concerns the model mechanims - e¤ort variation. I take
the simulated data and perform the following counterfactual. I keep c
at its mean
value and calculate the business cycle moments of the compensation scheme. I also
change the job creation equation such that e¤ort is constant in the expectation of
future pro…ts. Column 2 presents results for the model without e¤ort variation.
It is clear that if e¤ort is kept at an ordinary constant level, the model cannot
reproduce moments of the compensation scheme. The reason for that failure is
that in the counterfactual exercise we sever the link between the current state of
the economy and the probability of the two main events in the model: positive
incentive pay, and higher productivity through e¤ort variation. Moreover, with
e¤ort constant in the job creation equation, there are no incentives to post more
vacancies when the variance of the private information process is low. The results
of this counterfactual indicate that e¤ort variation induces variability in labor
market aggregates in the model. Note that e¤ort is given by c
t
=
j
t
2¸
:t.t¸1j
t
1j
2
t
. We
can see that the shock in ln j
t
changes the variability of e¤ort, or the variance of
the private information in denominator of c
. This e¤ect is the response of the
contract to the second moment shock in the private information process.
A model without uncertainty changes the moments of the bonus, bringing the
standard deviation of all variables down and increasing the distance between data
81
and simulated model correlations (see Table , column 1). Interestingly, the mechan-
ims that a¤ects the bonus moments is the e¤ort variation. If we perform the ex-
periment of shutting down e¤ort by keeping it at its mean value, we also increase
the distance between data and model moments (see Table, column 3).
Figures 11 and 12 show the impulse response function of model variables to a
positive innovation in aggregate productivity. Figure 11 displays the response of
labor market variables and performance pay outcomes to a 1 std innovation to the
uncertainty shock. Figure 12 shows the same variables’ reponse to the aggregate
shock. It is interesting to note the similarity between Panel A in Figures 11 and
12. A positive shock to j decreases the variance of j and works as a productivity
shock. Panel B in both …gures are also similar, but the response of bonus and
e¤ort is higher for the uncertainty shock
There are some caveats to the analysis above. First, the model is not rich
enough to reproduce closely all moments of the data. Second, though the data
is measured consistently with model de…nitions and the literature on performance
pay, the time range is short for assessment of time series moments (see the appendix
for a discussion of the PSID data).
82
3.3. Last Remarks
In this Chapter I study the interaction between uncertainty in employment re-
lationships and the business cycle. The current papers on this topic focus on two
types of e¤ects: 1) change in the real option value of investment and hiring (Bloom,
2009); and, 2) uncertainty as bad news predicting low productivity in the future
(Bachmann and Bayer, 2009). I suggest a third mechanism in which uncertainty
a¤ects the value of employment by changing incentives and e¤ort in contracts.
I extend a standard search model in order to include performance pay contracts
and uncertainty shocks, represented by time varying variance in the process of
private information held by workers. I calibrate and simulate the model in order
to replicate moments of performance related payment in the US data. Results
suggest that uncertainty shocks and improvement in performance pay technology
are capable of generating ampli…cation of high frequency variation in labor market
outcomes. Overall, as postulated in the motivation, if the technology has improved
and the shock size is larger, uncertainty becomes an important channel in reces-
sions, amplifying the high frequency variation in unemployment and vacancies.
The simulation results answer positively our initial question of whether business
cycles can be driven by uncertainty in employment relationships.
8
8
The mechanims in the model is suitable for explaining the Great Moderation. If we assume
that the variance of the innovation to the private information process is decreasing over time, we
83
1. Figures and Tables
5
5
6
0
6
5
7
0
S
t
d
o
f
c
h
a
n
g
e
in
e
m
p
lo
y
m
e
n
t
1970 1980 1990 2000 2010
Year
Dispersion in employment change Hp_trend
Figure 1 - Decli ne in Fi rm Instabi li ty
have that aggregate labor market variability decreases. There is one shortcoming to this story.
The decline in the variance of information is probably related to a secular change in technology
(e.g. the use of computers to monitor workers). Since the adoption of the new technology is
not likely to revert in recessions, the mechanims in the model cannot explain simultaneously the
Great Moderation and the Great Recession.
84
1
2
1
4
1
6
1
8
2
0
2
2
J
o
b
c
r
e
a
t
io
n
a
n
d
d
e
s
t
r
u
c
t
io
n
r
a
t
e
s
1970 1980 1990 2000 2010
Year
Job Destruction - HP trend Job Creation
Job Destruction Job Creation - HP t rend
Figure 2 - Decli ne in j ob fl ows
85
.
1
3
.
1
4
.
1
5
.
1
6
.
1
7
E
x
c
e
s
s
J
o
b
R
e
a
l
l
o
c
a
t
i
o
n
1990 1995 2000 2005
Year
Figure 3 - Decli ne in Job Reallocati on
86
2
2
.
5
3
3
.
5
4
P
e
r
c
e
n
t
o
f
e
m
p
l
o
y
m
e
n
t
1970 1980 1990 2000 2010
Year
Unemployment I nflows Unemployment Outflows
Figure 4 - Decli ne in Worker Flows: CPS 1976-2008
87
.
1
6
.
1
8
.
2
.
2
2
.
2
4
.
2
6
M
e
a
n
a
b
s
o
l
u
t
e
d
e
v
i
a
t
i
o
n
1980 1990 2000 2010
Year
Hourly earnings Hours
(CPS 1980-2008, private non-farm)
Figure 5 - Increase in Wage instability
88
0
.
0
5
.
1
.
1
5
.
2
.
2
5
.
3
.
3
5
.
4
.
4
5
.
5
.
5
5
.
6
M
e
a
n
a
b
s
o
l
u
t
e
d
e
v
i
a
t
i
o
n
1980 1990 2000 2010
Year
Hourly earnings _ Stayers Total earnings _ St ayers
(CPS 1980-2007 -Job Stayers )
Fi gure 6 - Increase i n total earni ngs i nstabi l i ty
89
0
.
0
5
.
1
.
1
5
.
2
.
2
5
.
3
.
3
5
.
4
.
4
5
.
5
.
5
5
.
6
M
e
a
n
a
b
s
o
l
u
t
e
d
e
v
i
a
t
i
o
n
1980 1990 2000 2010
Year
Total earnings_ Movers Hourly earnings _ Movers
(CPS 1980-2007 - Job Movers/Losers)
Fi gure 7 - Increase i n Wage i nstabi l i ty for Movers/Losers
90
.
1
.
2
.
3
.
4
.
5
F
r
a
c
t
i
o
n
o
f
S
a
m
p
l
e
76 78 80 82 84 86 88 90 92 94 96 98
Year
Performance Pay Received in Current Year Performance Pay Job
Covered by Collective Bargaining Agreement
(Source: Lemieux,MacLeod and Parent, 2009)
Figure 8 - Performance Pay Incidence - Job stayers
91
1
0
2
0
3
0
4
0
5
0
A
n
n
u
a
l
i
z
e
d
S
T
D
(
%
)
1960 1970 1980 1990 2000 2010
Year
Figure 9 - Monthly U.S. stock market volatility from CBOE
92
0
.
0
1
.
0
2
.
0
3
.
0
4
.
0
5
.
0
6
B
o
n
u
s
S
i
z
e
(
F
r
a
c
t
i
o
n
o
f
w
a
g
e
)
75 80 85 90 95 100
Year
(PSID-PP jobs)
Figure 10 - Increase in bonus size
93
Figure 11 -Impulse Response Function to 1 std shock to z
Panel A
Panel B
0 50 100
1.8
1.82
1.84
1.86
1.88
1.9
1.92
1.94
1.96
1.98
vacancy
0 50 100
1.8
1.9
2
2.1
2.2
2.3
2.4
2.5
unemployment
0 50 100
9
9.2
9.4
9.6
9.8
10
10.2
x 10
-3
bonus
0 50 100
-0.5
0
0.5
1
1.5
2
2.5
3
3.5
x 10
-3
effort
94
Figure 12 -Impulse Response Function to 1 std shock to p
Panel A
Panel B
0 50 100
1.8
1.82
1.84
1.86
1.88
1.9
1.92
1.94
1.96
1.98
vacancy
0 50 100
1.8
1.9
2
2.1
2.2
2.3
2.4
2.5
unemployment
0 50 100
0.0145
0.015
0.0155
0.016
0.0165
0.017
0.0175
bonus
0 50 100
-1
0
1
2
3
4
5
x 10
-3
effort
95
Table 1- Trend I ncrease in Earnings instability in the March CPS, 1979- 2007
Full sample - private non-farm
Dependent
variable
(instability
measure)
Constant Regression
coefficient
for time
trend
Cumulative
change
Mean of
dependent
variable
Total earnings 0.24726 *** 0.00107 *** 0.030 0.271
(0.00193) (0.00019)
Hourly
earnings 0.21111
***
0.00180 *** 0.050 0.249
(0.00150) (0.00016)
0.211
Total hours 0.18152 *** -0.00019 -0.005 0.175
(0.00176) (0.00016)
Job stayers
Dependent
variable
(instability
measure)
Constant Regression
coefficient
for time
trend
Cumulative
change
Mean of
dependent
variable
Total earnings 0.12874 *** 0.00240 *** 0.067 0.172
(0.00130) (0.00015)
Hourly
earnings 0.14554
***
0.00233 *** 0.065 0.188
(0.00134) (0.00015)
Total hours 0.05376 *** 0.00026 0.007 0.065
(0.00067) (0.00007)
Job movers/losers
Dependent
variable
(instability
measure)
Constant Regression
coefficient
for time
trend
Cumulative
change
Mean of
dependent
variable
Total earnings 0.46941 *** -0.00078 * -0.022 0.444
(0.00495) (0.00046)
Hourly
earnings 0.33114
***
0.00133 *** 0.037 0.356
(0.00372) (0.00036)
Total hours 0.39922 *** -0.00089 ** -0.025 0.349
(0.00466) (0.00042)
* 10% significance ** 5% significance *** 1 % significance
Sample Size: Full sample, 176728. Job stayers, 111641. Break in survey methodology in 1988.
Standard errors in parenthesis. See appendix for matching and sample selection.
96
Table 2- Trend I ncrease in Earnings I nstability for Different Demographic
Groups: J ob Stayers in the March CPS from 1979 to 2007
Job stayers less than 45 yrs old
Dependent
variable
(instability
measure)
Constant Regression
coefficient
for time
trend
Cumulative
change
Mean of
dependent
variable
Total
earnings 0.12791 *** 0.00308 *** 0.086 0.174
(0.00166) (0.00019)
Hourly
earnings 0.14518 *** 0.00290 *** 0.081 0.189
(0.00170) (0.00019)
Total hours 0.05614 *** 0.00023 ** 0.006 0.067
(0.00086) (0.00009)
Job stayers with high school or less
Dependent
variable
(instability
measure)
Constant Regression
coefficient
for time
trend
Cumulative
change
Mean of
dependent
variable
Total
earnings 0.13248 *** 0.00294 *** 0.082 0.181
(0.00181) (0 .00023)
Hourly
earnings 0.14636 *** 0.00279 *** 0.078 0.193
(0.00184) (0.00023)
Total hours 0.04932 *** 0.00019 * 0.005 0.059
(0.00010) (0.00088)
Sample Size: with high school or less, 68755. Less than 45yrs. old, 54561. Break in
methodology in 1988. See appendix for matching and sample selection.
* 10% significance ** 5% significance *** 1 % significance
Standard errors in parenthesis.
97
Table 3- Wage instability in different pay schemes in the PSI D: 1976 to 1996
Compensation scheme group Mean dispersion in hourly wages growth
Not Performance pay and not in Union 0.166
Performance pay and not in Union 0.173
Union and Not Performance pay 0.155
Union and Performance pay 0.162
Compensation scheme group
Fraction of group in
1976
Fraction of
group in 1995
Not Performance pay and not in Union 0.423 0.421
Performance pay and not in Union 0.275 0.390
Union and Not Performance pay 0.245 0.141
Union and Performance pay 0.058 0.049
Compensation scheme groups
compared
t test for differences in mean wage
volatility in different pay schemes
Performance pay and not in Union X Not
Performance pay and not in Union
0.593
Union and not in Performance pay X Not
Performance pay and not in Union
-2.596***
Performance pay and not in Union X
Union and Not Performance pay
3.055***
Notes: Sample size, 14267. Male heads of the household.
98
Table 4- Regression coefficients in the PSI Dfrom
1976 to 1996: effect of performance pay on wage
instability
Worker group Job stayers Job stayers
Constant 0.10548***
(0.01532)
0.13290
(0.15554)
Performance
pay dummy
0.00489
(0.00557)
0.02266**
(0.01107)
Union
Dummy
-.01133 **
(0.00557)
-0.00591
(-0.0097)
Tenure -0.00223**
(0. 00108)
Tenure
2
0.00108**
(0.00003)
Education -0.00256
(0.00789)
Married 0.00560
(0.00865)
Potential
experience
0.00534
(0.00575)
Experience
2
-0.00026
(0.00014)
Experience
3
0.00004**
(0.00002)
R-squared .02 0.3
Controls for
worker fixed
effects and
characteristics
no yes
Notes: Sample size, 14267, PSID, male heads of household. Standard
errors in parenthesis, clustered at the job match level.
***1% significance **5% significance
99
Table 5- Calibration of model parameters
Parameters of the idiosyncratic process and production technology
Log mean of idiosyncratic shock -0.05
Persistence of idiosyncratic shock 0.947
Std of the innovation of idiosyncratic shock 0.20
Discount rate 0.99
Labor share in the production function 0.64
Moments used to calibrate the idiosyncratic shock process
Excess job reallocation 0.14
Unemployment rate 0.055
Parameters of the performance pay technology
Marginal value of effort [.05 0.25]
Marginal cost of effort 0.5
Private information process Beta (p,p)
Moments used to calibrate the performance pay technology
Std bonus 0.13
Bonus size 0.037
Bonus Incidence 0.141
Moments used to calibrate the unionized model
Union wage premium 0.17
Note: Calculations for the bonus use performance pay jobs in the PSID from 1993-1998.
The bonus corresponds to the part of compensation in the PSID reported in the form of bonus,
commission or piece-rate. Bonus size is the ratio of bonus to total compensation, and bonus
incidence is the fraction of performance pay jobs that received incentive pay in a given yea.
Unemployment is calculated from the rate reported by the BLS in the 2000s.
Labor share in the production function comes from NIPA.
Excess job reallocation uses the quarterly BED data.
100
Table 6- Simulation results and moments to match
Moments to match Data moments Model moments
Excess job reallocation 0.14 0.18
Unemployment rate 0.055 0.07
Std bonus 0.13 0.057
Bonus size in 1998 0.057 0.058
Bonus Incidence in 1998 0.17 0.15
Union wage premium 0.17 0.25
Note: Calculations for the bonus use the PSID from 1993-1998. The bonus corresponds to the
part of compensation in the PSID reported in the form of bonus, commission or piece-rate. Bonus
size is the ratio of bonus to total compensation, and bonus incidence is the fraction of
performance pay jobs that received incentive pay in a given year.
Unemployment is calculated from the rate reported by the BLS in the 2000s.
Excess job reallocation uses the quarterly BED data.
Union wage premium comes fromNewmark and Kawaguchi (2001).
The model is simulated quarterly and model moments are aggregated annually for comparison
with the PSID data.
Table7- Moments toexplain
Change in the mean absolute
deviation of hourly wage growth
rate 0.065
Change in standard deviation of
employment growth rate
-0.042
Note: Calculations use the March CPS and LBD . The
change for hourly earnings instability uses the cumulative
increase estimated with the time trend for job stayers in
Table 1. The change in employment instability uses the
difference between the 2005 and the 1976 value of the
std of cross section employment growth rate in the LBD.
101
Table 8- Simulated moments with different pay schemes
Statistics Baseline Union
Performance
Pay
Beta (6, 6)
= .25
Mean |%change wage|
0.1513 0.1552 0.1743
Mean |%change
employment| 0.1933 0.2033 0.1833
Std (%change wage)
0.2021 0.2009 0.2285
Std (%change employment)
0.5588 0.6174 0.5765
Average wage
1.53 1.99 1.59
Unemployment
6.8 7.87 7.05
Value of search
152 156 162
102
Table 9- Simulated moments from performance pay model
Statistics
Parameters of Performance Pay Technology
Beta ( 1,1 )
=.05
Beta ( 4,4 )
=.1
Beta ( 6, 6 )
=.2
Beta ( 6, 6 )
=.25
Mean |%change wage|
0.1511 0.1537 0.1652 0.1743
Mean |%change employment|
0.1762 0.1762 0.1774 0.1833
Std (%change wage)
0.2021 0.2050 0.2189 0.2285
Std (%change employment)
0.5619 0.5618 0.5618 0.5765
Size of the bonus
0.0018 0.0081 0.0318 0.0579
Std of the bonus
0.0047 0.0159 0.0429 0.0575
Bonus Incidence
0.0300 0.0590 0.1197 0.1585
Average wage
1.54 1.56 1.62 1.59
Unemployment
6.85 6.86 6.95 7.05
Value of search
153 154 158 162
103
Table 10 - Calibration of Parameters
Elasticity of the Matching Function -0.40
Constant in the Matching Function 0.80
Utility function u(.) log
Discount Rate 0.99
Exogenous Destruction Rate x 0.08
Total Destruction Rate 0.10
Returns to Performance Pay * 0.29
Cost of Performance pay * 1.50
Unemployment Benefit * b 0.47
Vacancy Cost * 0.35
Beta Process
Beta
(p,p)
Beta
(1,1)
Process for Uniform Unif[0,1]
Note: *Free parameters of the baseline model chosen with minimization
of loss function
Table 11 - Calibration of Autoregressive Shock Processes
Process for Aggregate
Productivity Mean Autocorrelation Std of Innovation z
1 0.95 4.80E-04
Process for Private
Information Mean Autocorrelation
1 .95 *8E+01
Note: *Free parameter of the baseline model chosen with minimization of loss function
104
Table 12 - Simulation Results of the Baseline Model
Moments to match
Model Data
Bonus incidence 0.068 0.17
Size of Bonus 0.065 0.06
Corr(Bonus size,
unemployment) -0.2 -0.17
Corr(Bonus pay,
unemployment) -0.19 -0.14
Corr(Bonus incidence,
unemployment) -0.21 -0.31
Corr(Bonus incidence, Bonus
Size) 0.99 0.67
Std Incidence 0.22 0.11
Std Bonus Size 0.39 0.39
Std Aggregate Bonus 0.4 0.4
Other Key Model Moments
Beveridge curve 0.97 -0.89
Std of Unemployment 0.39 0.19
Std of Vacancy 0.26 0.2
Std Labor Market Tightness 0.15 0.38
Notes: Simulation in the first column uses parameters in Tables 10 and 11.
105
Table 13 - Simulation Results for Sensitive Analysis of Key Parameters
p = a= = Baseline
0 mean(a*) 0.291
Bonus incidence 0.02 0.1 0.14 0.068
Size of Bonus 0.02 0.1 0.12 0.065
Corr(Bonus size, unemployment) 0.99 -0.13 -0.2 -0.2
Corr(Bonus pay, unemployment) 0.99 -0.13 -0.18 -0.19
Corr(Bonus incidence, unemployment) 0.99 0 -0.2 -0.21
Corr(Bonus incidence, Bonus Size) 1 0.02 0.99 0.99
Std Incidence 0.02 0 0.218 0.22
Std Bonus Size 0.02 0.23 0.37 0.39
Std Aggregate Bonus 0.016 0.24 0.4 0.4
Beveridge Curve 0.83 0.82 0.97 0.97
Std of Unemployment 0.009 0.01 0.41 0.39
Std of Vacancy 0.0078 0.009 0.27 0.26
Std Labor Market Tightness 0.0052 0.007 0.16 0.15
Note: Simulations in columns 1 and 2 change only the value of p, and optimal effort, respectively. In column
3 I change only the value of by 1% . Baseline model uses parameters in Tables 10 and 11.
106
Table 14 - Regression Results for Cyclicality of Uncertainty
Dependent Variable Is Stock-Market Volatility - b
Explanatory Variable Is Period by
Period
Cross-Sectional Standard Deviation of Coefficient R squared Time span
Firm profit growth,c Compustat
quarterly 0.5320
(0.0640) 0.287 62Q305Q1
Firm stock returns,d CRSP monthly 0.5430
(0.0370) 0.287 62M706M12
Industry TFP growth,e SIC 4-digit yearly 0.4290
(0.1190) 0.282 19621996
Monthly Unemployment Rate (BLS)g 0.2868
(0.1958) 0.0038 62M706M12
Notes: a-Each column reports the coefficient from regressing the time series of stock-market volatility on the within period cross-sectional standard deviation (SD) of the explanatory
variable calculated from an underlying panel. All variables normalized to a SD of 1. Standard errors are given in italics in parentheses below. So, for example, column 1 reports
that the stock-market volatility index is on average 0.532 SD higher in a quarter when the cross-sectional spread of firms profit growth is 1 SD higher.
b-The stock-market volatility index measures monthly volatility on the U.S. stock market and is plotted in Figure 1. The quarterly, half-yearly, and annual values are calculated
by averaging across the months within the
period.
c-The standard deviation of firm profit growth measures the within-quarter cross-sectional spread of profit growth rates normalized by average sales, defined as (profitst-
and uses firms with 150+ quarters of data in Compustat quarterly accounts.
d-The standard deviation of firm stock returns measures the within month cross-sectional standard deviation of firm-level stock returns for firm with 500+ months of data in
the Center for Research in Securities Prices (CRSP) stock-returns file.
e-The standard deviation of industry TFP growth measures the within-year cross-industry spread of SIC 4-digit manufacturing TFP growth rates, calculated using the five-factor
TFP growth figures from the NBER data base.
f-Average units in cross section refers to the average number of units (firms, industries, or forecasters) used to measure the cross-sectional spread.
g- Labor Force Statistics from the Current Population Survey
16 years and over
2. Data Appendix
March CPS Data
The March CPS data used in Figures 1 to 7 were downloaded from the NBER
website using years 1980 to 2008. The redesign in 1988 changed the March sup-
plement question about earnings. Before 1989, total earnings from last year were
registered under one variable. After 1989, there is a question for earnings from the
107
primary job and an additional variable for earnings from a secondary job. For the
years after 1989 my earnings variable is the sum of primary and secondary earnings.
Appendix Table 1 shows that variables used for matching the March CPS across
years. Following Mandrian and Lefgen (1999), individuals are matched based on
their month-in sample, household identi…er, household number and line number.
After that, repeated observations due to errors in identi…ers are deleted. Also,
spurious matches with di¤erent sex and race in the two periods are eliminated. I
did not do further re…nements, since they would come at the cost of eliminating
some of the "true" matches.
In 1988 there were two releases of the March supplement. The one in the old
format is used in the 1987-88 match. The 1988B release is used in 1988-89. The
years 1994-95 are an exception. The …rst 1994 release contained errors in the
identi…ers. I use the BLS-corrected h_idnum. To account for this problem, this
year has to be matched by state of residence along with the four usual identi…ers.
Some caution is needed when using the matched sample, since not all variables are
corrected by this procedure. Years 1985-86 and 1995-96 cannot be matched due
to changes in the household identi…ers.
After 2002, the March Supplement sample was increased in order to cover a
higher number of Hispanic Households and low income families with uninsured
children (SCHIP). Since the oversample is taken from di¤erent rotation groups,
108
household identi…ers can be repeated, which complicates matching. I eliminate
the post 2002 oversample for comparability with earlier years. Appendix Figure 1
presents also match rates for the overall sample and including the SCHIP observa-
tions. Two steps are needed to eliminate the oversample. First, I delete individuals
with person weight equal to zero from 2002 to 2008. Second, I delete in 2002 and
2003 all observations with h_seq higher than the 2003 cuto¤ value 78864. In 2004
and 2005, I eliminated observations with h_seq higher than the 2004 cuto¤ value
78575.
Lastly, in 2005 the identi…ers were redesigned in order to facilitate year-to-year
matching: h_idnum was renamed h_idnum1 and a second identi…er was created,
h_idnum2. In the 2004-05, I use only h_idnum1. From 2005 on, both h_idnum1
and h_idnum2 need to be used to sort and merge observations.
Only half of the March sample can be potentially matched across years (rotation
groups 1-4 in period t and 5-8 in t+1). Among the successfully matched persons,
I classify observations according to their status in the period t and t + 1 March
interviews. Only individuals currently in the labor force are used. The sample is
also restricted from 25 to 64, so not to capture major transitions in and out of
the labor force. Further, only individuals classi…ed as private_nonfarm workers in
their longest job and currently in the labor force are kept in the sample. Values
of primary earnings that are topcoded or imputed are also excluded. This leaves
109
me with a sample of private nonfarm workers ranging from 10000 to 8000 workers
in each year. March supplement weights are used in all calculations and nominal
variables are de‡ated using the CPI of the reference year. In the computations for
total household income, only heads of household are kept and household weights
are used. Appendix Table 2 lists CPS identi…ers used in the analysis.
Successive changes in the March Supplement questionnaire do not prevent com-
parisons across years, but some care is needed in order to guarantee that variables
have the same meaning over time. I try to homogenize variables to the extent pos-
sible. The changes in data processing in 1988 (reading earnings with the primary
and secondary wages separatly) seems to have permanently moved the volatility
measures to a higher level. In the graphs, I choose to subtract the 1987-88 break
from all measures of volatility after 1987. Without this adjustment, the increase
in instability could be overstated. In the regression exercise I include a dummy
for the post 1987 period. This procedure seems to capture the break and does not
a¤ect substantially the estimates for the coe¢cient of the time trend.
One should worry whether the matched sample is representative of the overall
labor force. I use propensity score weights to correct for such bias. The propensity
score weights are calculated in the following way: I estimate in each year a probit
model of the probability of being matched on observables. The variables used
were sex, race, head of household status, age, age squared, dummy for educational
110
attainment, full time status, private sector job, unemployment in the …rst or second
interview and industry indicators for manufacturing and retail sectors. The …nal
weight used is the inverse of the probability predicted by the model multiplied by
the March supplement weight. In Appendix Table 3 I present characteristics of
the pooled matched sample at the time of the …rst March interview.
PSID Data
The PSID data used in Figure 8 and the calibration exercise comes from
Lemieux, Bentley and Parent (2009). See their paper for further details. The
sample consists of male heads of the household aged 18 to 65 with average hourly
earnings between $1 and $100 (in $1979). Workers in the public sector and self-
employed are excluded from the sample. Jobs are assigned as performance pay
if part of the worker’s compensation includes a variable pay component (bonus,
comission, piece-rate). From 1976 to 1992, the authors use mainly two questions
to construct de…nitions: the amount of money earned from working overtime, or
from bonus, comission or piece-rate, and for workers not paid by the hour or salary
exclusively, the form of pay received. All non-overtime workers that report bonus,
comission or piece rate are classi…ed as having a performance pay job. After 1993,
the interviews include a direct question about the amount earned in bonus, tips,
comission and overtime. For the sake of comparability, performance pay jobs are
de…ned as jobs with non-overtime pay but positive bonus, comission or piece-rate.
111
For some jobs, positive bonus pay is usually not received in every year. The authors
de…ne as performance pay any job that received at least once over the duration of
the job match pay in form of bonus, comission or piece-rate.
The computation algorithm is as follows. The problem consists of a search
for a …xed point in c and l. The algorithm contains an inter loop necessary to
solve the dynamic programming island problem and the invariant distribution of
islands over the labor force and idiosyncratic shocks, and an outer loop to obtain
the …xed point in the expected value of arriving in an island anywhere in the
stationary distribution, and the mass of searchers in the economy. See Kambourov
and Manoviskii (2007) for an example.
3. Derivation of equilibrium in performance pay markets
The …rm problem is:
: = max
1,j
1
j
[(1 + .c
)q
c
÷nq ÷jc
1q]
which can be rewriten as:
: = max
1,j
1
j
[(1 + .
j1
2¸
)q
c
÷nq ÷
j
2
1
2
2¸
q]
112
The …rst order conditions are as follows:
(.22) 1 : 1
j
[.
j
2¸
q
c
÷
j
2
1
¸
q] = 0
which implies:
1
=
.
2
1
j
[jq
c
]
1
j
[j
2
q]
(.23) q : 1
j
[(1 + .
j1
2¸
)cq
c1
÷n ÷
j
2
1
2
2¸
] = 0
which implies:
(.24) n = 1
j
[(1 + .
j1
2¸
)cq
c1
÷
j
2
1
2
2¸
]
Assume j is iid and private information. Since the bonus and employment are
decided before the realization of j. the …rm can take j as independent of q, which
simpli…es the solution as follows:
113
(.25) 1
=
.
2
1
j
[j]q
c1
[1
j
[j]
2
+ ·cj)]
Using (24) in (23) yields:
n = cq
c1
+ 1
j
[.
j1
2¸
cq
c1
÷
j
2
1
2
2¸
]
n = cq
c1
+ 1
j
[
j
2¸
.
2
2
1
j
[j]q
c1
[1
j
[j]
2
+ ·cj)]
cq
c1
÷
j
2
2¸
_
.
2
1
j
[j].q
c1
[1
j
[j]
2
+ ·cj)]
_
2
]
n = cq
c1
+
c.
2
4¸
1
j
[j]
2
(q
c1
)
2
(1
j
[j]
2
+ ·cj))
÷
1
8¸
1
j
[j]
2
(.q
c1
)
2
[1
j
[j]
2
+ ·cj)]
(.26) n = cq
c1
+
1
4¸
1
j
[j]
2
(.q
c1
)
2
(1
j
[j]
2
+ ·cj))
_
c ÷
1
2
_
Wage determination:
Combining the …rst order condition for the …rm with the participation con-
straint of the worker, wages must satisfy:
114
n = 1
j
[(1+.
j1
2¸
)cq
c1
÷
j
2
1
2
2¸
] = 1
j
[c÷(jc
1
÷¸c
2
+,1
_
·
j
(l+q(r. ).
0
)Q(. d
0
))]
which can be rearranged as follows:
(.27) 1
j
[cq
c1
+ (c
.cq
c1
÷¸c
2
) + ,1
_
·
j
(l + q.
0
)Q(. d
0
)] = c
where
(.28) c
=
j1
2¸
(.29) 1
=
.
2
1
j
[jq
c
]
1
j
[j
2
q]
=
.
2
1
j
[j]q
c1
[1
j
[j]
2
+ ·cj)]
[
Using (26) to (28), employment equilibrium satis…es:
115
1
j
[cq
c1
(1 +
1
j
[j].
2
4¸
1
j
[j]q
c1
(1
j
[j]
2
+ ·cj))
) ÷¸
j
2
4¸
2
_
.
2
1
j
[j]q
c1
(1
j
[j]
2
+ ·cj))
_
2
+,1
_
·
j
(l + q.
0
)Q(. d
0
)] = c
j
which can be rearranged as follows:
cq
c1
+
.
2
4¸
1
j
[j]
2
(q
c1
)
2
(1
j
[j]
2
+ ·cj))
_
c ÷
1
4
_
+ ,1
_
·
j
(l + q.
0
)Q(. d
0
) = c
j
3.1. Case of observable e¤ort
Now consider the case in which the impact of e¤ort on performance pay is observ-
able and constant. Without loss of generality, let j = 1 in all states of the world.
The worker chooses e¤ort to maximize n + c1-¸c
2
and c
=
1
2¸
. The …rm can
determine the optimal level of e¤ort by choosing a piece rate on e¤ort. Using the
fact that 1 = 2¸c, we have that:
: = max
o,j
1
j
[(1 + .c)q
c
÷nq ÷2¸c
2
q]
The …rst order conditions are as follows:
116
q : [(1 + .c)cq
c1
÷n ÷2¸c
2
] = 0
n = (1 +.c)cq
c1
÷2¸c
2
c : [.q
c
÷¸4cq] = 0 (.30)
c =
.q
c1
¸4
(.31)
1 = 2¸c = 2¸
.q
c1
¸4
=
.q
c1
2
(.32)
By o¤ering the compensation package n+c1, the …rm always obtains the level
of e¤ort c =
¸.j
1
¸4
. Whenever c = 1,2, c =
¸.cj
1
¸2
and the bonus is equal to the
marginal value of e¤ort, 1 =
¸.j
1
2
=
0)(a,.)
0o
= .cq
c1
.
117
3.2. Derivation of equilibrium conditions in performance pay markets
when there is a monitoring cost
Assume that in order to set up a contract with a bonus pay the …rm has to incur
the monitoring cost C1q. I derive below the …rm problem in order to show that
a decline in C has a similar e¤ect of an increase in ..
: = max
1,j
1
j
[(1 + c
)q
c
÷nq ÷jc
1q ÷C1q]
: = max
1,j
1
j
[(1 +
j1
2¸
)q
c
÷nq ÷
j
2
1
2
2¸
q ÷C1q]
First order conditions yield:
(.33) 1 : 1
j
[
j
2¸
q
c
÷
j
2
1
¸
q ÷Cq] = 0
1
=
1
j
[
1
2
jq
c
÷Cq
1
¸
]
1
j
[j
2
q]
(.34) q : 1
j
[(1 +
j1
2¸
)cq
c1
÷n ÷
j
2
1
2
2¸
÷C1] = 0
118
(.35) n = 1
j
[(1 +
j1
2¸
)cq
c1
÷
j
2
1
2
2¸
÷C1]
Assume j is iid and private information. Since bonus and employment are
decided before the realization of j. the …rm can take j as independent of q and
simplify the solution such that:
(.36) 1
=
1
2
1
j
[j]q
c1
÷
C
¸
[1
j
[j]
2
+ ·cj)]
Using the bonus in the …rst order condition of the …rm gives:
n = cq
c1
+ 1
j
[
j1
2¸
cq
c1
÷
j
2
1
2
2¸
÷C1]
which can be simpli…ed as follows:
n = cq
c1
+ [1
(
1[j]q
c1
2¸
(c ÷
1
2
) + C(
1
2¸
2
÷1))]
With a positive cost of using performance pay, and if [
1[j].j
1
2¸
(c÷
1
2
) ÷C(1 ÷
1
2¸
2
)] 0, both the bonus and the base pay decline with an increase in the cost of
119
the monitoring technology. Note that when C ÷0, [1(
1[j].j
1
2¸
(c ÷
1
2
) +C(
1
2¸
2
÷
1)) 0 for c ÷
1
2
0. In this case, we collapse to equation (12) for . equal to
1, ·cj) = 0 and j = 1. Also, for high values of C, the bonus is negative,
meaning that the performance pay technology is not feasible, since it is too costly
to monitor.
120
.
4
.
5
.
6
.
7
.
8
M
a
t
c
h
R
a
t
e
1980 1990 2000 2010
Year
Match rate without SCHI P Match rate with SCHIP sample
(March CPS 1980-2007 )
Appendi x Fi gure 1 - Match Rate: March CPS 1980-2007
121
Appendix Table 1- Variables used for
matching rotation groups across years :
March CPS from 1979 to 2007
Variable
1980-
1988
1988-
2008
Month-in-sample mis h_mis
HH identifier hhidnum h_idnum
HH number item9 h_hhnum
Line number lineno a_lineno
State - hg_st60
Sex sex a_sex
Race race a_race
HH sequence number hhseqnum h_seq
Note: Change in survey methodology in 1988
122
Appendix Table 2- Variables used in the analysis: March CPS
from 1979 to 2007
Variable 1980-1988 1988-2008
Wages and salaries earnings i51a wsal_val
Earnings (self-employed) i51b semp_val
LF status besr a_lfsr
Weeks worked last year i34wk wkswork
Hours worked last year i38 hrswk
Allocated earnings incwsflag i_ernval
Topcoded earnings flag51a tcernval
Household weight hhsupwgt hsup_wgt
HH total income hhinctot htotval
Part-Time Full-Time Status rwewkrs wewkrs
Class of worker - longest job i50cw weclw
Education highgrad2 schl1 - a_hga
Age age age
Industry - longest job rwemind wemind
Head of the HH relhead hhdrel
Union member lumember a_unmem
More than one employer i39 phmemprs
Weeks looking or on layoff i43wk lkweeks
Weeks looking in one strech i44 lkstrch
Note: Change in survey methodology in 1988
123
Appendix Table 3- Demographic
characteristics of the March CPS
sample: rotation groups 1-4 from 1979
to 2007
Demographic characteristic Percent
in the
sample
male 47.7
manufacturing job** 12.7
white 85.9
unemployed** 5.3
married 47,9
highschool 66.9
some college 17
in the labor force 49.5
full-time** 78.3
part-time** 18.1
private sector** 67.9
self-employed** 10
imputted wages** 14.7
topcoded wages** 4.1
age <25 33.5
age 25-35 13.4
age 35-45 15.2
age 45-55 13.2
age 55-65 10.6
age 65+ 13.8
union member** 3.4
Note: 1,345,109 obs
** ratio from In the Labor Force group
References
[1] Abraham, Katharine G. and Robert Shimer, (2001). "Changes in Unemploy-
ment Duration and Labor Force Attachment," NBER working paper 8513.
[2] Acemoglu, Daron, (1999). “Changes in Unemployment and Wage Inequality:
An Alternative Theory and Some Evidence,” American Economic Review, 89
(December), 1259—1278.
[3] Acemoglu, Daron, (2002). “Technical Change, Inequality and the Labor Mar-
ket,” Journal of Economic Literature 40 (March), 7-72.
[4] Alvarez, Fernando and Marcelo Veracierto, (1999). "Labor-Market Policies in
an Equilibrium Search Model," NBER Macroeconomics Annual 1999. B. S.
Bernanke and J. J. Rotemberg, Volume 14. Cambridge and London: MIT
Press, 2000, 265-304.
[5] Autor, David H. , Lawrence F. Katz, Melissa S. Kearney, (2008) . "Trends in
U.S. Wage Inequality: Revising the Revisionists," Review of Economics and
Statistics 90:2, 300-323.
[6] Bachmann, Ruediger and Christian Bayer, (2009). "Firm-Speci…c Productiv-
ity Risk over the Business Cycle: Facts and Aggregate Implications," mimeo.
[7] Baker, George, Robert Gibbons and Kevin J. Murphy, (1992). "Subjective
Performance Measures in Optimal Incentive Contracts," mimeo.
[8] Bjelland, Melissa, Bruce Fallick, John Haltiwanger and Erika McEntarfer,
(2008). "Employer-to-employer Flows in the United States: Estimates used
Linked Employer-employee Data," NBER working paper 13867.
[9] Blanchard, Olivier, and John Simon, (2001). "The Long and Large Decline in
U.S. Output Volatility," Brookings Papers on Economic Activity, 1, 135-64.
124
125
[10] Bloom, Nicholas, 2009. The Impact of Uncertainty Shocks, Econometrica, Vol.
77, No. 3 (May, 2009), 623–685.
[11] Card, David and John E. DiNardo, (2002). “Skill-Biased Technological
Change and Rising Wage Inequality: Some Problems and Puzzles,” Jour-
nal of Labor Economics 20 (October): 733-83.
[12] Celik, Sule, Chinhui Juhn, Kristin McCue (2009). "Understanding Earnings
Instability: How Important are Employment Fluctuations and Job Changes?"
mimeo
[13] Chugh, Sanjay, (2009). "Costly External Finance and Labor Market Dynam-
ics," mimeo.
[14] Comin, Diego, Erica L. Groshen and Bess Rabin, (2006). "Turbulent …rms,
turbulent wages?" NBER working paper 12032.
[15] Cooper, Russel, John Haltiwanger, and Jonathan L. Willis, (2007). "Implica-
tions of Search Frictions: Matching Aggregate and Establishment-level Ob-
servations," mimeo.
[16] Cunha, Flavio and James Heckman, (2007). "The Evolution of Inequality,
Heterogeneity and Uncertainty in Labor Earnings in the U.S. Economy," IZA
Discussion Paper No. 3115.
[17] Davis, Steven J. and James A. Kahn, (2008). "Interpreting the Great Moder-
ation: Changes in the Volatility of Economic Activity at the Macro and Micro
Levels," NBER working paper 14048.
[18] Davis, Steven J. , 2008. "The Decline of Job Loss and Why It Matters,"
American Economic Review: Papers & Proceedings 2008, 98:2, 263–267.
[19] Davis, Steven J. , R. Jason Faberman, and John Haltiwanger, (2006a). "The
Flow Approach to Labor Markets: New Data Sources and Micro–Macro
Links," Journal of Economic Perspectives, American Economic Association,
vol. 20(3), 3-26, Summer.
[20] Davis, Steven J. , John Haltiwanger , Ron Jarmin, and Javier Miranda,
(2006b). "Volatility and Dispersion in Business Growth Rates: Publicly
126
Traded versus Privately Held Firms," NBER Working Papers 12354, National
Bureau of Economic Research.
[21] Davis, Steven J. , John Haltiwanger, (1990). Gross Job Creation and De-
struction: Microeconomic Evidence and Macroeconomic Implications, NBER
Macroeconomics Annual 1990, Volume 5.
[22] D. McFadden, (1989). " A Method of Simulated Moments for Estimation of
Discrete Response Models Without Numerical Integration," Econometrica,
57(5):995-1026.
[23] Den Han, Wouter J. and Georg Klatenbrunner, (2005). "Anticipated Growth
and Business Cycles in Matching Models", mimeo.
[24] Dynan, Karen, Elmendorf, Douglas and Daniel E. Sichel, (2008). "The Evolu-
tion of Household Income Volatility," Federal Reserve Board working paper.
[25] Dynan, Karen, Elmendorf, Douglas and Daniel E. Sichel, (2006). "Financial
Innovation and the Great Moderation: What Do Household Data Say?" Fed-
eral Reserve Board working paper.
[26] Fallick, Bruce and Charles A. Fleischman, 2004. "Employer-to-Employer
Flows in the U.S. Labor Market: the Complete Picture of Gross Worker
Flows," Finance and Economics Discussion Series 2004-34, Board of Gov-
ernors of the Federal Reserve System.
[27] Farber, Henry, (2005). "What Do We Know About Job Loss in the US? Ev-
idence from the Displaced Worker Survey, 1984-2004," Working paper 498,
Princeton University.
[28] Farber, Henry, (2008). "Employment Insecurity: The Decline in Worker-Firm
Attachment in the United States," Working paper 530, Princeton University.
[29] Gottschalk, Peter and Robert Mo¢tt (1994), “The Growth of Earnings In-
stability in the U.S. Labor Market?” Brookings Papers on Economic Activity,
1994, 217-272.
[30] Gottschalk, Peter, Erika McEntarfer and Robert Mo¢tt (2008),"Trends in
the Transitory Variance of Male Earnings in the U.S., 1991-2003: Preliminary
Evidence from LEHD data", mimeo
127
[31] Hubbard, Thomas (2000). "The Demand for Monitoring Technologies: the
Case of Trucking," The Quarterly Journal of Economics.
[32] Jacobson, Louis S., Robert J. LaLonde, and Daniel G. Sullivan, (1993). “Earn-
ings Losses of Displaced Workers,” American Economic Review, 83(4): 685–
709.
[33] Jaimovich, Nir and Henry E. Siu, (2007). "The Young, the Old, and the
Restless: Demographics and Business Cycle Volatility," Federal Reserve Bank
of Minneapolis Research Department Sta¤ Report 387.
[34] Kambourov, Gueorgui and Iourii Manovskii, (2008) ."Rising Occupational and
Industry Mobility in the United States: 1968-1997," International Economic
Review, 49 (1) February 2008, pp. 41-79.
[35] Kambourov, Gueorgui and Iourii Manovskii, (2007) ."Occupational Mobility
and Wage Inequality," mimeo. University of Pennsylvania.
[36] Katz, Lawrence F. and David H. Autor, (1999). “Changes in the Wage Struc-
ture and Earnings Inequality,” In O. Ashenfelter and D. Card, eds. Handbook
of Labor Economics, volume 3, North Holland.
[37] Kim, Chang-Jin, and Charles Nelson (1999). "Has the U.S. Economy Become
More Stable? A Bayesian Approach Based on a Markov-Switching Model of
the Business Cycle," Review of Economics and Statistics, 81, 608-16.
[38] Krueger, Dirk and Fabrizio Perri, (2005). "Does Income Inequality Lead to
Consumption Inequality? Evidence and Theory." mimeo
[39] Lazear, Edward and Paul Oyer, (2003). "Internal and External Labor Markets:
A Personnel Economics Approach," NBER working paper 10192.
[40] Lemieux, Thomas (2007). "The changing nature of wage inequality," NBER
working paper 13523.
[41] Lemieux, Thomas, MacLeod, W Bentley and Daniel Parent, (2009a). "Per-
formance Pay and Wage Inequality," Quarterly Journal of Economics, 124(1),
February 2009, 1-49.
128
[42] Lemieux, Thomas, MacLeod W Bentley and Daniel Parent, (2009b). "Perfor-
mance Pay, Wage Flexibility, and Hours of Work," unpublished manuscript,
October 2008.
[43] Lubik, Thomas and Michael Krause, (2003). "The (Ir)relevance of Real Wage
Rigidity in the New Keynesian Model with Search Frictions," Economics
Working Paper Archive 504, The Johns Hopkins University,Department of
Economics
[44] Ljungqvist, Lars and Thomas Sargent, (2004). "European Unemployment and
Turbulence Revisited," Journal of the European Economic Association April–
May 2004 2(2–3):456 – 468.
[45] Lucas, Robert Jr. & Prescott, Edward C., (1974). "Equilibrium Search and
Unemployment," Journal of Economic Theory , Elsevier, vol. 7(2), 188-209,
February.
[46] MacLeod, W. Bentley and Parent, Daniel (1999), “Job Characteristics and
the Form of Compensation,” Research in Labor Economics, Vol. 18, edited by
S.W. Polachek. London: JAI Press, 177-242.
[47] Menkulasi, Jeta, (2009). "Rational Inattention and Changes in Macroeco-
nomic Volatility," job market paper.
[48] Michelacci, Claudio and Vincenzo Quadrini,(2008). "Financial Markets and
Wages," University of Southern California, mimeo.
[49] Mortensen, Dale T & Pissarides, Christopher A, (1994). "Job Creation and
Job Destruction in the Theory of Unemployment," Review of Economic Stud-
ies, vol. 61(3), 397-415, July.
[50] Moscarini, Giuseppe and Kaj Thomsson, (2007). "Occupational and Job Mo-
bility in the US," Scan. Journal of Economics,109(4), 807–836.
[51] Neumark, David and Daiji Kawaguchi, (2001). "Attrition Bias and Economic
Relationships Estimated with Matched CPS Files". NBER working paper
8663.
129
[52] Polivka, Anne E. and Stephen M. Miller (1995). "The CPS After the Redesign:
Refocusing the Economic Lens," BLS working paper.
[53] Shimer, Robert (2005). “Reassessing the Ins and Outs of Unemployment,”
University of Chicago, mimeo.
[54] Shimer, Robert (2003). "The Cyclical Behavior of Equilibrium Unemployment
and Vacancies," mimeo
[55] Schmitt-Grohé, Stephanie and Martín Uribe, (2004). Solving dynamic general
equilibrium models using a second-order approximation to the policy function,
Journal of Economic Dynamics and Control, Volume 28, Issue 4, January 2004,
Pages 755-775
[56] Shin, Donggyun and Gary Solon (2008). "Trends in Men’s Earnings Volatility:
What Does the Panel Study of Income Dynamics show?" NBER Working
Paper 14075.
[57] Stock, James, and Mark Watson, (2003). "Has the Business Cycle Changed?
Evidence and Explanations," Prepared for the Federal Reserve Bank of
Kansas City symposium, "Monetary Policy and Uncertainty," Jackson Hole,
Wyoming, August 28-30.
[58] Storesletten, Kjetil, Chris I Telmer and Amir Yaron, (2004). "Cyclical Dynam-
ics in Idiosyncratic Labor Market Risk," The Journal of Political Economy;
Jun 2004; 112, 3
[59] Tauchen, George, (1986). "Finite State Markov-Chain Approximations to Uni-
variate and Vector Autoregressions," Economics Letters, 1986, 20, 177-181.
doc_664320131.pdf
A stable value fund is a type of investment available in 401(k) plans and other defined contribution plans as well as some 529 or tuition assistance plans.
ABSTRACT
Title of Document: STABLE FIRMS AND UNSTABLE WAGES.
Ana Luisa Gouvea Abras, PhD, 2010
Directed By: Professor John Haltiwanger, Department of
Economics
In this work I study recent developments in firm employment and earnings instability
in the US economy over the last 30 years. Despite the decline in aggregate and firm
level volatility, earnings instability has increased steadily for job stayers since the late
seventies. I measure and model these phenomena as a result of a decline in labor
market institutions that compress wage volatility, and an increase in the incidence of
compensation schemes that attach wages to worker performance.
STABLE FIRMS AND UNSTABLE WAGES
By
Ana Luisa Gouvea Abras
Dissertation submitted to the Faculty of the Graduate School of the
University of Maryland, College Park, in partial fulfillment
of the requirements for the degree of
Doctor of Philosophy
2010
Advisory Committee:
Professor John Haltiwanger ,Chair
Professor John Shea
Professor Katharine Abraham
Assistant Professor Pablo D.Erasmo
Assistant Professor Sanjay Chugh
© Copyright by
Ana Luisa Gouvea Abras
2010
ii
Acknowledgements
I thank my dissertation committee: John Haltiwanger, John Shea, and Katharine
Abraham. This work would not have been possible without their help. For every-
thing they taught me, I thank the professors in the macro sequence, Borang
Aruoba, Sanjay Chugh, and Pablo D’Erasmo. My greatest intellectual indebt-
edness though is to my advisor, John Haltiwanger. Countless people helped me
along in graduate school. I also thank my sister Leticia Abras, and Abby Alpert for
their support.
Contents
List of Tables v
List of Figures vi
Chapter 1. Trends in Employment and Wage Instability 1
1.1. Introduction 1
1.2. New evidence from the March CPS 16
Chapter 2. Stable Firms and Unstable Wages 29
2.1. An island model of the labor market 30
2.2. Simulation results 48
Chapter 3. Uncertainty in Employment Relationships and the Business
Cycle 57
3.1. Model 62
iii
3.2. Calibration and Simulation 72
3.3. Last Remarks 82
1. Figures and Tables 83
2. Data Appendix 106
3. Derivation of equilibrium in performance pay markets
111
Appendix. References 124
iv
List of Tables
Table 1 95
Table 2 96
Table 3 97
Table 4 98
Table 5 99
Table 6 100
Table 7 100
Table 8 101
Table 9 102
Table 10 103
Table 11 103
Table 12 104
Table 13 105
Table 14 106
v
List of Figures
Figure 1 83
Figure 2 84
Figure 3 85
Figure 4 86
Figure 5 87
Figure 6 88
Figure 7 89
Figure 8 90
Figure 9 91
Figure 10 92
Figure 11 93
Figure 12 94
vi
CHAPTER 1
Trends in Employment and Wage Instability
1.1. Introduction
The purpose of this dissertation is twofold. In the …rst two chapters I study
the rise of earnings instability in light of recent changes in volatility both at the
macroeconomic and the …rm level. Despite the moderation in the variance of
macroeconomic and …rm outcomes from 1979 to 2007, earnings instability for job
stayers increased over the same sample period. I present both theory and evidence
on these apparently contradictory phenomena. I …nd that earnings instability
for job stayers increased over the same sample period using the Matched March
CPS. I also measure earnings instability using the PSID from 1976 to 1996. I
…nd that jobs that received some form of bonus or commission have higher wage
volatility than jobs with wages subject to collective bargaining. I use my empirical
…ndings in order to guide construction and simulation of a model of the labor
market that explains increased wage volatility by combining a decline in labor
market institutions that compress wage volatility and an increase in the use of pay
schemes attached to worker performance. I calibrate the model to match standard
1
2
moments of the US labor market such as unemployment and job turnover, but
also values of size, standard deviation of bonus pay, and incidence of performance
related payment in the PSID. Simulations results suggest that moving the economy
from unionized markets to performance pay arrangements explain the bulk of the
decline in …rm volatility, and 29% of the increase in wage instability present in the
data in the last 30 years.
In the third chapter I turn to the analysis of a model of business cycle with
performance pay contracts. Extensive empirical evidence documents that worker
and job ‡ows are high and variable even for narrowly de…ned industries. Gross
reallocation rates are large both in booms and recessions, suggesting a constant
reshu-ing of resources taking place in the economy (Davis, Haltiwanger and Schuh,
1996). I extend a standard search model to include performance pay contracts and
analyze whether the uncertainty in employment relationships brought by contracts
help explain high frequency moments of compensation schemes, vacancies, and
unemployment in the US economy. I use a non-standard set of moments to calibrate
the model: values of size, incidence, and cyclicality of bonus payment in the PSID.
I …nd that a model that targets the moments of compensation schemes can explain
at least half of the high frequency variation in unemployment and vacancies in
the economy. I develop in the model bundled shocks. Besides the standard labor
productivity variation, I include in the model uncertainty shocks, represented by
3
time varying private information at the employment level. Uncertainty a¤ects the
value of employment by changing incentives and e¤ort in contracts, and decreases
the value of a job by making it harder to assess outcomes. Economic downturns
correspond to periods with increasing noise in the principal-agent problem in the
economy. To that extent, I develop a theory of recessions based on uncertainty
in employment relationships. Simulation results suggest that uncertainty shocks
are capable of generating high frequency variation in unemployment and vacancies
without resorting to high variance in labor productivity shocks, overcoming a well
known problem of labor search models (Shimer, 2003).
1.1.1. Empirical Evidence on Firm and Earnings Instability
Macroeconomic outcomes in the US and other major developed countries became
less volatile in the mid-1980’s and volatility remained low through 2006. This
widely discussed phenomenon, known as the Great Moderation, is re‡ected in the
decline in the variance of GDP, in‡ation and other aggregate series. This trend in
macroeconomic outcomes has been accompanied by a decline in business growth
rate volatility. In this work, I focus on an aspect of the economy that has not been
touched by increasing stability : labor market earnings. Evidence from a variety
of sources over the last 25 years shows a rise in the variance of household earnings
4
in the US. Greater heterogeneity in job outcomes manifests itself in di¤erent ways
besides variability of wages. Lower average tenure, higher occupational mobility,
and a greater job loss rate in previously secure high-skilled positions all suggest a
more ‡uid labor market. I search in this work for ways to reconcile evidence that
earnings volatility has increased while …rm volatility has decreased over the last
two decades.
My work provides an extended empirical analysis using Matched March CPS
data from 1980 to 2008. In a sample of job stayers in private non-farm jobs, I
…nd that volatility in both hourly earnings and total earnings displays an upward
trend. The increase in hourly earnings instability for job stayers over this period
is 35%. I also measure earnings instability using the PSID from 1976 to 1996. I
…nd that jobs that receive some form or bonus or commission have higher volatility
than jobs with wages subject to collective bargaining.
To attempt to understand these patterns in the data, I develop a general equi-
librium model of the labor market with worker and …rm heterogeneity. I extend the
frictional labor market model of Lucas and Prescott (1974). My extensions involve
the inclusion of di¤erent pay setting mechanisms in di¤erent sectors or islands in
the labor market. The way the model works is as follows. Due to search frictions,
wages and employment are heterogeneous in separated local labor markets. In
5
some markets, wages are awarded according to performance, while in other mar-
kets institutional arrangements prevent wages from being equal to the marginal
product of labor in all states of the world. The institutions that I emphasize are
unions and wage norms, both of which tend to compress the wage distribution and
decrease wage instability. These institutions were prevalent in the early eighties,
but have declined in importance since.
I postulate that the driving force of this change in labor market arrangements
is a decrease in the cost of monitoring workers. Improvements in information
technology have allowed for better evaluation of worker performance and make it
easier to o¤er wages aligned to productivity. New IT diminishes the asymmetry
of information between …rms and workers and raises the gains from operating un-
der performance pay arrangements. Since compensation becomes more responsive
to idiosyncratic conditions under performance pay, the cross section dispersion
of wage growth increases. This mechanism is consistent with the empirical evi-
dence discussed below that reports an increase over the last 30 years in the use of
compensation arrangements attached to worker performance.
Theory and measurement are linked since the model is used to illustrate how
technological change a¤ects employment and wage instability. I calibrate the model
to match standard moments from the labor market in the 2000’s. The main goal of
6
the simulation exercise is to evaluate the ability of changes in labor market institu-
tions to explain the path of wage volatility. I perform this exercise by keeping the
underlying idiosyncratic shock process constant and changing only the technology
of compensation in the economy. Simulation results suggest that a model with new
compensation technologies that attach wages to worker performance works quali-
tatively in the right direction of explaining the diverging trends in …rm and wage
instability, and appears to account for a substantial fraction of the quantitative
change observed in the data.
There are a number of recent papers that motivate my consideration of alterna-
tive pay arrangements. The …rst paper is Lemieux, MacLeod and Parent (2009a,
henceforth LMP). The authors test the e¤ect of performance pay on wages in the
PSID and ask whether returns to worker and job characteristics di¤er according
to pay schemes. They …nd that compensation in performance pay jobs is more
closely tied to both observed (by the econometrician) and unobserved productive
characteristics of workers. The increase in the incidence of performance pay over
time provides an important channel through which technological changes in the
cost of monitoring and in returns to skill a¤ect wage inequality. Performance pay
is closely linked to the idea that wages are tied to e¤ort and productivity of the
7
worker. A shift to paying wages that equal performance outcomes means poten-
tially more ‡exible wages and a departure from norms and rigidity that could
regulate behavior in the labor market.
A change in the technology of compensation is central to the explanation I
advance for the increase in earnings instability. The second set of papers relevant
to my hypothesis include Hubbard (2000) and MacLeod and Parent (1999). Hub-
bard argues that the use of on-board computers in the trucking industry provided
managers with a better way to monitor production processes. IT in monitoring
is productivity enhancing and potentially capable of explaining changing wage
incentives. MacLeod and Parent use several data sources to document the re-
lationship between type of job and compensation. The authors …nd that jobs
with high power incentives (piece or commission rates) tend to be associated with
more worker autonomy and that tight labor market conditions increase the use of
bonuses and promotions. Moreover, the authors report anecdotal evidence that
shows an increasing use of software for evaluating worker performance and a boom
of services for monitoring workers. Lemieux, MacLeod and Parent (2009b) argue
that performance pay jobs seem to be associated with higher wage ‡exibility, and
that wages respond more to conditions in their local labor markets. Based on the
evidence from those papers and evidence below, I allow di¤erent wage schemes in
8
my model and show how declining costs of monitoring can move the economy from
"rigid" compensation schemes to an increased use of pay-for-performance.
1.1.2. Evidence on macroeconomic and …rm-level instability
The variances of GDP, investment, and aggregate income began declining in the
mid-eighties. Stock and Watson (2003) report that the standard deviation of four-
quarter GDP per capita growth in the US declined about forty percent comparing
the 20-year-windows before 1984 and after 1984. Several papers document and dis-
cuss the causes of the increased aggregate stability that followed the eighties (Kim
and Nelson, 1999, Stock and Watson, 2005, Blanchard and Simon, 2001). More
interesting for our purposes are the trends in job turnover and business volatility
for the same period. Turnover rates, as measured by creation and destruction of
jobs, have decreased steadily in the US economy after the 1983 recession. A sim-
ilar trend is observed by Davis, Faberman and Haltiwanger (2006) for the entire
economy in the nineties using Business Employment Dynamics data. In the same
vein, Davis, Haltiwanger, Jarmin and Miranda (2006, henceforth DHJM) report an
overall decrease in the volatility of growth rates of businesses in the US beginning
in the late 70’s.
1
1
Previous work - Comin et al (2006) - focused on publicly traded …rms, which display rising
volatility in recent years. Davis, Haltiwanger, Jarmin and Miranda (2006) partially overturn the
results of Comin et al (2006) for …rm volatility with COMPUSTAT data, showing that once the
9
Figures 1 to 3 show the secular decline in business volatility and turnover
rates in the US economy over the period 1976 to 2005. I present the evidence on
…rm volatility using di¤erent measures and data sources to demonstrate that the
decline in …rm instability is a robust feature of the data. Figure 1 displays the
cross section standard deviation of the growth rate of employment, computed using
the Longitudinal Business Database (LBD), which contains annual observations on
employment and payroll for all U.S. businesses.
2
This measure of …rm volatility
is cyclical, and displays its highest level in the pre-nineties period. There is a
declining trend in volatility when we compare the periods before and after the the
early eighties.
Figure 2 shows turnover rates measured using job ‡ows data from the LBD.
Job creation and destruction rates represent the amount of job churning in the
economy. Both series display a steady decreasing trend over my sample period.
3
Figure 3 shows the quarterly excess job reallocation rate for the whole private
sector calculated using the BLS Business Employment Dynamics (BED) database.
The excess job reallocation rate provides a measure of cross sectional dispersion in
establishment growth rates. It measures the amount of turnover that exceeds what
sample is increased to include both private and publicly owned …rms, there has been an overall
decrease in …rm level volatility.
2
Source: Davis, Faberman and Haltiwanger (2006a).
3
Source: DFHJM.
10
is necessary to account for the net employment growth in the economy.
4
Note that
despite the di¤erent data source and measure, we still see a decline in business
volatility over the sample period.
Labor market outcomes are the result both of churning jobs between …rms, and
of churning workers across labor market states. There is no long, consistent time
series measuring worker ‡ows for the US economy, which makes it hard to identify
long run trends in overall accessions and separations. It is possible, however, to
document trends for the subset of worker transitions in and out of employment
using data from the Current Population Survey (CPS). Figure 4 shows quarterly
averages of unemployment in‡ows and out‡ows using the CPS from 1976 to 2008.
Worker ‡ows fell almost by half from the early 1980s to the mid 1990s and there-
after. The evidence discussed below of decreases in tenure and increases in residual
inequality and earnings volatility has not been associated with rising instability of
…rm employment, or with higher job and worker ‡ows.
4
Excess job reallocation equals the sum of gross job creation and destruction less the absolute
value of net employment growth. The excess reallocation rate is equivalent to the employment-
weighted mean absolute deviation of establishment growth rates about zero. See Davis, Halti-
wanger and Schuh (1996). I use a similar measure for change in earnings in the CPS in Section
2 in order to calculate wage instability.
11
1.1.3. Evidence on earnings instability
Since the work of Gottschalk and Mo¢tt (1994) calculating labor earnings instabil-
ity using the PSID, several papers have devoted attention to documenting recent
trends in earnings volatility in the US economy.
5
Despite di¤erences in results,
methods, and measurement, overall the evidence suggests that the labor market is
becoming more unstable; workers seem less able now to hold jobs with predictable
earnings.
Dynan, Elmendorf and Sichel (2008), using the PSID, document a steady rise
in instability of household earnings since the late 70’s. The authors …nd an in-
creasing trend in the standard deviation of percentage changes in several measures
of earnings, such as total household income, household head earnings, combined
head and spouse earnings, head annual hours and head real earnings per hour.
6
Below, I present similar evidence using Matched March CPS data from 1980 to
2008.
A related result is analyzed in Cunha and Heckman (2007). The authors sep-
arate trends in the predictable and unpredictable components of earnings at the
time agents make relevant job market decisions. They estimate that the variance
5
See Cameron and Tracy (1998), Haider (2001), and Hertz (2006) for examples.
6
Shin and Solon (2008) repeat the exercise of Dynan et al (2008) using di¤erent earnings measures
and …nd a smaller increase in wage instability.
12
in the unpredictable part of earnings at the time of schooling choice has increased
when comparing cohorts born in the sixties and late seventies.
Two additional facts about recent US labor market trends are noteworthy in
this context: …rst, occupational mobility increased up to the mid 90’s and stabilized
thereafter (Moscarini and Thomsson, 2007). Second, wage inequality increased in
overall measures prior to the early 90’s.
7
Several papers study the evidence of rising
wage inequality in the US (Katz and Autor, 1999, Acemoglu, 1999, 2002, Violante,
2002, Piketty and Saez, 2003). The empirical evidence clearly suggests that recent
earnings gains have been highest in the highest wage percentiles. Increases are
also evident in other measures of inequality including the 90/10 gap, college/high
school gap and residual inequality (accounting for age, gender, experience and
education). In this paper I focus on instability rather than inequality. Though
these two phenomena are likely to have similar origins, they do not follow the
same trend over time. Hence I treat them as separate pieces of evidence.
1.1.4. Alternative explanations for the rise in earnings instability
7
According to Autor, Katz and Kearney (2005), wage inequality kept increasing for the 90-50
wage percentiles after the mid-90s, but remained stable or decreased for some groups in the lower
half of the wage distribution.
13
Like most complex events, the recent rise in earnings instability can accommodate
several possible explanations. I discuss here several possible explanations related
to secular changes in the labor force or higher "turbulence" in the labor market.
The composition of the US labor force has changed over the last 30 years. The
population is aging even while the tenure distribution is apparently decreasing
(Farber, 2008). Also, skilled workers occupy a growing share of jobs (Autor, Katz
and Kearney, 2005). It is unlikely that these changes in labor force composition
can provide a consistent explanation of rising earnings instability, since experienced
and skilled workers should be less susceptible to wage instability than other groups.
Financial innovation has allowed households to self-insure against increasing
wage instability, according to Dynan, Elmendorf and Sichel (2008). Though the
authors argue that this link is important in explaning the Great Moderation, they
are silent about the events in the labor market that could have triggered higher
income instability. Financial innovation has a¤ected both …rms and workers, and
…nancial constraints can make employment more sensitive to shocks.
8
However, it
is unclear a priori why …nancial innovation would change compensation schemes
used in the labor market.
8
See Chugh (2009).
14
Cunha and Heckman (2007) …nd that the variance in the unpredictable part
of earnings at the time of schooling choice has increased over the last 20 years.
They speculate that this is linked to higher "turbulence" or skill depreciation after
job loss (Ljungqvist and Sargent, 2004). Earnings losses of displaced workers have
been detected by several authors in the literature (see Farber, 2005 for a summary).
Though Ljungqvist and Sargent use turbulence to explain rising European unem-
ployment, it can also explain rising earnings uncertainty if the rate of skill loss has
increased. The main drawback of this reasoning is that the rate of involuntary job
loss, the type most likely to lead to declines in earnings, has if anything decreased
since the early eighties (Davis, 2008). It would take a large increase in the loss in
skills following job loss to o¤set that trend.
Another plausible source of higher volatility is discussed in Violante (2002).
The author uses a model with search frictions that links new vintage speci…c skills
to workers matched to di¤erent machines. He shows that in such a model an
increase in the pace of technological change spreads the wage distribution of similar
workers. Workers face losses from separation since they have to learn new vintage
abilities, and uncertainty in outcomes increases with turnover.
As discussed by Comin, Groshen and Rabin (2006), several models imply that
higher turbulence for …rms will lead to more turbulent wages. Coincident …rm and
worker trends can be explained as resulting from "bad luck" - larger idiosyncratic
15
…rm shocks translate into unstable wages. Since the …rm evidence discussed in
the previous section does not suggest higher idiosyncratic …rm shocks, however,
a story based on changes in the size and variance of the shock process a¤ecting
…rms is unlikely to explain simultaneous occurrence of rising wage instability and
declining …rm instability. Models in which shocks to occupations, jobs or vintages
accelerated generally imply that both worker and …rm instability should have gone
in the same direction. The literature has yet to come to grips with the con‡ict
between trends in labor market and in …rm outcomes.
9
The evidence highlighted above is discussed in Davis and Kahn (2008). Despite
the ongoing volume of research on the Great Moderation and its relationship to
…rm behavior, little attention has been given to reconciling the evidence of macro-
economic and …rm moderation with evidence of growing earnings instability. Davis
and Kahn suggest an explanation based on employment relationships having be-
come more ‡exible. They argue that employers are increasingly capable of using
wages as a margin of adjustment. Less unionization, weakening restrictions on
9
I do not consider the problem of consumption volatility and its response to income shocks.
As argued in Krueger and Perri (2009), consumption response to income shocks is higher for
individuals who do not own real state or business. This suggests that …nancial constraints matter
for the transmission of earnings volatility to consumption and wealth volatility. Whether the
increase in earnings instability is related to changes in the trends of consumption volatility for
the US economy is an open question. To the extent the …nancial innovation has increased since
the early eighties, the connection between the two volatility outcomes is likely to have decreased
with better access to …nancial markets.
16
minimum wages, and more ‡exible pay schemes are consistent with fewer job ‡ows
and more earnings volatility. Davis and Kahn suggest this explanation without
explicitly modeling it. If wage institutions are the key to explaining the puzzle,
we need to model the underlying factors that have lead to the adoption of pay
schemes under which workers face more variability.
1.2. New evidence from the March CPS
The ideal data to study the relationship between the volatilities in …rm and
earnings outcomes is matched longitudinal data on …rms and their employees. To
the best of my knowledge, Comin, Groshen and Rabin (2006) is the only work in
this vein. They use the Federal Reserve Bank of Cleveland’s Community Salary
Survey (wages and employment for speci…c occupations for identi…ed …rms) to link
higher …rm volatility and the rising variance of wages. The result is in line with
their previous work with …rm volatility in the COMPUSTAT data. However, as
mentioned above, DHJM …nd that …rm volatility has declined over time in a more
representative sample of …rms.
I adopt a route that is more roundabout but that does not require as much
information. I use matched March CPS data to construct measures of earnings
growth for short panels. The cross sectional variation in the earnings growth
data allows me to answer questions such as: Are trends for job stayers and job
17
movers di¤erent? Do labor market conditions like the unemployment rate matter
for volatility? I use answers to such questions to guide my model construction.
The data I use are the March CPS …les from 1980 to 2008. The CPS was
not designed for longitudinal analysis. Groups are interviewed for 4 consecutive
months, dropped from the sample for 8 months, then reinterviewed for another 4
months. Given this structure, around half of the sample in each month will appear
again a year later and can potentially be matched. I match rotation groups from
March to March in order to construct short panels that give earnings growth for
a relatively large sample. Mandrian and Lefgren (1999) develop an algorithm to
match observations and evaluate the quality of the match results from 1980-98,
which I extend up to 2008. I link individuals based on their CPS identi…cation
codes. Since there is some level of mismatch, I further restrict observations to
matches that have the same sex and race across the two observations.
There are some advantages in using the CPS instead of other data previously
analyzed for similar questions, such as the PSID. The CPS is used to study both
standard micro labor topics and aggregate ‡ows in and out of employment. It
collects earnings information not only from heads and spouses, as in the PSID,
but from all members of the household. The sample size is also larger and more
18
representative of the labor force. Hence, using the CPS allows me to address
competing explanations that rely on compositional changes in the labor market.
These advantages come at a cost. Matched CPS data only provide information
for one-year changes. None of the intertemporal structure discussed in the work
that initiated the study of variance in transitory and permanent components of
earnings (Gottschalk and Mo¢tt, 1994) can be captured with the CPS. I am forced
to focus only on short-term changes.
Amore worrisome problemis that the CPS does not provide tenure information.
The tenure distribution has likely changed over my sample period. Farber (2008)
presents evidence on tenure using CPS Tenure Supplements from1973 to 2006. The
results are puzzling - job tenure is decreasing while the job loss trend as measured
with the Displaced Worker Survey (DWS) is not increasing. Farber argues that
the DWS might not be capturing all instances of separations. This explanation is
unlikely to capture the entire story since other measures also point to lower job
loss in the last 20 years (Davis, 2008).
The lack of information on tenure makes it harder to evaluate competing ex-
planations of earnings instability that rely on increased mobility. There is evidence
that job-to-job and occupational mobility have increased since the late 70’s (see
Moscarini and Thomsson, 2007, and Fallick and Fleishman, 2004, for evidence with
19
monthly CPS, and Kambourov and Manouskii, 2007, for evidence with the PSID).
Nevertheless, mobility trends are more cyclical than the results I present later for
earnings instability for job stayers. While earnings instability increased steadily
over my sample period, Bjelland et al (2008) report that the pace of employer-to-
employer ‡ows as a fraction of employment and separations has remained low in
the post-2001 period following the recession.
One should worry whether the matched sample is representative of the overall
labor force for which I want to measure the trend in volatility. The probability
of being matched in two consecutive March interviews depends on observables
such as marital status, age, employment, etc. I correct for such selection in the
following exercises by using propensity score weights in all weighted measures. See
the Appendix on sample selection for details on this method.
10
The variables used in the analysis are total annual wage and salary earnings,
hourly earnings and total annual hours worked. Those variables are either asked
directly in the March Supplement or can be constructed, and refer to the previous
10
Each year is matched to the following year’ survey. For instance, 1980 refers to the merge of
1980-81 and corresponds to calendar years 1979-1980. Years 1985-86 and 1995-1996 could not be
matched due to problems with the household identi…ers. The exercises reported exclude married
women from the sample for reasons discussed in Footnote 12. For more details on matching and
sample selection, see Appendix 1.
20
calendar year.
11
With the short panels, I calculate measures of the dispersion in
growth rates in earnings and hours for di¤erent groups. Assume we have earnings c
for person i in periods t and t+1. The growth rate of c is given by G
cit
=
c
ti+1
c
it
.5(c
ti+1
+c
it
)
.
The …rst exercise is similar to Davis and Kahn (2008).
12
I measure instability
as the cross-section weighted average of absolute growth rates. This measure is
analogous to the excess job reallocation rate calculated at the …rm level.
(1.1) o
t
= \ciq/tcd_¹·c:cqc([G
cit
[)
Figure 5 shows this measure of hourly earnings instability and total hours
instability for the sample of private non-farm workers (excluding married women
13
)
11
Total household income, Total earnings, Hours worked in the previous year and Weeks worked
in the previous year are asked directly. From these I construct Total hours worked= Hours
worked per weekX Weeks worked, and Hourly earnings=Total earnings/ Total hours worked.
12
Davis and Kahn (2008) measure consumption volatility using quarterly data from the interview
segment of the Consumer Expenditure Survey. The authors compute the absolute value of the
log change in consumption expenditures for each household and then average over households.
This average value for the magnitude of household-level consumption changes is their measure
of consumption volatility. In results not reported I calculate two other dispersion measures: the
weighted average of individual growpth rates demeaned by the year average growth rate, and
the cross section standard deviation of growth rates. All measures display similar results for the
trend in earnings instability.
13
I exclude married women from the sample. The trend for total hours instability in the sample
including married women shows a decline in hours volatility. This is likely due to the increase in
labor force attachment for this group over the sample period. The exclusion of married women
from the sample does not change results for earnings volatility substantially and has the advantage
of not confounding long term changes in the composition of the labor force with changes in the
stability of earnings within employment relationships.
21
from 1980 to 2007. There is no notable trend in total hours instability, but hourly
earnings instability displays an increasing trend.
Figures 6 and 7 separate workers between job stayers and job movers/losers.
Job stayers are de…ned as workers who report in both March interviews being em-
ployed and having worked full time full year in the previous year without changing
employers.
14
As of March of their second interview, stayers have at least two years
of job tenure. Job movers/losers are workers who report experiencing unemploy-
ment or job change prior to one of the March interviews.
15
Figure 6 shows an
increase in total earnings instability for job stayers. Figure 7 shows no increase
14
March CPS data are retrospective, and I infer worker ‡ows from 3 variables: 1) "For how many
employers did ...work in 20..? If more than one at same time, only count it as one employer". 2)
"Weeks was ... looking for work or on layo¤ from a job? ". 3) "Were the weeks ... was looking
for work (or on layo¤) all in one stretch?". For full time full year workers with one employer
in each period, the problem is immaterial, since these workers stay in the same job. A more
comprehensive measure of job stayers includes part time part year workers with no more than
one employer in each period and no weeks looking for a job or on layo¤. Those might not be
stayers in case they exited the labor force at the end of period t and reentered in t+1 with a
di¤erent employer. Results with the comprehensive measure of stayers are virtually the same as
with full time full year workers. The fraction of job stayers does not display a trend over time in
my sample. Job movers/losers are workers that report unemployment or more than one employer
in the previous year in one or two March interviews. There might be some stayers in this group
if they are in the beginning of their job tenure in the beginning of t or the end of their tenure
in the end t+1. The fraction of those workers is no more than 5% of the overall sample in each
year, and also displays no trend over time. The comprehensive measure of job stayers and the
job movers/losers constitute two mutually exclusive groups.
15
Note that I am not separating job movers into those that experience unemployment and those
that transit directly between di¤erent employers. The consequences for wage instability are po-
tentially di¤erent since displaced workers are more likely to experience earnings losses (Jacobson
et al, 1993).
22
in total earnings instability for job movers/losers. Hourly earnings instability in-
creased for both groups of workers. The lack of trend in total earnings instability
for job movers/losers is probably due to two opposing e¤ects: higher hourly earn-
ings instability and smaller worker and job ‡ows.
In order to compute the long-run change in instability over the entire period
I estimate linear trends using individual o
it
as the dependent variable. Tables
1 and 2 give coe¢cients for the linear trend and implied cumulative growth of
instability.
16
Table 1 reports results for the entire sample of private non-farm
workers, job stayers and job movers/losers. Total earnings and hourly earnings
instability increased for both the full sample and job stayers. Job movers display
rising instability in hourly earnings but a decrease in total earnings and total hours
instability.
In table 2, I examine job stayers with high school or less education and
job stayers who are less than 45 years old. The increase in earnings instability for
the samples of younger and less educated job stayers is higher than the increase in
instability for the overall sample of stayers. Younger and less educated workers are
16
I calculate the total increase in instability using the value of the coe¢cient, ,, of the time
trend in a linear regression. For instance, the increase in instability for total earnings for the full
sample over 28 years is given by 28 +
´
, = .029, where
´
, is the estimated coe¢cient on the time
trend for total earnings instability.
23
a declining fraction of the population over the sample period. This decline along
with their higher and increasing instability dampens the overall instability trend
for job stayers.
My last exercise looks at di¤erences between performance pay and non-performance
pay jobs. The March CPS does not provide detailed information about the type
of pay, which prevents the identi…cation of performance pay jobs. I replicate to
the extent possible the CPS instability measures by calculating one-year percent
changes in hourly earnings in the PSID from 1976 to 1996 for job stayers.
17
Following the literature, I de…ne performance pay jobs as those receiving some
pay in the form of a commission, bonus or piece-rate over the duration of the
17
I thank Daniel Parent for providing the data from LMP. The sample consists of male heads of
the household aged 18 to 65 with average hourly earnings between $1.00 and $100.00 (in $79)
Due to the longitudinal feature of the PSID, I can de…ne job stayers as workers that remain in
the same job match. I construct one-year changes in hourly earnings for job stayers using worker
that remained in the same job match. Note that in the case that the job match is observed for
more than one year, I have the growth rate for the same individual in more than one time period.
In the CPS I only observe the growth rate of an individual once, when she is matched accross
two consecutive interviews. See appendix for details on the CPS and PSID samples.
24
worker-…rm match.
1819
I also look at unionized jobs, de…ned as jobs with wages
subject to collective bargaining. I separate jobs into four mutually exclusive groups:
workers in performance pay with no collective barganing, workers with collective
bargaining and no performance pay, workers not in performance pay or collective
bargaining, and workers in both collective bargaining and performance pay.
20
Table
3 presents mean hourly earnings instability for those four groups over the sample
period. Table 3 also presents t-statistics for di¤erences in mean instability between
18
As in the literature, I de…ne performance-pay jobs as employment relationships in which part
of the worker’s total compensation includes a variable pay component (bonus, a commission,
piece-rate) at least once during the course of the relationship.
The issue of measuring incidence of performance-pay in the beginning and end of the sample
arises. The classi…cation of jobs according to pay understates the fraction of performance pay
in the two end points of the sample. Conditional on job duration, a job is observed fewer times
at the two ends, thus it is less likely to display positive bonus, commission, or piece-rate. One
solution to this problem is to rebalance the sample using regression methods. As indicated in
Lemieux at al (2009), reweighting the sample does not a¤ect substantially incidence graphs or
regression results using performance pay dummies.
19
Tips are not included in the de…nition of performance pay jobs. Though they constitute a
form of incentive pay (done by the consumer and not the employer), the questions about form of
pay change over time in the PSID. For interview years 1976-1992, the question about pay refers
speci…cally to any amounts earned from bonuses, overtime, or commissions in addition to wages
and salaries earned. Starting with interview year 1993, there are separate questions about the
amounts earned in bonuses, commissions, tips, and overtime for the previous calendar year. For
the sake of comparability, overtime and tips are excluded from the de…nition of performance pay.
This procedure is likely to understate the incidence of performance pay jobs, and causes a bias
if the fraction of workers receiving tips is changing over time. Using the data starting in 1993, I
compare incidence of performance pay and size of incentive in terms of total wages between the
full sample and the sample without jobs reporting positive tips. I …nd no signi…cant change in
results.
20
The sample size is too small to calculate separate time trends for these subgroups. I choose to
pool all observations. I compute 'ca
[qI|
[) using growth rates in hourly earnings for each job
group. Results use PSID sampling weights.
25
groups.The results indicate that earnings instability is signi…cantly higher for non-
union performance pay jobs than for union non-performance pay jobs. For non-
union jobs there is no signi…cant di¤erence in instability between performance and
non-performance pay jobs. Union jobs display less variability than non-union jobs
regardless of whether performance pay is observed.
Mean di¤erences in wage instability can obscure the e¤ect of performance pay
and unions on volatility if performance pay or union status are correlated with
other factors that are potentially associated with instability. I use the following
regression exercise to net out the e¤ect of worker and job match characteristics as
well as conditions in the local labor market. I regress individual [q
it
[ on a dummy
for performance pay jobs and a dummy for collective bargaining. The control
variables used are worker …xed e¤ects, tenure, experience, year e¤ects, 1-digit oc-
cupation and industry dummies, unemployment at the county level and a measure
of 1-digit industry-level …rm instability.
21
The coe¢cients for the performance pay
dummy and union dummy are presented in Table 4. Column 1 presents results
without worker …xed e¤ects and characteristics. The dummy for unionized job is
negative and statistically di¤erent from zero. Colums 2 presents results including
worker …xed e¤ects and characteristics. Regression results in Column 2 indicate
21
Standard errors are clustered at the job match level. The data for …rm-level instability come
from DJHM (2006). See their paper for de…nitions of volatility and dispersion in …rm outcomes
and data construction.
26
that the e¤ect of performance pay on wage instability is positive when control
variables are included (column 2), but not when control variables are excluded
(column 1). The e¤ect of the union dummy is not statistically di¤erent from zero
once I include controls in the regression. This suggests that job stayers in perfor-
mance pay jobs have characteristics such as higher educational level and tenure
that decreases their wage instability. Nevertheless, the e¤ect of bonus or comission
on instability is positive.
Figure 8 displays the incidence of performance pay jobs in the PSID over time
for my sample period. It also shows the fraction of jobs that received a bonus,
commission or piece-rate in a given year, and the fraction of unionized jobs.
22
One
can see a clear rise in the incidence of performance pay jobs, which is accompanied
by a decline in unionization. A simple back-of-the-envelope calculation using the
average instability for each group over the period, and the change in incidence of
wage setting institutions from 1976 to 1996, gives an increase of 1.27% in hourly
eanings instability.
23
22
Note that not all performance pay jobs receive a bonus in a particular year. Performance pay
jobs are de…ned as jobs that get a bonus sometime during the job match.
23
In the back-of-the-envelope calculation I take the average value of wage instability in each
group, and weight each group by their fraction in the PSID sample in 1976 and 1996. The
di¤erence between the instability in the two time periods measures the portion of the increase in
wage instability due to a change in composition of wage schemes. I also estimate the time trend
coe¢cient for the regression on wage instability with the sample of job stayers in the PSID. The
total increase in wage instability the estimated time trend is 7.2%.
27
To summarize our results, the main message we take is that rising wage insta-
bility reached several segments of the labor market. This phenomenon is unlikely
to represent a …gment of the data, since the results are robust to di¤erent data
sources and methods. Nevertheless, aggregate measures mask large degrees of
heterogeneity between groups.
The change I report is more related to the behavior of earnings than hours.
While earnings instability is cyclical, especially for job movers/losers, the long-
term rising trend in instability cannot be due to increased transitions in and out
of unemployment. As discussed in the previous section, worker and job ‡ows seem
to be decreasing over the same period.
The most important result concerns job stayers in the March CPS. Those work-
ers do not report any major job transitions and are thus by de…nition in a "stable"
employment relationship. The fact that dispersion for this group displays a sub-
stantial trend increase gives more con…dence that the phenomenon of rising insta-
bility a¤ects ongoing employment relationships. Secular changes in mobility, skill
loss after displacement and demographic characteristics of the labor force could
still matter for instability. Nevertheless, given that the rise in hourly earnings
instability is large for job stayers, I choose to focus on the latter group for the
remainder of this paper.
28
Lastly, the exercise with the PSID indicates that jobs with some form of bonus
pay have higher wage instability than other jobs. This suggests that the formof pay
matters for wage instability outcomes. Based on that, I argue in the next section
that main mechanism driving the increase in earnings instability is an institutional
change in wage determination. The model is built upon this conjecture.
The dissertation proceeds as follows. The remainder of Chapter 1 discusses the
evidence on …rm and wage instability. Chapter 2 presents a model of performance
pay and unionized markets in order to tackle the diverging long run trends in
employment and wage instability. Chapter 3 presents a business cycle model of
performance pay with uncertainty shocks.
CHAPTER 2
Stable Firms and Unstable Wages
What I refer to as an institutional change in wage setting is a shorthand for a
series of events in the labor market that have happened in the past three decades:
less unionization, fewer restrictions on minimum wages, and more ‡exible pay
schemes attached to …rm and worker performance. Institutional changes have
been proposed as an explanation for the rise in wage inequality in the US. I argue
below that the same changes might help to explain increased earnings instability
of job stayers.
My conjecture is that there are two equilibria in wage setting institutions. The
…rst prevailed during the eighties, when monitoring worker productivity was too
costly and the wage had to be tied to job characteristics. The second is the current
labor market in which information technology has allowed for performance based
pay schemes. Some institutions naturally belong to the eighties steady-state, such
as minimum wages and unions. Performance pay is more related to recent events,
so can be identi…ed with the 2000’s model.
29
30
2.1. An island model of the labor market
I move below to a structural general equilibrium model of the labor market.
I start with an indirect search version of the Lucas and Prescott (1974) model of
frictional labor markets. That set up is used in several wage inequality and unem-
ployment studies (Jovanovic, 1987, Alvarez and Veracierto, 1999, Veracierto, 2008,
Kambourov and Manovskii, 2007). I choose to build on Alvarez and Veracierto
(1999).
I describe …rst the features of the environment that hold in all sectors of the
economy, regardeless of their choice of pay scheme. Then I proceed to discuss the
speci…c elements that apply to …rms that use performance pay contracts versus
those that use union/norm wage setting.
Environment:
There is a continuum of local labor markets dubbed islands that are separated
geographically. Islands are constantly hit by idiosyncratic productivity shocks and
movement of workers between islands requires one period of search.
Islands have an idiosyncratic productivity process, . that follows a Markov
process that can take values
1
<
2
< ... <
n
and has transition matrix Q(.
0
).
At the beginning of every period, each island is characterized by a pair (r
t
.
t
) where
r is the labor force and the current productivity shock. Accordingly, feasibility
31
in the market implies that q(r. ) _ r, where q(r. ) is employment, and the labor
force in the island evolves with the arrival of new agents from unemployment, l.
joining those that worked in the previous period, such that r
0
= l + q(r. ). The
employment rule and the Markov process for idiosyncratic productivity generate
an invariant distribution of islands over labor force and productivity given by
(A
0
.
0
) =
_
f(a,.):l+j(a,.)2A
0
g
Q(.
0
)(dr d).
There is a measure one of potential workers with linear preferences over con-
sumption, c
t
. I assume complete markets. The timing is such that after ob-
serving (r. ) and total compensation, n(q(r. ). ), workers decide on whether
to stay or leave their local labor market. Search is indirect, hence workers who
leave their market face one period of searching and arrive randomly next period
to a new island. Those who stay work at the given wage rate. I denote the
expected value of unemployment as c, and the expected value of employment
as ·(r. ). The agents problem is described by ·(r. ) = max¦c. n(q(r. ). ) +
,1
_
·(l + q(r. ).
0
)Q(. d
0
)¦, where agents take q(r. ) and the wage determi-
nation as given.
Each island has a continuum of producers that share a common island-speci…c
productivity shock. The production technology uses labor, q. e¤ort, c, and has
decreasing returns to scale, c, where 0 _ c _ 1 indexes the elasticity of output
32
with respect to q. Output is given by 1(q. ) = q
c
.I assume there are two types
of productive arrangments. In performance pay jobs the worker exerts positive
e¤ort and output is given by 1(q. ) = (1 + .c)q
c
, where c stands for worker
e¤ort and . is the marginal contribution of e¤ort to output. The performance pay
job uses monitoring and sets up a contract to de…ne compensation. In unionized
jobs e¤ort is zero and output is given by 1(q. ) = q
c
, which is equivalent to
setting . equal to zero.
1
Unions are the case when no monitoring technology is
used. We can interpret the productive arrangement in the unionized case as if the
worker exerts an "ordinary" level of e¤ort, which I normalize to zero. I denote the
marginal product of labor by ,(q. ) = (1 + .c)cq
c1
.
In equilibrium, employment in the island has to be consistent with individual
decisions. If ·(r. ) o, all individuals in the market are strictly better staying
than leaving, and q(r. ) = r. If ·(r. ) = o, agents are indi¤erent between staying
and leaving, and q(r. ) = q(), where q() solves c = n(q(). ) + ,1
_
·(l +
q().
0
)Q(. d
0
). Using q(r. ) = r if ·(r. ) o, and q(r. ) = q() if ·(r. ) = o,
in the agents problem we obtain the functional equation ·(r. ) = max¦c. n(r. )+
,1
_
·(l+q(r. ).
0
)Q(. d
0
)¦. The employment rule for this problem is such that
q(r. ) = min¦r. q()¦.
2
1
We can interpret the productive arrangement in the unionized case as the case that the worker
exerts an "ordinary" level of e¤ort, which I normalize to zero.
2
See Alvarez and Veracierto (1999) for a complete derivation of the problem.
33
I model below two types of labor markets according to their wage setting insti-
tutions: markets with only performance pay jobs and markets with only unionized
jobs. Both market types are in the same framework, but di¤er on how total com-
pensation or the wage rate is determined.
Wage setting in performance pay markets: The performance pay model I use
is based on Baker, Gibbons and Murphy (1994). I extend the baseline set up in
the island model in order to include an e¤ect of worker choice of e¤ort on output
outcomes. Assume that the marginal contribution of worker e¤ort to …rm output
is given by :. Wage contracts between …rms and workers cannot be written on :,
since it is too complex to be objectively assessed. However, there is a veri…able
performance measure, 1, which is an imperfect measure of :. In order to simplify
notation, assume that : can only take values of .q
c
or 0, and 1 can take values
of .q
c
or 0. The …rm observes 1 and :, but only 1 is contractible.
At each period, the worker can choose an action that stochastically determines
both output and performance. The relationship between worker e¤ort, c, and
the …rm’s outcome is such that Pr o/
= .qc
[ c) = c, where c is between 0
and 1. The probability of observing a positive performance measure is given by
Pr o/(1 = .q
c
[ c) = jc, where j is a random variable with mean 1(j) and
variance ·c: (j), bounded above so that Pr o/(1 = .q
c
[ c) _ 1. We can think of
j as the di¤erence between the e¤ect of e¤ort on performance and output. There
34
are states of world when j is large and high e¤ort contributes more to performance
measures than to the value of the …rm. When j is small, we have the opposite
case, and high e¤ort would likely generate large value for the …rm, but would not
increase performance measures. I assume that …rms do not know j, while workers
observe j after deciding whether to stay on the island, but prior to choosing e¤ort.
From the viewpoint of the …rm and the worker, e¤ort and bonus are stochastic
prior to the realization of j. The problem of the …rm is to o¤er a compensation
package prior to the realization of j that aligns e¤ort to productivity, and the
problem of the worker is to choose the optimal level of e¤ort once j is realized.
The sequence of events is such that …rms and workers start the period knowing
the state of the economy (r. ). and the variance and mean of j. At the island
level there is a spot market for binding wage contracts. The assumption of binding
contracts is common in the literature, since revelation of j to the worker and worker
e¤ort can be thought of as occurring simultaneously. The contracts estipulate a
base pay, and a bonus paid in case a positive performance measure is observed.
More speci…cally, the pay scheme o¤ers a base pay, n(r. ), and a bonus, 1, paid
if 1 = .q
c
.
The …rm takes the base pay as given and decides on the size of the bonus
and employment. The worker then decides whether to take the contract or not.
After hiring takes place, the worker observes j and chooses e¤ort. The worker is
35
privately informed about j, hence the …rm has to o¤er a compensation scheme
based on the expected value of j and the schedule for the worker’s optimal choice
of e¤ort. Before observing j, the expected value of the bonus for the worker is
given by 1
j
[jc
1]. Exerting e¤ort is costly for the worker. I assume that the
disutility caused by the e¤ort level c equals ¸c
2
. I also assume that j is iid and
that the …rm and the worker are atomistic, taking the base pay as given.
Worker problem:
The Bellman equation for the worker is given by:
(2.1)
·
j
(r. ) = max¦c. 1
j
[max
o
n(r. )+jc1÷¸c
2
+,1
_
·
j
(l
j
+q(r. ).
0
)Q(. d
0
)]¦
The choice of e¤ort and bonus is then equivalent to a one period game between
the worker and the …rm. Optimal e¤ort maximizes the current return from working
and is equal to c
=
j1
2¸
.
The worker accepts the performance pay job only if it gives an expected value
higher than searching. The worker choice of taking the job or searching gives the
minimum base pay that clears the local market:
36
(2.2) 1
j
[max
o
n(r. ) + jc1 ÷¸c
2
+ ,1
_
·
j
(l
j
+ q(r. ).
0
)Q(. d
0
)]¦ _ c
(2.3) n(r. ) _ 1
j
[c ÷(jc
1 ÷¸c
2
+ ,1
_
·
j
(l + q(r. ).
0
)Q(. d
0
))]
Firm problem:
The technology is such that 1
j
[1(q. )] = 1
j
[(1 +.c)q
c
]. On average, worker
e¤ort increases output by 1
j
[.cq
c
]. The …rm problem is to choose 1 and q to
maximize pro…ts taking into account the incentive constraint for the worker:
: = max
1,j
1
j
[(1 + .c
)q
c
÷nq ÷jc
1q] (2.4)
s.t. c
=
j1
2¸
(2.5)
The …rst order conditions are as follows:
(2.6) 1 : 1
j
[.
j
2¸
q
c
÷
j
2
1
¸
q] = 0
37
(2.7) q : 1
j
[(1 + .
j1
2¸
)cq
c1
÷n ÷
j
2
1
2
2¸
] = 0
The …rst order conditions imply:
(2.8) 1
=
.
2
1
j
[jq
c
]
1
j
[j
2
q]
(2.9) n = 1
j
[(1 + .
j1
2¸
)cq
c1
÷
j
2
1
2
2¸
]
From (10), …rms pay the expected bene…t of e¤ort upfront in the form of base
pay, .
j1
2¸
cq
c1
÷
j
2
1
2
2¸
. After the worker observes j, she chooses optimal e¤ort.
Equilibrium employment:
The base pay that clears the market depends on supply and demand for labor.
3
Using (4) and (10), we have:
3
See appendix for the derivation of performance pay market equilibrium conditions.
38
(2.10)
n = 1
j
[(1+.
j1
2¸
)cq
c1
÷
j
2
1
2
2¸
] _ 1
j
[c÷(jc
1
÷¸c
2
+,1
_
·
j
(l+q(r. ).
0
)Q(. d
0
))]
which can be rearranged as follows:
(2.11) 1
j
[cq
c1
+ (c
.cq
c1
÷¸c
2
) + ,1
_
·
j
(l + q.
0
)Q(. d
0
)] _ c
In (12), the expected net bene…t of e¤ort is given by the second term in paren-
theses, c
.cq
c1
÷ ¸c
2
. The …rst best would be for the worker to exert e¤ort
until the marginal cost equals marginal bene…t, or c
11
=
¸.cj
1
2¸
, independently of
j. Because the worker is privately informed on e¤ort and j, this outcome cannot
be achieved, and e¤ort is given by c
=
j1
2¸
.
4
4
Note that the expected bene…t of e¤ort is quadratic in e¤ort. The …rm and the worker achieve
the maximum bene…t in the a
J1
case. The two extreme cases are when e¤ort is zero, and there is
no probability of positive performance or value; and when a=
o¸¸
1
~
, and the worker is exerting
too much e¤ort in order to increase the chances of receiving a bonus. Note that the existence of a
perfect performance measure allows for the implementation of the …rst best. Assume without loss
of generality that ·ar(j) = 0, c = 1,2, and j = 1, but output is not contractible. The worker
chooses e¤ort to maximize the current return n + a/ ÷ ¸a
2
. Using the fact that in this case
n = (1+¸a)c-q
o1
÷a/, we have that a
=
¸o:¸
1
2~
, which implies a
= a
J1
. This is a standard
result in contract theory. Given the preference assumptions, whenever there is a performance
measure that responds to e¤ort in the same way that output respondes to e¤ort, the …rst best
can be implemented (see Baker, 1992).
39
Next consider the optimal bonus choice and the base pay. Since the size of
the bonus and employment are decided before the realization of j. the …rm can
treat j as independent of q. so that the optimal bonus can be simpli…ed as 1
=
1[¸
2
.j
]
1[
2
j]
=
¸
2
1[j].j
1
[1[j]
2
+·ov(j)]
. When idiosyncratic productivity is high or the labor
force in the island is low, it pays for both sides of the market to increase the bonus
and e¤ort. The bonus is thus sensitive to local labor market conditions. In a
similar fashion, for high values of the marginal contribution of e¤ort to output
., performance pay is a more productive arrangement, and the bonus increases.
Also, the higher the variance of the objective measure of performance, the smaller
the optimal bonus and the smaller the e¤ect of productivity on pay. When j
has higher variance, the performance measure is a noisier signal of the actual
worker contribution to output and the …rm has to settle for weak incentives. Weak
incentives then induce a smaller e¤ort choice by the worker. The converse is true
when the variance of j is low. In this case, the …rm can provide a strong incentive
using the bonus.
The variance of j has a similar e¤ect on base pay. Substituting the optimal
bonus into the …rm …rst order condition in equation (10) yields:
(2.12) n = cq
c1
+
1
4¸
1
j
[j]
2
(.q
c1
)
2
(1
j
[j]
2
+ ·c
j))_
c ÷
1
2
_
40
The use of incentive pay based on performance a¤ects the marginal product
of labor and the base pay. The base pay is decreasing in ·c
j) if c 1
2
.
5
The
intuition is the same as in the case of the optimal bonus. When 1 is a noisy
signal of the contribution of e¤ort to outcomes, the optimal level of e¤ort and
the marginal value of labor are low, which decreases not only the odds of having
a positive realization of 1 but the base pay that clears the market. Note that,
neglecting the participation constraint, pro…ts are quadratic in bonus. Optimal
bonus level is given by 1
=
¸
2c
1[j].cj
1
1[j
2
]
=
1
2c
1[j]
1[j
2
]
1
11
, where 11 denotes …rst
best. The coe…cient
1
2c
1[j]
1[j
2
]
is the distortion brought by the performance measure.
For the case that c = 1,2, the …rms does not need to compensate the worker in
the base pay with the expected marginal return to e¤ort. The …rm can o¤er a base
pay cq
c1
, and a bonus
1[j]
1[j
2
]
1
11
with probability jc. This case is equivalent
to o¤ering a piece rate on a performance measure scaled to the expected marginal
vale of e¤ort in the marginal revenue. As the performance measure becomes a
5
Note that the expected bene…t of e¤ort is quadratic in e¤ort. The …rm and the worker achieve
the maximum bene…t in the a
J1
case. The two extreme cases are when e¤ort is zero, and there is
no probability of positive performance or value; and when a=
o¸¸
1
~
, and the worker is exerting
too much e¤ort in order to increase the chances of receiving a bonus. Note that the existence of a
perfect performance measure allows for the implementation of the …rst best. Assume without loss
of generality that ·ar(j) = 0, c = 1,2, and j = 1, but output is not contractible. The worker
chooses e¤ort to maximize the current return n + a/ ÷ ¸a
2
. Using the fact that in this case
n = (1+¸a)c-q
o1
÷a/, we have that a
=
¸o:¸
1
2~
, which implies a
= a
J1
. This is a standard
result in contract theory. Given the preference assumptions, whenever there is a performance
measure that responds to e¤ort in the same way that output respondes to e¤ort, the …rst best
can be implemented (see Baker, 1992).
41
perfect signal of the e¤ect of e¤ort on output (1
j
[j] ÷ 1 and 1
j
[j
2
] ÷ 1), we
approach the …rst best, which is o¤ering a piece rate of one. For c 1,2, e¤ort is
very productive. In order to induce e¤ort variation the worker receives more than
cq
c1
in the base pay. The …rm then sinks 1
j
[.ccq
c1
÷jc1] in the base pay
and o¤ers a piece rate smaller than one on the scaled performance measure.
The cuto¤ rule for the level of employment that clears the local market in each
island depends on the expected payo¤ of working under a performance pay regime.
If ·
j
(r. ) c, all workers stay and q = r. Otherwise we have that employment
at the island level solves:
(2.13) 1
j
[cq
c1
+ (c
.cq
c1
÷¸c
2
) + ,1
_
·
j
(l + q.
0
)Q(. d
0
)] = c
which can be rearranged as follows:
cq
c1
+
.
2
4¸
1
j
[j]
2
(q
c1
)
2
(1
j
[j]
2
+ ·c
j))_
c ÷
1
4
_
+ ,1
_
·
j
(l + q
.
0
)Q(. d
0
) = c
Whenever c
1
4
, the expected value of working is decreasing in the variance
of the performance measure. The less noisy the performance measure, the easier
42
it is to align e¤ort to idiosyncratic conditions in the market. Moreover, an in-
crease in the return to e¤ort, ., leads to a higher expected value of working under
performance pay.
Note that an improvement in monitoring technology represented by either a
smaller ·c
j) or a higher ., raises welfare in the economy. The current return toworking in a performance pay job is given by 1
j
[n + c1j ÷¸c
2
] . Substituting the
optimal choice of e¤ort in the previous equation yields 1
j
_
n +
j1
2¸
1j ÷¸
_
j1
2¸
_
2
_
=
1
j
_
n +
j
2
1
2
2¸
÷
j
2
1
2
4¸
_
= 1
j
_
n +
j
2
1
2
4¸
_
. Since both terms inside the brackets are
decreasing in ·c
j),6
the expected value of working increases with improved tech-
nology. This e¤ect in general equilibrium raises the reservation wage of unemployed
workers and the value of non-employment, c. The value to the worker of the in-
crease in the bonus outweights the utility cost of the increase in e¤ort.
The goal of the simulation exercise presented in the next section is to evaluate
whether the improvement in the technology of compensation translates into more
wage instability. In order to build intuition on the results, let’s look in partial
equilibrium at the expected current return of working under performance pay.
Denote \
o.
the variance of the marginal product of e¤ort on output with respect
to the productivity shock, and ·c
) the variance of the idiosyncratic shock. \o.
=
6 µ
2
1
2
4~
=
µ
2
4~
2
_
¸
2
J[µ]:¸
1
(J[µ]
2
+uo
µ))_
2
=
¸
2
16~
1
µ
[j
2
]
(J[µ]:¸
1
)
2
(J[µ]
2
+uo
µ))2
=
¸
2
16~
J[µ]
2
¸1
)
2
(J[µ]
2
+uo
µ))43
(.q
c
)
2
·c
) is increasing in .. Better technology in performance pay means thatthe worker has more valuable information on how her e¤ort a¤ects the output.
This is a standard result in linear performance pay contracts (Baker, 1992). More
information for the worker indicates that she can alter signi…cantly e¤ort in order
to a¤ect output. The …rm wants the worker to use that information to improve
outcomes, and gives higher incentives to generate more e¤ort variation. Since
e¤ort variation is costly, the …rm has to compensate the worker in the base pay,
n = 1
j
[(1 +.c
)cq
c1
÷j1c
]. The higher e¤ort variation induces higher wage
instability by making the base pay more responsive to idiosyncratic shocks. In
partial equilibrium, the variance of n with respect to in equation (12) increases
with improvement in technology.
7
Note that this is an optimal behavior, and the
improvement in technology raises the overall return of working under performance
pay.
Value of unemployment:
7
Assume that - follows and AR(1) with autorregressive coe¢cient j, mean zero, and variance of
the innovation o
2
. Then ·ar
= ·ar(-cqo1
+
1
4~
J[µ]
2
(¸:¸
1
)
2
(J[µ]
2
+uo
µ))_
c ÷
1
2
_
) =
_
cq
o1
_
2
·ar(-) +
2
_
1
4~
J[µ]
2
(¸¸
1
)
2
(J[µ]
2
+uo
µ))_
c ÷
1
2
_
c
2
1¡
2
_
. In partial equilibrium, the variance of wages with respect to
the idiosyncratic shock increases with improvement in the technology of performance pay. The
variance of wages captures the increase in e¤ort variation for higher ¸ or lower ·ar(j). Note that
the variance of wages is increasing in the variance of the innovation to -. There are two ways that
the variance of wages can increase: either the shock process is more volatile, or the parameters
¸ and ·ar(j) change such that there is an improvement in performance pay technology.
44
In the case that only one type of pay scheme exists, the value of unemployment
is such that workers who leave their market receive the expected value of arriving
anywhere in the invariant distribution,
j
(dr d), of performance pay markets.
(2.14) c = ,
_
·(r. )
j
j
(dr d)¦
Equilibrium of the model with performance pay. The competitive equilibrium
is a set of prices (1, n), allocations q, functions ·
j
(r. ), e¤ort level c, numbers
c. and l. and invariant distributions,
j
(dr. d) such that:
1) c and 1 satisfy the …rm and worker problem:
(2.15) c
=
j1
2¸
(2.16) 1
=
.
2
1
j
[jq
c
]
1
j
[j
2
q]
=
.
2
1
j
[j]q
c1
[1
j
[j]
2
+ ·c
j)]2) ·
j
(r. ) is given by:
(2.17)
·
j
(r. ) = max¦c. 1
j
[max
o
n(r. ) +jc1÷¸c
2
+,1
_
·
j
(l +q(r. ).
0
)Q(. d
0
)]¦
45
3) In performance pay markets, q(r. ) satis…es
q : 1
j
[(1 + .
j1
2¸
)cq
c1
÷n ÷
j
2
1
2
2¸
] = 0
and n satis…es
n = cq
c1
+
1
4¸
1
j
[j]
2
(.q
c1
)
2
(1
j
[j]
2
+ ·c
j))_
c ÷
1
2
_
Employment at the island level satis…es feasibility 0 _ q _ r, and is consistent
with individual decisions. Two cases can occur:
i) if 1
j
[n(r. ) + jc
1
÷ ¸c
2
+ ,1
_
·
j
(l + q(r. ).
0
)Q(. d
0
)] c, then
q = r and wages are given by the FOC of the …rm:
n = 1
j
[(1 + .
j1
2¸
)cr
c1
÷
j
2
1
2
2¸
]
ii) if 1
j
[n(r. ) + jc
1
÷¸c
2
+ ,1
_
·
j
(l
j
+ q(r. ).
0
)Q(. d
0
)] = c, then
wages are given by the FOC of the …rm:
n = 1
j
[(1 + .
j1
2¸
)cq
c1
÷
j
2
1
2
2¸
]
where q satis…es:
46
cq
c1
+
.
2
4¸
1
j
[j]
2
(q
c1
)
2
(1
j
[j]
2
+ ·c
j))_
c ÷
1
4
_
+ ,1
_
·
j
(l + q.
0
)Q(. d
0
) = c
The numbers c and l, and the invariant distribution
j
satisfy:
c = ,
_
\
j
j(dr. d)
l = 1 ÷
_
q(r. )
j
(dr d)
j
(1
0
.
0
) =
_
f(a,.):l+j(a,.)2A
0
g
Q(.
0
)
j
(dr d)
The de…nition of competitive equilibrium for the unionized sector is analogous.
Wage setting in unionized markets. The union can be thought of working in the
following fashion: for each level of idiosyncratic productivity, a minimum level of
pay, n(), is established for workers that stay in unionized islands.
8
The contract
is such that in unionized jobs the level of e¤ort is constant, which I normalize
to zero, and output is given by q
c
. Wages equal the marginal product of labor,
n = cq
c1
. When the minimum pay binds, employment is such that n() =
8
See Alvarez and Shimer, 2008, for a model in which the union chooses the minimum pay to
maximize the present discounted value of unionized workers. I assume that the minimum is
exogenous and calibrate it to reproduce plausible levels of the union wage premium.
47
,(q(). ), where q() is the maximum level of employment for idiosyncratic shock
level , given the minimum wage and …rm optimization.
In the case that r < q(), the minimum pay constraint does not bind and
workers decide between receiving spot wages in their market or searching.
(2.18) ·
&
(r. ) = max¦n + ,
_
·
&
(l + q.
0
)Q(. d
0
). c¦
In the case that q() < r. either some workers leave until the point that
·
&
(r. ) = c and the minimum constraint does not bind, or the constraint binds
and a fraction of workers is forced to search, so that n() = n. A lottery assigns
workers to either searching or working in the last case. Workers that search receive
the expected value of unemployment, c
&
.
The Bellman equation when q() < r is given by:
(2.19) ·
&
(r. ) = max¦
r ÷q
r
c +
q
r
_
n() + ,
_
·
&
(l + q. ).
0
)Q(. d
0
)
_
. c¦
where q() is such that ,(q(). ) = n().
aj
a
is the probability of searching,
and
j
a
is the probability of staying.
Value of unemployment:
48
The value of unemployment under union wage setting is de…ned as the expected
value of arriving anywhere in the invariant distribution,
&
(dr d), of unionized
markets.
c = ,
_
·
&
(r. )
&
(dr d)¦
2.2. Simulation results
2.2.1. Calibration and moments to match
In this section, I address whether a model that matches the changes in wage setting
institutions observed in the US economy can generate the observed decline in job
and worker ‡ows and the observed increase in volatility in wages. Table 5 presents
parameter values and labor market moments that help discipline the calibration of
the model. The ultimate test of the model is its ability to reproduce the moments
in Table 7, namely the increase in the mean dispersion of wages and the decline in
the standard deviation of the employment growth rate, using only changes in the
technology of compensation in the economy.
9
9
The value for the increase in wage instability comes from the calculations in Table 1 for the
sample of job stayers. The value of the decrease in employment instability comes from the LBD
for the sample of continuing business.
49
As is standard in the literature, I assume that the idiosyncratic shock process
follows an ¹1(1), such that |
t+1
) =
1 ÷ j) + j ln(t
) + c
t+1
, where c
t+1
~
`(0.
2
c
). I approximate this AR(1) using a discrete Markov process with the
Tauchen (1986) method. The variance in the innovation to productivity is directly
linked to the volatility of employment and wages in the model. There is no closed
form solution relating the shock process to moments in the model. I calibrate the
parameters of the shock process so that it matches the levels of unemployment
and job reallocation in Table 6. The value of the standard deviation of labor
productivity estimated from plant-level data is around .5 (Syverson, 2003). Also,
the standard deviation of the innovation to the idiosyncratic component of …rm
pro…tability estimated in search models is around .22 (Cooper et al, 2007). The
excess job reallocation rate in the BED data is around .14 in the early 2000s. The
average unemployment rate reported by the BLS during the same period is around
5.5%. The time period in the model is equivalent to 3 months and the discount rate
corresponds to an annual interest rate of 4%. The labor share in the production
function is the value implicit in the NIPA accounts.
I calibrate the private information process and the cost and returns to e¤ort
as follows. I assume that j comes from a symmetric 1ctc(j. j)
10
distribution
10
I use j = .25 in order to match the moments of the bonus in the simulated data with values
obtained from the PSID in the late nineties. In later simulation exercises I use j in the [.05 .25]
range in order to check the sensitivity of the bonus moments to this parameter.
50
with mean 1(j) and variance \ c
j). The range of j is such that for a givendraw of the private information and resulting optimal e¤ort level, we have that
j
/(1 = .qc
[ c
)=jc
_ 1, and c
= j1
,2¸ is in the interval [0. 1]. The
payment of the bonus comes from a Bernoulli trial with probability of success jc
.
For each successful draw of the Bernoulli distribution I include the optimal bonus
in the total compensation. The size, variance, and incidence of the bonus in the
model depend on how productive the performance pay arrangement is.
11
I choose
.. ¸ and 1ctc(j. j) such that the moments of the bonus paid in the simulation are
close to their levels in the PSID for the group of performance pay jobs. As in the
literature, I calculate the bonus pay as the sum of earnings received in the form
of tips, commission, piece-rate or bonus. The size of the bonus pay is the ratio
of the bonus pay to total earnings in a given year. The incidence of bonus pay is
the number of jobs that received a bonus in a given year over the total number
of jobs classi…ed as performance pay. I calculate the size and incidence of bonus
in each year and …nd that both values present a trend increase, consistent with
11
As in the literature, I calculate the bonus pay as the sum of earnings received in the form
commission, piece-rate or bonus. The size of the bonus pay is the ratio of the bonus pay to
total earnings in a given year. The incidence of bonus pay is the number of jobs that received a
bonus in a given year over the total number of jobs classi…ed as performance pay. The standard
deviation is the cross section standard deviation of bonus. I calculate the size and incidence
of bonus in each year and …nd that both values present a trend increase, consistent with my
hyphotesis that the performance pay technology has improved over this time period. See Figure
10 for trend increase in the bonus size.
51
my hyphotesis that the performance pay technology has improved over this time
period. I present in Table 5 the incidence, variance and size of the bonus payment
estimated using PSID data from 1993 to 1998. Table 6 shows the moments to
match in the data and their values in the simulated performance pay model.
The employment and earnings instability measures are computed by simulating
a panel of islands in the economy. I compute cross section dispersion measures
across islands. The goal of the simulation exercise is to reproduce the moments in
Table 7 by changing the technology of compensation, represented by parameters
of the private information process j, and the return to e¤ort ..
In table 8, I compare the predictions of three island models: a model with
performance pay markets; a model with only unionized markets; and a "baseline"
model in which wages are equal to the marginal product of labor in all states of
the world, and in which e¤ort is normalized to zero, so that ,(. r) = q
c
and
n(. r) = cq
c1
. I keep the underlying idiosyncratic shock process constant and
calculate the same moments using the baseline, performance pay, and the "union"
model.
12
In the "union" model I set the lower bound for wages so that the average
12
The size and incidence of the bonus in the PSID in 1998 are respectively 0.057 and .1705.
Note that the model simulation produces quarterly data. I aggregate wage and bonus payments
in the simulated data in order to compare them with the annual data in the CPS and PSID.
The LBD data are also annual. In Table 8 I calculate the standard deviation of percent change
in employment considering time aggregation. Time aggregation does not a¤ect the results for
employment instability, but it makes simulated data comparable to the LBD.
52
wage in the economy reproduces the observed union wage premium when compared
to the performance pay model.
13
The unionized and performance pay models use
the wage determination described in the previous section.
The …rst thing to note is that wage instability is higher and employment in-
stability is lower under the performance pay model compared to the union model.
These results hold using either mean absolute changes or the cross section stan-
dard deviation of percent changes as the measure of dispersion. Note that the
idiosyncratic productivity process is held …xed across the three models. Moreover,
since the bonus constitutes a small fraction of total compensation, the di¤erence
in wage instability is not an artifact of introducing uncertainty with respect to the
bonus pay. The use of incentives also a¤ects the employment margin. Employment
instability is lower under performance pay, suggesting that under this wage setting
arrangement it is easier to adjust the employment margin. Intuitively, under per-
formance pay, the …rm can adjust the base wage downward when productivity is
lower, but cannot do so under unions.
Table 8 contains polar cases with the economy operating under only one type
of compensation scheme. A more realistic model would allow for unionized and
performance pay jobs to coexist. In such a model, technological advance in the
13
See Newmark and Kawaguchi (2001) for estimates of union wage premium with the March
CPS.
53
form of higher . or lower ·c
j) would relocate workers to the performance paysector. I plan to explore such a model in future drafts.
In Table 9 I present simulation results for the case in which only performance
pay is used. I change the technology of private information and the return to e¤ort
such that the variance of j decreases and the return to e¤ort increases. Note that
Beta (1,1) is a mean preserving spread of Beta (4,4), which in turn is a mean
preserving spread of Beta (6,6). As expected, the instability of wages is higher for
Beta (6,6) and when . is equal to .25. The technology of compensation can a¤ect
the wage instability in two ways. First, through the bonus payment. Since the size
of the bonus is higher when the performance pay arrangement is more productive
with higher ., the level of e¤ort and the probability of receiving a bonus are also
higher. More productive islands will o¤er a higher likelihood of receiving bonus
pay and the cross section of wage growth outcomes will become more dispersed.
Second, as discussed in the previous section, improvement in technology makes the
base pay more responsive to the idiosyncratic shock. Better technology increases
optimal e¤ort variation, which is compensated in the base pay. The increase in
. is isomorphic to a model with a physical cost of setting up a performance pay
arrangement, and represents better monitoring technology.
14
14
See appendix for the case of positive monitoring cost.
54
Though . is a free parameter, there is some discipline in this exercise: the
natural boundary of the parameters is imposed by j
/(1 = .qc
[ c
)=jc
_ 1.
The parameters of performance pay productivity cannot be increased above the
range in which the probability of receiving a bonus is smaller than one. Also,
higher . increases the mean, variance and incidence of bonus. For the case that
. equals .25, I reproduce a empirically reasonable size and incidence of the bonus
pay in the late nineties.
We can now compare the simulation results with the …rm and wage instability
changes in the data reported in Table 7. If the economy moves from unionization
to performance pay adoption the wage instability increases by .019, and the …rm
instability decreases by 0.040 in the model simulations. These results represent
one fourth of the observed increase in wage instability and nearly all the decrease
in …rm instability in the data.
2.2.2. Last Remarks
This paper studies the relationship between recent trends in earnings and employ-
ment volatility. Evidence from a variety of sources indicates that both …rm level
instability and aggregate measures of job and worker ‡ows have declined during
55
the 1976-2007 period, while measures of earnings instability from the March CPS
rose over this period. The increase in wage instability in the March CPS is greater
for job stayers than for job movers/losers and for the overall sample of private non
farm workers. This result suggests that changes inside employment relationships
contributed to the rise in earnings volatility. I also measure wage instability for
job stayers in the PSID from 1976 to 1996. I …nd that wage instability is higher
for jobs that receive some form of bonus or commission.
I argue that technological change in compensation schemes has allowed …rms to
adjust wages more easily in response to idiosyncratic shocks, instead of hiring and
…ring workers. I illustrate this phenomenon in a general equilibrium search model
in which total compensation depends on a performance measure. A decrease in the
cost of monitoring workers is equivalent to a technological change in compensation.
The outcome of the new technology in wage setting is that wages are more aligned
to productivity, which implies higher earnings instability and lower employment
instability.
56
The exploration of more sophisticated monitoring technologies and productive
arrangements, and modelling coexistence of di¤erent pay schemes in the economy,
are left for future research.
15
15
An useful extension of theory would be to consider model with both technologies operating over
time and endogenous switching between types. Assume that workers can direct search towards a
type of market. Though they cannot choose a speci…c island to go, they can decide on whether
to move to the unionized or the performance pay sector. They bear the same cost of searching,
which is one period of forgone labor earnings.
Let’s consider the case when the two types of wage settings coexist in the economy. The problem
of the worker in a performance pay job is the same as before:
\
¡
(r, -) = max¦c, 1
µ
[max
o
n(r, -) + ja1 ÷¸a
2
+ ,1
_
·
¡
(l
¡
+ q, -
0
)Q(-, d-
0
)]¦
The problem of the worker in the unionized sector is analogous:
\
u
(r, -) = max¦c, n(r, -) + ,1
_
\
u
(l
¡
+ q, -
0
)Q(-, d-
0
)¦
The value of unemployment now takes into account that the worker can direct search to markets:
c = max¦,1
_
\
¡
(l + q, -)j
¡
(dr d-)), ,1
_
\
u
(l + q, -
0
)j
u
(dr d-)¦
When the variance of j decreases or ¸ increases, \
u
increases, which sustains a higher value
of searching. Unemployed workers increase their reservation wage and the marginal product
must increase in unionized islands. In an equilibrium with positive unemployment workers must
relocate from unionized to performance pay markets.
.
CHAPTER 3
Uncertainty in Employment Relationships and the
Business Cycle
Several recent papers have raised the question of whether uncertainty a¤ects
the business cycle. Aggregate and …rm level uncertainty have been shown em-
pirically to behave countercyclically. Bloom (2009) reports various measures of
…rm employment and stock value instability, all which vary negatively with the
cycle. On the household side, Storesletten et al (2004) present evidence with the
PSID that idiosyncratic labor income risk has a variance that increases by 75%
as the economy moves from peak to trough. Recessions are periods with higher
turnover. Figure 7 presents a measure of total earnings instability
1
for workers
in the Matched March CPS that experience some form of unemployment or job
change. Earnings instability is hump shaped during economic downturns.
2
Figure
9, from Bloom (2009), presents the Chicago Board of Exchange (CBOE) index of
1
I measure instability as the cross-section weighted average of absolute growth rates. This mea-
sure is analogous to the excess job reallocation rate calculated at the …rm level.
2
A previous literature on job ‡ows has raised the hyphotesis that ‡uctuations in the intensity
of shifts in employment opportunities across establishments a¤ects business cycle dynamics. See
Davis et al, 1990.
57
58
market volatility calculated using volatility of index option prices. One can see
a clear spike in the period corresponding to the recent credit crunch. The index
is supposed to represent market expectations of volatility in stock prices, and it
increases in all major periods of economic turmoil such as the two oil shocks, and
the Black Monday. In Table 14 I present evidence on the cyclicality of uncertainty.
The dependent variable is stock marlet volatility measured with variance of option
prices in the Chicago Board of Exchange. The …rst three regressions come from
Bloom (2009) and use as independent variables measures of cross section standard
deviation of …rm pro…t growth, …rm stock return, and industry TFP growth. The
last regression uses monthly unemployment rate from the CPS. All measures are
positively correlated with the uncertainty series from the CBOE.
In this work, I address the question of whether more information at the em-
ployment relationship level is consistent with more uncertainty in recessions, and
particularly in the current downturn. The literature so far has focused on model-
ing this evidence as re‡ecting time varying variance in productivity. Models with
time varying variance correctly produce countercyclical uncertainty. Nevertheless,
anecdotal evidence has shown that the revolution in information technology has de-
creased the level of uncertainty in employment relationships, bringing the question
of how information and uncertainty interact with the cycle. The current papers on
uncertainty and the business cycle focus on two types of e¤ects: 1) change in the
59
real option value of investment and hiring (Bloom, 2009); and, 2) uncertainty as
bad news predicting low productivity in the future (Bachmann and Bayer, 2009).
I suggest a third mechanism in which uncertainty a¤ects the value of employment
by changing incentives and e¤ort in contracts. Uncertainty decreases the value of
a job by making it harder to assess outcomes, or by increasing the noise in the
principal-agent problem in the economy. There are two types of uncertainty in
the literature. The …rst is used in Bachman and Bayer (2009) and Bloom (2009).
Uncertainty in their case is represented by changes in the cross-sectional dispersion
of …rm-speci…c Solow residual innovarions (variance in TFP). This is related to the
idea that the economy is not only hit by TFP level shocks, but the the variance of
TFP also changes stochastically over time. In terms of modeling choice, the paper
closer to my set up is den Haan and Kaltenbrunner (2005), who also use search
and matching frictions in the labor market. In deen Han and Kaltenbrunner the
amount of vacancy posting depends on expectations of futute productivity. There
is a regime switching between periods of higher and lower productivity growth.
Recessions then coincide with expectations of lower productivitity growth in the
future and a¤ect hiring in the present. I suggest a third mechanism that uses the
wage setting in performance pay markets. In those markets there is private infor-
mation in terms of the e¤ect of worker e¤ort on productivity. I model a second
moment shock as time varying variance in the private information process. When
60
futute pro…ts are expected to be higher due to relaxing the private information
problem (lower variance of the private information process), more vacancies are
posted. The private information determines e¤ort, which enters the production
function. Hence, changes in the private information process work indirectly as
changes in the total factor productivity including e¤ort as an imput. There is not
direct evidence of uncertainty in information. Nevertheless, measures of volatility
in variance of stock options and in standard deviation of GDP forecasts from the
Philadelphia Federal Reserve Bank’s biannual Livingstone survey are both counter-
cyclical. On the household side, variance of income and measures of cross-section
earnings instability covarie positively with unemployment.
I advance a theory of recessions that does not rely on the assumption of time
varying variance of productivity. I use in the model a di¤erent level of uncertainty
that relies on time varying quality of information in employment contracts. More
speci…cally, I model a type of incentive that has increased in relevance in the US
economy: performance pay contracts. Figure 2 has the fraction of jobs in the PSID
among male heads of the household that receive some form of incentive pay. The
proportional of jobs that receive bonus, commission or piece-rate has increased
steadily since the late 70’. The bene…ts of using performance pay contracts are
twofold. First, I reproduce in the model simulation moments of the data that can
discipline calibration by using the evidence on bonus pay and cyclicality in the
61
PSID as a benchmark. Second, the contract produces a direct link between uncer-
tainty in information in employment relationships and turnover. This relationship
allows for evaluating the e¤ect of uncertainty on business cycles.
The way the model works is as follows. There are search frictions in the econ-
omy. The representative …rm decides on which employment matches to retain
looking at aggregate shocks and the distribution of uncertainty shocks. The wage
rate in job matches is de…ned by a contract that establishes a base pay and a bonus
paid in case positive performance is observed. The worker has private knowledge
on how she can a¤ect both output and measured performance through e¤ort choice.
The …rm does not observe e¤ort and cannot contract on output. Hence the need
of a performance pay contract to give incentives for the worker to exert more e¤ort
in high states of the world.
The source of uncertainty is the process that gives the private information
held by the workers. I assume that the process that gives the private informa-
tion has time varying variance. Recessions are periods when the variance of the
private information process is high. Hence economic downturns are characterized
by higher di¢culty in assessing the value of employment relationships. The un-
certainty in information can function as a propagation mechanism in the model
by exacerbating the standard e¤ect of the decline in productive during recessions.
Since higher variance in private information decreases the value of employment
62
contracts, the …rm decreases hiring and we have unemployment commoving with
variance in information. In the limit, if there is no variance in the distribution of
the private information, the model reduces to a standard labor search framework
with performance pay contracts. The question then is whether the model is con-
sistent with both improvement in information technology and ampli…cation of the
business cycle through uncertainty.
3.1. Model
The model structure is based on a standard DSGE framework with labor search
frictions (see Lubik and Krause, 2003). I build on it wage contracts as in Baker,
Gibbons and Murphy (2004).
The household problem is given by:
(3.1) max
ct,occctt
,
t
[n(c
t
) ÷:
t
,(c
t
)]
st.
(3.2) c
t
+ c::ct
t
= :
t
n
t
+ (1 ÷:
t
)/ + 1
t
c::ct
t+1
63
where c is consumption, n is the wage rate, / is the unemployment bene…t, :
is the fraction of the labor force working in a given period, and 1 is the return
on assets. The labor force is normalized to one. Hence unemployment is given by
n = 1 ÷:.
First order conditions yield the discount factor :
(3.3)
1
1
t
= 1
t
_
,
n
0
(c
t+1
)
n
0
(c
t
)
_
=
The …rm problem is given by:
(3.4) max
·t,at
1(1
t
÷
t
:
t
÷··
t
)
st.
(3.5) :
t
= 1
j
(1 ÷j
t
)
t1
+ ·
t1
¡(o
t1
))
where 1 is output, is the wage bill, · is the cost of vacancy posting, and
· are vacancies. Labor market tightness is o =
·
&
. and the …ll rate for vacancies
64
¡(o
t
) comes from the matching process, taken as given by …rms and workers. At
each period a fraction j
t
of jobs is destroyed. The creation and destruction of jobs
enter the law of motion for employment. Output is subject to both aggregate .
t
,
and idiosyncratic shock . The aggregate shock follows an AR(1) process, and the
idiosyncratic shock is drawn every period from a distribution ,() with support
[0. 1].The …rm chooses at each period a fraction of jobs below the threshold ,
which are destroyed. The remaining jobs have average productivity H() that
comes from the truncated distribution H() =
_
1
.
)(.)
11(.)
d. Given the fraction of
jobs destroyed, and the exogenous separation rate j
a
, total job destruction in the
economy is equivalent to j
a
+ (1 ÷j
a
)1(). Total output for the e¤ort level equal
to zero is given by .
t
H():
t
.
First order conditions yield the job creation equation:
(3.6)
·
¡(o
t
)
= 1[1
j
(1 ÷j
t
)(
_
1 + .c
t+1
_
.
t+1
H() ÷
t+1
+
·
¡(o
t+1
)
)]
where ¸ =
_
1 + .c
t+1
_
.
t+1
H(). c
t
is optimal e¤ort by the worker, and the
parameter . gives the productivity of performance pay arrangements. Note that
the output depends on both e¤ort and ., which governs the productivity of the
performance pay contract. I assume that the marginal contribution : of worker
65
e¤ort to …rm output is given by .c
t+1
.
t+1
t+1
. Wage contracts between …rms and
workers cannot be written on the marginal contribution, since it is too complex
to be objectively assessed. However, there is a veri…able performance measure, 1,
which is an imperfect measure of :. In order to simplify notation, assume that :
can only take values of .c
t+1
.
t+1
t+1
or 0, and 1 can take values of .c
t+1
.
t+1
t+1
or 0. The …rm observes 1 and :, but only 1 is contractible.
At each period, the worker can choose an action that stochastically determines
both output and performance. The relationship between worker e¤ort, c, and the
…rm’s outcome is such that Pr o/
= .ct+1
.
t+1
t+1
[ c) = c, where c is between
0 and 1. The probability of observing a positive performance measure is given
by Pr o/(1 = .q
c
[ c) = jc, where j is a random variable with mean 1(j). and
variance ·c: (j), bounded above so that Pr o/(1 = .c
t+1
.
t+1
t+1
[ c) _ 1. We
can think of j as the di¤erence between the e¤ect of e¤ort on performance and
output. There are states of world when j is large and high e¤ort contributes
more to performance measures than to the value of the …rm. When j is small,
we have the opposite case, and high e¤ort would likely generate large value for
the …rm, but would not increase performance measures. I assume that …rms do
not know j, while workers observe j after deciding whether to stay on the island,
but prior to choosing e¤ort. From the viewpoint of the …rm and the worker, e¤ort
and bonus are stochastic prior to the realization of j. The problem of the …rm is
66
to o¤er a compensation package prior to the realization of j that aligns e¤ort to
productivity, and the problem of the worker is to choose the optimal level of e¤ort
once j is realized. The sequence of events is such that …rms and workers start the
period knowing the state of the economy and the process for j.
The wage determination uses the ‡ow equations for the value of a job match for
the …rm J, and the value of employment \ and unemployment l for the worker.
The worker chooses the level of e¤ort according to:
(3.7) \
t
= 1
j
(max
ot
n
t
+ j
t
1
t
c
t
÷¸c
2
t
+ 1((1 ÷j
t
)\
t+1
+ j
t
l
t+1
))
First order conditions yield:
(3.8) c
t
=
j
t
1
t
2¸
where 1 is the bonus paid in case positive performance is observed and 1
j
(j
t
1
t
c
t
)
is the expected value of bonus pay.
The …rm determines bonus 1 and base pay n according to:
67
(3.9) max
1t,&t
J
t
= 1
j
(.
t
t
(1 + .c
t
) ÷n
t
÷j
t
1
t
c
t
+ 1(1 ÷j
t+1
)J
t+1
)
st.
1
j
(n
t
+ j
t
1
t
c
t
÷¸c
2
t
+ 1((1 ÷j
t
)\
t+1
+ j
t
l
t+1
)) _
/ + 1(,(o
t+1
)(1 ÷j
t+1
)\
t+1
+ (1 ÷,(o
t+1
)(1 ÷j
t+1
)l
t+1
)
c
t
=
j
t
1
t
2¸
Using the fact that the participation constraint binds and l = \, …rst order
conditions yield:
(3.10) 1
t
=
.
t
t
.1j
t
1j
2
t
(3.11) n
t
= / ÷1
j
(j
t
1
t
c
t
÷¸c
2
t
)
68
The value of a job is given by:
(3.12) J
t
= 1
j
(.
t
t
(1 + .c
t
) ÷/ + j
t
1
t
c
t
÷¸c
2
t
÷j
t
1
t
c
t
+ 1(1 ÷j
t+1
)J
t+1
)
The job destruction threshold depends on the condition that the value of the
marginal job at is zero:
.
t
(1 + .c
t
) ÷/ ÷¸c
2
t
= 0
The aggregate resource constraint is:
(3.13) 1
j
(c
t
+ ··
t
) = 1
j
(.
t
(1 + .c
t
):
t
H() + n
t
/)
The competitive equilibriumis a set of prices and numbers ¦c
t
. :
t
. ·
t
. n
t
. 1
t
. c
t
. n
t
. 1
t
.
t
. j
t
¦.
and stochastic processes for ., , and j that satisfy the equations below.
I assume that . follows an ¹1(1) process ln .
t+1
= j
:
ln .
t
+
:
t+1
, j follows
an ¹1(1) process ln j
t+1
= j
j
ln j
t
+
j
t+1
, the private information is drawn from
a symmetric 1ctc(j. j) distribution, and
t
follows an uniform distribution with
support [0. 1].
69
c
t
=
j
t
1
t
2¸
(3.14) 1
t
=
.
t
t
.1j
t
1j
2
t
(3.15) n
t
= / ÷1
j
(j
t
1
t
c
t
÷¸c
2
t
)
.
t
(1 + .c
t
) ÷/ ÷¸c
2
t
= 0
(3.16) 1
j
(c
t
+ ··
t
) = 1
j
(.
t
(1 + .c
t
):
t
H() + n
t
/)
(3.17)
1
1
t
= 1
t
_
,
n
0
(c
t+1
)
n
0
(c
t
)
_
=
70
(3.18) :
t
= 1
j
(1 ÷j
t
)
t1
+ ·
t1
¡(o
t1
))
(3.19)
·
¡(o
t
)
= 1[1
j
(1 ÷j
t
)(
_
1 + .c
t+1
_
.
t+1
H() ÷
t+1
+
·
¡(o
t+1
)
)]
(3.20) n
t
= 1 ÷·
t
(3.21) j
t
= j
a
+ (1 ÷j
a
)1().
I assume that . follows an ¹1(1) process ln .
t+1
= j
:
ln .
t
+
:
t+1
. The private
information is drawn from a symmetric 1ctc(j. j) distribution. The variance of
the private information changes over time. I assume accordingly that j follows an
¹1(1) process ln j
t+1
= j
j
ln j
t
+
j
t+1
. In periods when j is low the variance of
1ctc is high and that decreases the bonus and e¤ort. The information structure is
71
such that agents know j or the distribution of the private information when agree-
ing on the contract, but do not know the realization of j. I further assume that
draws of j are iid over time, and agents use the process of j to predict only the
variance of the private information distribution. Due to the assumption of symmet-
ric process for j, its mean is 0.5. Given the independence of j and , the average
e¤ort in the economy depends on the shocks processes given by .H()j. Note that
there is still heterogeneity in terms of e¤ort and productivity, but I assume that
it aggregates such that we can think of the economy as governed by the values
of .H()j. There are several assumptions used to obtain the simpli…cation in the
aggregation. The …rst is that all shocks are independent, j is iid and the same
for all jobs. The production function is given by (1 + .c
) .H():. Second, the
individual worker in a job does not internalize his e¤ect on total output. We can de-
compose output in two independent terms: .
t+1
H():
t
which aggregates trivially,
and
_
1 + .c
t+1
_
. E¤ort is given by c
t
=
j
t
2¸
:t.t¸1j
t
1j
2
t
. Given the assumptions on the
shock processes, we can consider
j
t
2¸
:tt¸1j
t
1j
2
t
as an aggregate term, and for all jobs
is given by
_
1
.
.)(.)
11(.)
d =
_
1
.
.
1.
d. Hence 1 =
_
1 + .
j
t
2¸
:tt¸1j
t
1j
2
t
_
1
.
.
1.
d
_
.H():.
Using the expressions for the bonus and e¤ort we have that higher variance of
the private information decreases bonus and e¤ort: 1
t
=
.t:t¸1j
t
1j
2
t
=
.t:t¸1j
t
(1+·ov(j))
, c
t
=
j
t
1t
2¸
=
j
t
2¸
.t:t¸1j
t
(1+·ov(j))
. Total compensation n
tcto|
is procyclical and given by n
tcto|
=
n + j1c = / + ¸c
2
. The net e¤ect of higher variance of the private information
72
on the value of the job is given by
0Jt
0·ov(j)
=
01(.t:t(1+¸o
t
)b¸o
2
t
+1(1j
t+1
)J
t+1
)
0·ov(j)
.
Note that the e¤ect on the current return of the job depends on the productivity
of the performance pay contract, .:
t
.
t
.
0o
t
0·ov(j)
÷¸2c
0o
t
0·ov(j)
. Hence, improvement
in monitoring represented by lower ·c
j) or higher . technology increases the linkbetween the variance of j and job creation.
3.2. Calibration and Simulation
Since the main interest is in business-cycle dynamics - the interactions between
market structure and aggregate ‡uctuations in labor demand - I rely on local ap-
proximation as a solution method. For business cycle purposes, …rst and second-
order approximations often yield a good picture of model dynamics (Schmitt-Grohe
and Uribe, 2004, henceforth SGU). This is of course a simpli…cation of the het-
erogeneity in employment relationships. Yet, the model produces the elements
necessary to evaluate the e¤ect of uncertainty on business cycle: time varying
uncertainty, unemployment, and turnover.
Tables 10 and 11 presents the model parameters that have to be calibrated. I
take a two step approach to the calibration and simulation. First, I use standard
parameters in the labor search literature to pin down the …rst approximation of
all values in Table 1. Second, I minimize a loss function to obtain estimates of
73
the free parameters of the model. The moments used in the second stage come
directly from the PSID data for performance pay jobs.
3
There are two reasons for
choosing moments of performance pay compensation schemes in order to calibrate
the model. First, to the best of my knowledge, the PSID moments use all aggregate
data available on wage setting in contracts, helping to pin down parameters that
have no counterpart in the literature. Second, I do not assume wage rigidity,
which is usually necessary to generate empirically reasonable aggregate properties
in standard DSGE labor search models. To the extent that performance pay
schemes became pervasive in the US labor market, I use in the model a wage
setting that is both ‡exible and empirically founded.
I use as in the literature a log utility function. The model is quarterly, and
the discount rate is set at .99. The steady state vacancy, labor market tightness,
the elasticity and constant of the matching function ` = ¬n
c
·
1c
are obtained
using data estimates of average unemployment rate (6%) in the economy, the
normalization of the labor force to one, and the …ll (.7) and …nding rate (.6) of
jobs. The exogenous separation probability is .08 and total job destruction is 0.10.
In the …rst stage, I guess the remaining parameters.
3
See chapter 1 for de…nitions of PSID variables, and the appendix for a discussion of the data.
74
I calibrate the productivity and cost of performance pay, the unemployment
bene…t, the ‡ow cost of vacancy posting, and the variance to the innovation of
the uncertainty shock in order to match moments in the PSID such as the size
4
and incidence of the bonus, and the correlation of total bonus and bonus size with
unemployment at business cycle frequency, the correlation of incidence with unem-
ployment and bonus size, and the standard deviation of bonus size and incidence.
I do not target the volatility of labor market variables such as unemployment, va-
cancies, and labor market tightness. The mean of ·c
j) comes from the choice ofa symmetric Beta process, with average j normalized to one.
The correlations and standard deviations are analogous to the standard busi-
ness cycle statistics but make use of the information in the PSID about compen-
sation schemes. I take the linearly detrended series of bonus, bonus size, bonus
incidence, and unemployment rate in order to calculate moments. The model
mechanism is to change future pro…ts and vacancy posting using the changes in
the incentive for e¤ort variation given by bonus. Hence, I use direct evidence on
the cyclicality of bonus pay in the data. The goal of the model is to generate labor
market volatility through uncertainty. I use the standard deviations as moments
of the compensation scheme to discipline the model since introducing excessive
4
See previous de…nitions of PSID moments in Chapter 1.
75
volatility in e¤ort and bonus could generate high levels of variance in labor market
aggregates. I also use correlations of incentive pay with unemployment since the
model implies as in the data that bonus size and its probability of positive incentive
pay in a given period depend on productivity and should decrease in recessions.
The criteria function used to decide on the calibration is given by min 1(.. /. ¸. ·) =
r
2
, where r is the di¤erence between model simulation and data moments. I
evaluate 1 over part of the parameter space around the initial guess.
5
At this stage
I weight all moments equally in the loss function. In principle one should focus on
the more reliable moments of the data, and the ones that also better describe the
model mechanisms. The solution is supposed to emulate the simulated method
of moments. Since relevant parameters of the data such as the shock process for
uncertainty and the productivity of contracts cannot be directly calculated from
the data, one has to use indirect inference with data moments in order to estimate
free parameters.
The idiosyncratic process is assumed uniform with support [0. 1]. The values
discussed so far cover all parameters in Table 10 and Table 11 except for the
aggregate productivity shock. I normalize the mean of the aggregate shock to one.
5
I also use diferent initial points in order to check for the problem of local minima in the criteria
function. This procedure is restricted by the convergence on internal loops of the simulation. All
values of the parameter space evaluated have to lead to convergence of the steady state of the
model and approximation functions.
76
The AR(1) process for . corresponds approximately to TFP in the model. I choose
the process for z such that the model without uncertainty shocks reproduces the
standard deviation output in the US economy, which is approximately 1,7%. The
model is not sensitive to the choice of autocorrelation in the shock process, so I
follow the literature and set it to .95.
As in most business cycle models, the variance of innovation to shocks governs
the bulk of the volatility of aggregate variables. In principle, any variance of
vacancy and unemployment can be obtained with the appropriate choice of shock
volatility. I discipline the calibration of the variance in the uncertainty process
by using the moments of the bonus pay in the PSID, including the variance and
ciclicality of aggregate bonus. I also conduct a sensitivity analysis of the parameters
of the shock process by looking at the moments of the bonus as I increase the
variance of j.
Table 12 presents results of the baseline model and the data moments. For a
reasonable size and cyclicality of bonus pay, the model explains more than twice the
volatility of unemployment and more than one half of the volatility of vacancies and
labor market tightness Though the model overshoots the correlation of bonus size
and incidence and the standard deviation of incidence, all remaining simulated
moments have the right sign and order of magnitude. Unlike in the standard
77
DSGE labor search model, results do not depend on a large value of the variance
of labor productivity shocks or the assumption of wage rigidity. Note that the
model is driven by two uncorrelated shocks. As we discuss below, the introduction
of uncertainty shocks is key for reproducing the ciclicality of compensation scheme
variables, since the model driven by only TFP shocks performs poorly in several
dimensions.The uncertainty shocks work indirectly as a productivity shock, since
they lead to more e¤ort variation, which enters the production function and …rm’s
expectation of future pro…ts. Below I discussion the impulse response functions
and counterfactual exercises of shutting down the e¤ort mechanism.
The Beveridge curve is not reproduced. In DSGE models with endogenous job
destruction the response of destruction to shocks is faster than creation, and the
two rates end up with a positive correlation at business cycle frequency. One can
get the right Beveridge curve with the model at the cost of assuming a constant
destruction rate. This is not a moment target by the model, hence I choose to keep
job destruction as a margin of adjustment, since empirically it seems to increase
in recessions. As discussed in the literature, the shape of the Beveridge curve is
not a priori clear. On the one hand, a shock to productivity increases pro…ts and
vacancy creation, reducing unemployment. On the other hand, higher productivity
reduces the threshold for destruction and unemployment, increasing labor market
78
tightness. Higher vacancy to unemployment ratio reduces incentives for vacancy
posting. If we shut down the endogenous job destruction margin, only the …rst
e¤ect is at work.
The ultimate test of the model is generating a propagation mechanism for
recessions that increases turnover by introducing uncertainty. Since I represent
uncertainty as time varying information process in performance pay contracts, the
metric for evaluating the model comes from the sensitivity analysis of the two main
parameters of the performance pay technology - the productivity of the contract,
., and the standard deviation of the innovation to the uncertainty shock - and its
propagation mechanism - e¤ort variation.
I conduct the following analysis. Both the incidence and size of the bonus
present a trend increase in the PSID.
6
This trend suggests that the technology of
performance pay has improved over time. Table 13 displays simulation results for
di¤erent values of free parameters. Columns 1 displays simulation results for a
low value of the variance of the innovation to j. From column 1 we can infer that
the model driven by TFP shocks performs poorly both at replicating moments
of compensation schemes and generating volatility in aggregate variables. When
we compare column 1 to column 4, it is clear that uncertainty shocks drive most
6
See Figure 8 for bonus incidence and Figure 10 for bonus size.
79
of the cycle. As we move towards column 4, the model …t improves. A model
that is driven mostly by TFP shocks (column 1) produces countercyclical bonus,
unlike in the data. The introduction of uncertainty shocks ‡ips the sign of the
correlation between bonus and unemployment. It also raises the variance of bonus
pay. As a by-product, the uncertainty shocks improve the …t of the model in terms
of replicating the volatility of aggregate and labor market variables (columns 3 and
4).
Column 3 displays results with the baseline calibration except for the higher
value of productivity in performance pay contracts. An increase in the productivity
of the contract is in line with the PSID evidence that there is a trend increase in the
size and incidence of the bonus. Results in column 3 indicate that improvement in
technology is consistent with more aggregate volatility.
7
Note that the productivity
of performance pay is relevant for model …tness. A one percent increase in ., all else
equal, helps the model explain two percent more of unemployment when compared
to the baseline calibration, without raising the volatility of the PSID moments of
compensation. This results suggest that the productivity of the contract is relevant
for model dynamics, since it a¤ects the volatility of vacancies and unemployment
outcomes.
7
Though column 3 has a lower value for the loss function criteria, it violates the assumption that
under the baseline calibration TFP shocks alone reproduce the empirical value of the output
standard deviation.
80
The last experiment concerns the model mechanims - e¤ort variation. I take
the simulated data and perform the following counterfactual. I keep c
at its mean
value and calculate the business cycle moments of the compensation scheme. I also
change the job creation equation such that e¤ort is constant in the expectation of
future pro…ts. Column 2 presents results for the model without e¤ort variation.
It is clear that if e¤ort is kept at an ordinary constant level, the model cannot
reproduce moments of the compensation scheme. The reason for that failure is
that in the counterfactual exercise we sever the link between the current state of
the economy and the probability of the two main events in the model: positive
incentive pay, and higher productivity through e¤ort variation. Moreover, with
e¤ort constant in the job creation equation, there are no incentives to post more
vacancies when the variance of the private information process is low. The results
of this counterfactual indicate that e¤ort variation induces variability in labor
market aggregates in the model. Note that e¤ort is given by c
t
=
j
t
2¸
:t.t¸1j
t
1j
2
t
. We
can see that the shock in ln j
t
changes the variability of e¤ort, or the variance of
the private information in denominator of c
. This e¤ect is the response of the
contract to the second moment shock in the private information process.
A model without uncertainty changes the moments of the bonus, bringing the
standard deviation of all variables down and increasing the distance between data
81
and simulated model correlations (see Table , column 1). Interestingly, the mechan-
ims that a¤ects the bonus moments is the e¤ort variation. If we perform the ex-
periment of shutting down e¤ort by keeping it at its mean value, we also increase
the distance between data and model moments (see Table, column 3).
Figures 11 and 12 show the impulse response function of model variables to a
positive innovation in aggregate productivity. Figure 11 displays the response of
labor market variables and performance pay outcomes to a 1 std innovation to the
uncertainty shock. Figure 12 shows the same variables’ reponse to the aggregate
shock. It is interesting to note the similarity between Panel A in Figures 11 and
12. A positive shock to j decreases the variance of j and works as a productivity
shock. Panel B in both …gures are also similar, but the response of bonus and
e¤ort is higher for the uncertainty shock
There are some caveats to the analysis above. First, the model is not rich
enough to reproduce closely all moments of the data. Second, though the data
is measured consistently with model de…nitions and the literature on performance
pay, the time range is short for assessment of time series moments (see the appendix
for a discussion of the PSID data).
82
3.3. Last Remarks
In this Chapter I study the interaction between uncertainty in employment re-
lationships and the business cycle. The current papers on this topic focus on two
types of e¤ects: 1) change in the real option value of investment and hiring (Bloom,
2009); and, 2) uncertainty as bad news predicting low productivity in the future
(Bachmann and Bayer, 2009). I suggest a third mechanism in which uncertainty
a¤ects the value of employment by changing incentives and e¤ort in contracts.
I extend a standard search model in order to include performance pay contracts
and uncertainty shocks, represented by time varying variance in the process of
private information held by workers. I calibrate and simulate the model in order
to replicate moments of performance related payment in the US data. Results
suggest that uncertainty shocks and improvement in performance pay technology
are capable of generating ampli…cation of high frequency variation in labor market
outcomes. Overall, as postulated in the motivation, if the technology has improved
and the shock size is larger, uncertainty becomes an important channel in reces-
sions, amplifying the high frequency variation in unemployment and vacancies.
The simulation results answer positively our initial question of whether business
cycles can be driven by uncertainty in employment relationships.
8
8
The mechanims in the model is suitable for explaining the Great Moderation. If we assume
that the variance of the innovation to the private information process is decreasing over time, we
83
1. Figures and Tables
5
5
6
0
6
5
7
0
S
t
d
o
f
c
h
a
n
g
e
in
e
m
p
lo
y
m
e
n
t
1970 1980 1990 2000 2010
Year
Dispersion in employment change Hp_trend
Figure 1 - Decli ne in Fi rm Instabi li ty
have that aggregate labor market variability decreases. There is one shortcoming to this story.
The decline in the variance of information is probably related to a secular change in technology
(e.g. the use of computers to monitor workers). Since the adoption of the new technology is
not likely to revert in recessions, the mechanims in the model cannot explain simultaneously the
Great Moderation and the Great Recession.
84
1
2
1
4
1
6
1
8
2
0
2
2
J
o
b
c
r
e
a
t
io
n
a
n
d
d
e
s
t
r
u
c
t
io
n
r
a
t
e
s
1970 1980 1990 2000 2010
Year
Job Destruction - HP trend Job Creation
Job Destruction Job Creation - HP t rend
Figure 2 - Decli ne in j ob fl ows
85
.
1
3
.
1
4
.
1
5
.
1
6
.
1
7
E
x
c
e
s
s
J
o
b
R
e
a
l
l
o
c
a
t
i
o
n
1990 1995 2000 2005
Year
Figure 3 - Decli ne in Job Reallocati on
86
2
2
.
5
3
3
.
5
4
P
e
r
c
e
n
t
o
f
e
m
p
l
o
y
m
e
n
t
1970 1980 1990 2000 2010
Year
Unemployment I nflows Unemployment Outflows
Figure 4 - Decli ne in Worker Flows: CPS 1976-2008
87
.
1
6
.
1
8
.
2
.
2
2
.
2
4
.
2
6
M
e
a
n
a
b
s
o
l
u
t
e
d
e
v
i
a
t
i
o
n
1980 1990 2000 2010
Year
Hourly earnings Hours
(CPS 1980-2008, private non-farm)
Figure 5 - Increase in Wage instability
88
0
.
0
5
.
1
.
1
5
.
2
.
2
5
.
3
.
3
5
.
4
.
4
5
.
5
.
5
5
.
6
M
e
a
n
a
b
s
o
l
u
t
e
d
e
v
i
a
t
i
o
n
1980 1990 2000 2010
Year
Hourly earnings _ Stayers Total earnings _ St ayers
(CPS 1980-2007 -Job Stayers )
Fi gure 6 - Increase i n total earni ngs i nstabi l i ty
89
0
.
0
5
.
1
.
1
5
.
2
.
2
5
.
3
.
3
5
.
4
.
4
5
.
5
.
5
5
.
6
M
e
a
n
a
b
s
o
l
u
t
e
d
e
v
i
a
t
i
o
n
1980 1990 2000 2010
Year
Total earnings_ Movers Hourly earnings _ Movers
(CPS 1980-2007 - Job Movers/Losers)
Fi gure 7 - Increase i n Wage i nstabi l i ty for Movers/Losers
90
.
1
.
2
.
3
.
4
.
5
F
r
a
c
t
i
o
n
o
f
S
a
m
p
l
e
76 78 80 82 84 86 88 90 92 94 96 98
Year
Performance Pay Received in Current Year Performance Pay Job
Covered by Collective Bargaining Agreement
(Source: Lemieux,MacLeod and Parent, 2009)
Figure 8 - Performance Pay Incidence - Job stayers
91
1
0
2
0
3
0
4
0
5
0
A
n
n
u
a
l
i
z
e
d
S
T
D
(
%
)
1960 1970 1980 1990 2000 2010
Year
Figure 9 - Monthly U.S. stock market volatility from CBOE
92
0
.
0
1
.
0
2
.
0
3
.
0
4
.
0
5
.
0
6
B
o
n
u
s
S
i
z
e
(
F
r
a
c
t
i
o
n
o
f
w
a
g
e
)
75 80 85 90 95 100
Year
(PSID-PP jobs)
Figure 10 - Increase in bonus size
93
Figure 11 -Impulse Response Function to 1 std shock to z
Panel A
Panel B
0 50 100
1.8
1.82
1.84
1.86
1.88
1.9
1.92
1.94
1.96
1.98
vacancy
0 50 100
1.8
1.9
2
2.1
2.2
2.3
2.4
2.5
unemployment
0 50 100
9
9.2
9.4
9.6
9.8
10
10.2
x 10
-3
bonus
0 50 100
-0.5
0
0.5
1
1.5
2
2.5
3
3.5
x 10
-3
effort
94
Figure 12 -Impulse Response Function to 1 std shock to p
Panel A
Panel B
0 50 100
1.8
1.82
1.84
1.86
1.88
1.9
1.92
1.94
1.96
1.98
vacancy
0 50 100
1.8
1.9
2
2.1
2.2
2.3
2.4
2.5
unemployment
0 50 100
0.0145
0.015
0.0155
0.016
0.0165
0.017
0.0175
bonus
0 50 100
-1
0
1
2
3
4
5
x 10
-3
effort
95
Table 1- Trend I ncrease in Earnings instability in the March CPS, 1979- 2007
Full sample - private non-farm
Dependent
variable
(instability
measure)
Constant Regression
coefficient
for time
trend
Cumulative
change
Mean of
dependent
variable
Total earnings 0.24726 *** 0.00107 *** 0.030 0.271
(0.00193) (0.00019)
Hourly
earnings 0.21111
***
0.00180 *** 0.050 0.249
(0.00150) (0.00016)
0.211
Total hours 0.18152 *** -0.00019 -0.005 0.175
(0.00176) (0.00016)
Job stayers
Dependent
variable
(instability
measure)
Constant Regression
coefficient
for time
trend
Cumulative
change
Mean of
dependent
variable
Total earnings 0.12874 *** 0.00240 *** 0.067 0.172
(0.00130) (0.00015)
Hourly
earnings 0.14554
***
0.00233 *** 0.065 0.188
(0.00134) (0.00015)
Total hours 0.05376 *** 0.00026 0.007 0.065
(0.00067) (0.00007)
Job movers/losers
Dependent
variable
(instability
measure)
Constant Regression
coefficient
for time
trend
Cumulative
change
Mean of
dependent
variable
Total earnings 0.46941 *** -0.00078 * -0.022 0.444
(0.00495) (0.00046)
Hourly
earnings 0.33114
***
0.00133 *** 0.037 0.356
(0.00372) (0.00036)
Total hours 0.39922 *** -0.00089 ** -0.025 0.349
(0.00466) (0.00042)
* 10% significance ** 5% significance *** 1 % significance
Sample Size: Full sample, 176728. Job stayers, 111641. Break in survey methodology in 1988.
Standard errors in parenthesis. See appendix for matching and sample selection.
96
Table 2- Trend I ncrease in Earnings I nstability for Different Demographic
Groups: J ob Stayers in the March CPS from 1979 to 2007
Job stayers less than 45 yrs old
Dependent
variable
(instability
measure)
Constant Regression
coefficient
for time
trend
Cumulative
change
Mean of
dependent
variable
Total
earnings 0.12791 *** 0.00308 *** 0.086 0.174
(0.00166) (0.00019)
Hourly
earnings 0.14518 *** 0.00290 *** 0.081 0.189
(0.00170) (0.00019)
Total hours 0.05614 *** 0.00023 ** 0.006 0.067
(0.00086) (0.00009)
Job stayers with high school or less
Dependent
variable
(instability
measure)
Constant Regression
coefficient
for time
trend
Cumulative
change
Mean of
dependent
variable
Total
earnings 0.13248 *** 0.00294 *** 0.082 0.181
(0.00181) (0 .00023)
Hourly
earnings 0.14636 *** 0.00279 *** 0.078 0.193
(0.00184) (0.00023)
Total hours 0.04932 *** 0.00019 * 0.005 0.059
(0.00010) (0.00088)
Sample Size: with high school or less, 68755. Less than 45yrs. old, 54561. Break in
methodology in 1988. See appendix for matching and sample selection.
* 10% significance ** 5% significance *** 1 % significance
Standard errors in parenthesis.
97
Table 3- Wage instability in different pay schemes in the PSI D: 1976 to 1996
Compensation scheme group Mean dispersion in hourly wages growth
Not Performance pay and not in Union 0.166
Performance pay and not in Union 0.173
Union and Not Performance pay 0.155
Union and Performance pay 0.162
Compensation scheme group
Fraction of group in
1976
Fraction of
group in 1995
Not Performance pay and not in Union 0.423 0.421
Performance pay and not in Union 0.275 0.390
Union and Not Performance pay 0.245 0.141
Union and Performance pay 0.058 0.049
Compensation scheme groups
compared
t test for differences in mean wage
volatility in different pay schemes
Performance pay and not in Union X Not
Performance pay and not in Union
0.593
Union and not in Performance pay X Not
Performance pay and not in Union
-2.596***
Performance pay and not in Union X
Union and Not Performance pay
3.055***
Notes: Sample size, 14267. Male heads of the household.
98
Table 4- Regression coefficients in the PSI Dfrom
1976 to 1996: effect of performance pay on wage
instability
Worker group Job stayers Job stayers
Constant 0.10548***
(0.01532)
0.13290
(0.15554)
Performance
pay dummy
0.00489
(0.00557)
0.02266**
(0.01107)
Union
Dummy
-.01133 **
(0.00557)
-0.00591
(-0.0097)
Tenure -0.00223**
(0. 00108)
Tenure
2
0.00108**
(0.00003)
Education -0.00256
(0.00789)
Married 0.00560
(0.00865)
Potential
experience
0.00534
(0.00575)
Experience
2
-0.00026
(0.00014)
Experience
3
0.00004**
(0.00002)
R-squared .02 0.3
Controls for
worker fixed
effects and
characteristics
no yes
Notes: Sample size, 14267, PSID, male heads of household. Standard
errors in parenthesis, clustered at the job match level.
***1% significance **5% significance
99
Table 5- Calibration of model parameters
Parameters of the idiosyncratic process and production technology
Log mean of idiosyncratic shock -0.05
Persistence of idiosyncratic shock 0.947
Std of the innovation of idiosyncratic shock 0.20
Discount rate 0.99
Labor share in the production function 0.64
Moments used to calibrate the idiosyncratic shock process
Excess job reallocation 0.14
Unemployment rate 0.055
Parameters of the performance pay technology
Marginal value of effort [.05 0.25]
Marginal cost of effort 0.5
Private information process Beta (p,p)
Moments used to calibrate the performance pay technology
Std bonus 0.13
Bonus size 0.037
Bonus Incidence 0.141
Moments used to calibrate the unionized model
Union wage premium 0.17
Note: Calculations for the bonus use performance pay jobs in the PSID from 1993-1998.
The bonus corresponds to the part of compensation in the PSID reported in the form of bonus,
commission or piece-rate. Bonus size is the ratio of bonus to total compensation, and bonus
incidence is the fraction of performance pay jobs that received incentive pay in a given yea.
Unemployment is calculated from the rate reported by the BLS in the 2000s.
Labor share in the production function comes from NIPA.
Excess job reallocation uses the quarterly BED data.
100
Table 6- Simulation results and moments to match
Moments to match Data moments Model moments
Excess job reallocation 0.14 0.18
Unemployment rate 0.055 0.07
Std bonus 0.13 0.057
Bonus size in 1998 0.057 0.058
Bonus Incidence in 1998 0.17 0.15
Union wage premium 0.17 0.25
Note: Calculations for the bonus use the PSID from 1993-1998. The bonus corresponds to the
part of compensation in the PSID reported in the form of bonus, commission or piece-rate. Bonus
size is the ratio of bonus to total compensation, and bonus incidence is the fraction of
performance pay jobs that received incentive pay in a given year.
Unemployment is calculated from the rate reported by the BLS in the 2000s.
Excess job reallocation uses the quarterly BED data.
Union wage premium comes fromNewmark and Kawaguchi (2001).
The model is simulated quarterly and model moments are aggregated annually for comparison
with the PSID data.
Table7- Moments toexplain
Change in the mean absolute
deviation of hourly wage growth
rate 0.065
Change in standard deviation of
employment growth rate
-0.042
Note: Calculations use the March CPS and LBD . The
change for hourly earnings instability uses the cumulative
increase estimated with the time trend for job stayers in
Table 1. The change in employment instability uses the
difference between the 2005 and the 1976 value of the
std of cross section employment growth rate in the LBD.
101
Table 8- Simulated moments with different pay schemes
Statistics Baseline Union
Performance
Pay
Beta (6, 6)
= .25
Mean |%change wage|
0.1513 0.1552 0.1743
Mean |%change
employment| 0.1933 0.2033 0.1833
Std (%change wage)
0.2021 0.2009 0.2285
Std (%change employment)
0.5588 0.6174 0.5765
Average wage
1.53 1.99 1.59
Unemployment
6.8 7.87 7.05
Value of search
152 156 162
102
Table 9- Simulated moments from performance pay model
Statistics
Parameters of Performance Pay Technology
Beta ( 1,1 )
=.05
Beta ( 4,4 )
=.1
Beta ( 6, 6 )
=.2
Beta ( 6, 6 )
=.25
Mean |%change wage|
0.1511 0.1537 0.1652 0.1743
Mean |%change employment|
0.1762 0.1762 0.1774 0.1833
Std (%change wage)
0.2021 0.2050 0.2189 0.2285
Std (%change employment)
0.5619 0.5618 0.5618 0.5765
Size of the bonus
0.0018 0.0081 0.0318 0.0579
Std of the bonus
0.0047 0.0159 0.0429 0.0575
Bonus Incidence
0.0300 0.0590 0.1197 0.1585
Average wage
1.54 1.56 1.62 1.59
Unemployment
6.85 6.86 6.95 7.05
Value of search
153 154 158 162
103
Table 10 - Calibration of Parameters
Elasticity of the Matching Function -0.40
Constant in the Matching Function 0.80
Utility function u(.) log
Discount Rate 0.99
Exogenous Destruction Rate x 0.08
Total Destruction Rate 0.10
Returns to Performance Pay * 0.29
Cost of Performance pay * 1.50
Unemployment Benefit * b 0.47
Vacancy Cost * 0.35
Beta Process
Beta
(p,p)
Beta
(1,1)
Process for Uniform Unif[0,1]
Note: *Free parameters of the baseline model chosen with minimization
of loss function
Table 11 - Calibration of Autoregressive Shock Processes
Process for Aggregate
Productivity Mean Autocorrelation Std of Innovation z
1 0.95 4.80E-04
Process for Private
Information Mean Autocorrelation
1 .95 *8E+01
Note: *Free parameter of the baseline model chosen with minimization of loss function
104
Table 12 - Simulation Results of the Baseline Model
Moments to match
Model Data
Bonus incidence 0.068 0.17
Size of Bonus 0.065 0.06
Corr(Bonus size,
unemployment) -0.2 -0.17
Corr(Bonus pay,
unemployment) -0.19 -0.14
Corr(Bonus incidence,
unemployment) -0.21 -0.31
Corr(Bonus incidence, Bonus
Size) 0.99 0.67
Std Incidence 0.22 0.11
Std Bonus Size 0.39 0.39
Std Aggregate Bonus 0.4 0.4
Other Key Model Moments
Beveridge curve 0.97 -0.89
Std of Unemployment 0.39 0.19
Std of Vacancy 0.26 0.2
Std Labor Market Tightness 0.15 0.38
Notes: Simulation in the first column uses parameters in Tables 10 and 11.
105
Table 13 - Simulation Results for Sensitive Analysis of Key Parameters
p = a= = Baseline
0 mean(a*) 0.291
Bonus incidence 0.02 0.1 0.14 0.068
Size of Bonus 0.02 0.1 0.12 0.065
Corr(Bonus size, unemployment) 0.99 -0.13 -0.2 -0.2
Corr(Bonus pay, unemployment) 0.99 -0.13 -0.18 -0.19
Corr(Bonus incidence, unemployment) 0.99 0 -0.2 -0.21
Corr(Bonus incidence, Bonus Size) 1 0.02 0.99 0.99
Std Incidence 0.02 0 0.218 0.22
Std Bonus Size 0.02 0.23 0.37 0.39
Std Aggregate Bonus 0.016 0.24 0.4 0.4
Beveridge Curve 0.83 0.82 0.97 0.97
Std of Unemployment 0.009 0.01 0.41 0.39
Std of Vacancy 0.0078 0.009 0.27 0.26
Std Labor Market Tightness 0.0052 0.007 0.16 0.15
Note: Simulations in columns 1 and 2 change only the value of p, and optimal effort, respectively. In column
3 I change only the value of by 1% . Baseline model uses parameters in Tables 10 and 11.
106
Table 14 - Regression Results for Cyclicality of Uncertainty
Dependent Variable Is Stock-Market Volatility - b
Explanatory Variable Is Period by
Period
Cross-Sectional Standard Deviation of Coefficient R squared Time span
Firm profit growth,c Compustat
quarterly 0.5320
(0.0640) 0.287 62Q305Q1
Firm stock returns,d CRSP monthly 0.5430
(0.0370) 0.287 62M706M12
Industry TFP growth,e SIC 4-digit yearly 0.4290
(0.1190) 0.282 19621996
Monthly Unemployment Rate (BLS)g 0.2868
(0.1958) 0.0038 62M706M12
Notes: a-Each column reports the coefficient from regressing the time series of stock-market volatility on the within period cross-sectional standard deviation (SD) of the explanatory
variable calculated from an underlying panel. All variables normalized to a SD of 1. Standard errors are given in italics in parentheses below. So, for example, column 1 reports
that the stock-market volatility index is on average 0.532 SD higher in a quarter when the cross-sectional spread of firms profit growth is 1 SD higher.
b-The stock-market volatility index measures monthly volatility on the U.S. stock market and is plotted in Figure 1. The quarterly, half-yearly, and annual values are calculated
by averaging across the months within the
period.
c-The standard deviation of firm profit growth measures the within-quarter cross-sectional spread of profit growth rates normalized by average sales, defined as (profitst-
and uses firms with 150+ quarters of data in Compustat quarterly accounts.
d-The standard deviation of firm stock returns measures the within month cross-sectional standard deviation of firm-level stock returns for firm with 500+ months of data in
the Center for Research in Securities Prices (CRSP) stock-returns file.
e-The standard deviation of industry TFP growth measures the within-year cross-industry spread of SIC 4-digit manufacturing TFP growth rates, calculated using the five-factor
TFP growth figures from the NBER data base.
f-Average units in cross section refers to the average number of units (firms, industries, or forecasters) used to measure the cross-sectional spread.
g- Labor Force Statistics from the Current Population Survey
16 years and over
2. Data Appendix
March CPS Data
The March CPS data used in Figures 1 to 7 were downloaded from the NBER
website using years 1980 to 2008. The redesign in 1988 changed the March sup-
plement question about earnings. Before 1989, total earnings from last year were
registered under one variable. After 1989, there is a question for earnings from the
107
primary job and an additional variable for earnings from a secondary job. For the
years after 1989 my earnings variable is the sum of primary and secondary earnings.
Appendix Table 1 shows that variables used for matching the March CPS across
years. Following Mandrian and Lefgen (1999), individuals are matched based on
their month-in sample, household identi…er, household number and line number.
After that, repeated observations due to errors in identi…ers are deleted. Also,
spurious matches with di¤erent sex and race in the two periods are eliminated. I
did not do further re…nements, since they would come at the cost of eliminating
some of the "true" matches.
In 1988 there were two releases of the March supplement. The one in the old
format is used in the 1987-88 match. The 1988B release is used in 1988-89. The
years 1994-95 are an exception. The …rst 1994 release contained errors in the
identi…ers. I use the BLS-corrected h_idnum. To account for this problem, this
year has to be matched by state of residence along with the four usual identi…ers.
Some caution is needed when using the matched sample, since not all variables are
corrected by this procedure. Years 1985-86 and 1995-96 cannot be matched due
to changes in the household identi…ers.
After 2002, the March Supplement sample was increased in order to cover a
higher number of Hispanic Households and low income families with uninsured
children (SCHIP). Since the oversample is taken from di¤erent rotation groups,
108
household identi…ers can be repeated, which complicates matching. I eliminate
the post 2002 oversample for comparability with earlier years. Appendix Figure 1
presents also match rates for the overall sample and including the SCHIP observa-
tions. Two steps are needed to eliminate the oversample. First, I delete individuals
with person weight equal to zero from 2002 to 2008. Second, I delete in 2002 and
2003 all observations with h_seq higher than the 2003 cuto¤ value 78864. In 2004
and 2005, I eliminated observations with h_seq higher than the 2004 cuto¤ value
78575.
Lastly, in 2005 the identi…ers were redesigned in order to facilitate year-to-year
matching: h_idnum was renamed h_idnum1 and a second identi…er was created,
h_idnum2. In the 2004-05, I use only h_idnum1. From 2005 on, both h_idnum1
and h_idnum2 need to be used to sort and merge observations.
Only half of the March sample can be potentially matched across years (rotation
groups 1-4 in period t and 5-8 in t+1). Among the successfully matched persons,
I classify observations according to their status in the period t and t + 1 March
interviews. Only individuals currently in the labor force are used. The sample is
also restricted from 25 to 64, so not to capture major transitions in and out of
the labor force. Further, only individuals classi…ed as private_nonfarm workers in
their longest job and currently in the labor force are kept in the sample. Values
of primary earnings that are topcoded or imputed are also excluded. This leaves
109
me with a sample of private nonfarm workers ranging from 10000 to 8000 workers
in each year. March supplement weights are used in all calculations and nominal
variables are de‡ated using the CPI of the reference year. In the computations for
total household income, only heads of household are kept and household weights
are used. Appendix Table 2 lists CPS identi…ers used in the analysis.
Successive changes in the March Supplement questionnaire do not prevent com-
parisons across years, but some care is needed in order to guarantee that variables
have the same meaning over time. I try to homogenize variables to the extent pos-
sible. The changes in data processing in 1988 (reading earnings with the primary
and secondary wages separatly) seems to have permanently moved the volatility
measures to a higher level. In the graphs, I choose to subtract the 1987-88 break
from all measures of volatility after 1987. Without this adjustment, the increase
in instability could be overstated. In the regression exercise I include a dummy
for the post 1987 period. This procedure seems to capture the break and does not
a¤ect substantially the estimates for the coe¢cient of the time trend.
One should worry whether the matched sample is representative of the overall
labor force. I use propensity score weights to correct for such bias. The propensity
score weights are calculated in the following way: I estimate in each year a probit
model of the probability of being matched on observables. The variables used
were sex, race, head of household status, age, age squared, dummy for educational
110
attainment, full time status, private sector job, unemployment in the …rst or second
interview and industry indicators for manufacturing and retail sectors. The …nal
weight used is the inverse of the probability predicted by the model multiplied by
the March supplement weight. In Appendix Table 3 I present characteristics of
the pooled matched sample at the time of the …rst March interview.
PSID Data
The PSID data used in Figure 8 and the calibration exercise comes from
Lemieux, Bentley and Parent (2009). See their paper for further details. The
sample consists of male heads of the household aged 18 to 65 with average hourly
earnings between $1 and $100 (in $1979). Workers in the public sector and self-
employed are excluded from the sample. Jobs are assigned as performance pay
if part of the worker’s compensation includes a variable pay component (bonus,
comission, piece-rate). From 1976 to 1992, the authors use mainly two questions
to construct de…nitions: the amount of money earned from working overtime, or
from bonus, comission or piece-rate, and for workers not paid by the hour or salary
exclusively, the form of pay received. All non-overtime workers that report bonus,
comission or piece rate are classi…ed as having a performance pay job. After 1993,
the interviews include a direct question about the amount earned in bonus, tips,
comission and overtime. For the sake of comparability, performance pay jobs are
de…ned as jobs with non-overtime pay but positive bonus, comission or piece-rate.
111
For some jobs, positive bonus pay is usually not received in every year. The authors
de…ne as performance pay any job that received at least once over the duration of
the job match pay in form of bonus, comission or piece-rate.
The computation algorithm is as follows. The problem consists of a search
for a …xed point in c and l. The algorithm contains an inter loop necessary to
solve the dynamic programming island problem and the invariant distribution of
islands over the labor force and idiosyncratic shocks, and an outer loop to obtain
the …xed point in the expected value of arriving in an island anywhere in the
stationary distribution, and the mass of searchers in the economy. See Kambourov
and Manoviskii (2007) for an example.
3. Derivation of equilibrium in performance pay markets
The …rm problem is:
: = max
1,j
1
j
[(1 + .c
)q
c
÷nq ÷jc
1q]
which can be rewriten as:
: = max
1,j
1
j
[(1 + .
j1
2¸
)q
c
÷nq ÷
j
2
1
2
2¸
q]
112
The …rst order conditions are as follows:
(.22) 1 : 1
j
[.
j
2¸
q
c
÷
j
2
1
¸
q] = 0
which implies:
1
=
.
2
1
j
[jq
c
]
1
j
[j
2
q]
(.23) q : 1
j
[(1 + .
j1
2¸
)cq
c1
÷n ÷
j
2
1
2
2¸
] = 0
which implies:
(.24) n = 1
j
[(1 + .
j1
2¸
)cq
c1
÷
j
2
1
2
2¸
]
Assume j is iid and private information. Since the bonus and employment are
decided before the realization of j. the …rm can take j as independent of q, which
simpli…es the solution as follows:
113
(.25) 1
=
.
2
1
j
[j]q
c1
[1
j
[j]
2
+ ·c
j)]Using (24) in (23) yields:
n = cq
c1
+ 1
j
[.
j1
2¸
cq
c1
÷
j
2
1
2
2¸
]
n = cq
c1
+ 1
j
[
j
2¸
.
2
2
1
j
[j]q
c1
[1
j
[j]
2
+ ·c
j)]cq
c1
÷
j
2
2¸
_
.
2
1
j
[j].q
c1
[1
j
[j]
2
+ ·c
j)]_
2
]
n = cq
c1
+
c.
2
4¸
1
j
[j]
2
(q
c1
)
2
(1
j
[j]
2
+ ·c
j))÷
1
8¸
1
j
[j]
2
(.q
c1
)
2
[1
j
[j]
2
+ ·c
j)](.26) n = cq
c1
+
1
4¸
1
j
[j]
2
(.q
c1
)
2
(1
j
[j]
2
+ ·c
j))_
c ÷
1
2
_
Wage determination:
Combining the …rst order condition for the …rm with the participation con-
straint of the worker, wages must satisfy:
114
n = 1
j
[(1+.
j1
2¸
)cq
c1
÷
j
2
1
2
2¸
] = 1
j
[c÷(jc
1
÷¸c
2
+,1
_
·
j
(l+q(r. ).
0
)Q(. d
0
))]
which can be rearranged as follows:
(.27) 1
j
[cq
c1
+ (c
.cq
c1
÷¸c
2
) + ,1
_
·
j
(l + q.
0
)Q(. d
0
)] = c
where
(.28) c
=
j1
2¸
(.29) 1
=
.
2
1
j
[jq
c
]
1
j
[j
2
q]
=
.
2
1
j
[j]q
c1
[1
j
[j]
2
+ ·c
j)][
Using (26) to (28), employment equilibrium satis…es:
115
1
j
[cq
c1
(1 +
1
j
[j].
2
4¸
1
j
[j]q
c1
(1
j
[j]
2
+ ·c
j))) ÷¸
j
2
4¸
2
_
.
2
1
j
[j]q
c1
(1
j
[j]
2
+ ·c
j))_
2
+,1
_
·
j
(l + q.
0
)Q(. d
0
)] = c
j
which can be rearranged as follows:
cq
c1
+
.
2
4¸
1
j
[j]
2
(q
c1
)
2
(1
j
[j]
2
+ ·c
j))_
c ÷
1
4
_
+ ,1
_
·
j
(l + q.
0
)Q(. d
0
) = c
j
3.1. Case of observable e¤ort
Now consider the case in which the impact of e¤ort on performance pay is observ-
able and constant. Without loss of generality, let j = 1 in all states of the world.
The worker chooses e¤ort to maximize n + c1-¸c
2
and c
=
1
2¸
. The …rm can
determine the optimal level of e¤ort by choosing a piece rate on e¤ort. Using the
fact that 1 = 2¸c, we have that:
: = max
o,j
1
j
[(1 + .c)q
c
÷nq ÷2¸c
2
q]
The …rst order conditions are as follows:
116
q : [(1 + .c)cq
c1
÷n ÷2¸c
2
] = 0
n = (1 +.c)cq
c1
÷2¸c
2
c : [.q
c
÷¸4cq] = 0 (.30)
c =
.q
c1
¸4
(.31)
1 = 2¸c = 2¸
.q
c1
¸4
=
.q
c1
2
(.32)
By o¤ering the compensation package n+c1, the …rm always obtains the level
of e¤ort c =
¸.j
1
¸4
. Whenever c = 1,2, c =
¸.cj
1
¸2
and the bonus is equal to the
marginal value of e¤ort, 1 =
¸.j
1
2
=
0)(a,.)
0o
= .cq
c1
.
117
3.2. Derivation of equilibrium conditions in performance pay markets
when there is a monitoring cost
Assume that in order to set up a contract with a bonus pay the …rm has to incur
the monitoring cost C1q. I derive below the …rm problem in order to show that
a decline in C has a similar e¤ect of an increase in ..
: = max
1,j
1
j
[(1 + c
)q
c
÷nq ÷jc
1q ÷C1q]
: = max
1,j
1
j
[(1 +
j1
2¸
)q
c
÷nq ÷
j
2
1
2
2¸
q ÷C1q]
First order conditions yield:
(.33) 1 : 1
j
[
j
2¸
q
c
÷
j
2
1
¸
q ÷Cq] = 0
1
=
1
j
[
1
2
jq
c
÷Cq
1
¸
]
1
j
[j
2
q]
(.34) q : 1
j
[(1 +
j1
2¸
)cq
c1
÷n ÷
j
2
1
2
2¸
÷C1] = 0
118
(.35) n = 1
j
[(1 +
j1
2¸
)cq
c1
÷
j
2
1
2
2¸
÷C1]
Assume j is iid and private information. Since bonus and employment are
decided before the realization of j. the …rm can take j as independent of q and
simplify the solution such that:
(.36) 1
=
1
2
1
j
[j]q
c1
÷
C
¸
[1
j
[j]
2
+ ·c
j)]Using the bonus in the …rst order condition of the …rm gives:
n = cq
c1
+ 1
j
[
j1
2¸
cq
c1
÷
j
2
1
2
2¸
÷C1]
which can be simpli…ed as follows:
n = cq
c1
+ [1
(
1[j]q
c1
2¸
(c ÷
1
2
) + C(
1
2¸
2
÷1))]
With a positive cost of using performance pay, and if [
1[j].j
1
2¸
(c÷
1
2
) ÷C(1 ÷
1
2¸
2
)] 0, both the bonus and the base pay decline with an increase in the cost of
119
the monitoring technology. Note that when C ÷0, [1(
1[j].j
1
2¸
(c ÷
1
2
) +C(
1
2¸
2
÷
1)) 0 for c ÷
1
2
0. In this case, we collapse to equation (12) for . equal to
1, ·c
j) = 0 and j = 1. Also, for high values of C, the bonus is negative,meaning that the performance pay technology is not feasible, since it is too costly
to monitor.
120
.
4
.
5
.
6
.
7
.
8
M
a
t
c
h
R
a
t
e
1980 1990 2000 2010
Year
Match rate without SCHI P Match rate with SCHIP sample
(March CPS 1980-2007 )
Appendi x Fi gure 1 - Match Rate: March CPS 1980-2007
121
Appendix Table 1- Variables used for
matching rotation groups across years :
March CPS from 1979 to 2007
Variable
1980-
1988
1988-
2008
Month-in-sample mis h_mis
HH identifier hhidnum h_idnum
HH number item9 h_hhnum
Line number lineno a_lineno
State - hg_st60
Sex sex a_sex
Race race a_race
HH sequence number hhseqnum h_seq
Note: Change in survey methodology in 1988
122
Appendix Table 2- Variables used in the analysis: March CPS
from 1979 to 2007
Variable 1980-1988 1988-2008
Wages and salaries earnings i51a wsal_val
Earnings (self-employed) i51b semp_val
LF status besr a_lfsr
Weeks worked last year i34wk wkswork
Hours worked last year i38 hrswk
Allocated earnings incwsflag i_ernval
Topcoded earnings flag51a tcernval
Household weight hhsupwgt hsup_wgt
HH total income hhinctot htotval
Part-Time Full-Time Status rwewkrs wewkrs
Class of worker - longest job i50cw weclw
Education highgrad2 schl1 - a_hga
Age age age
Industry - longest job rwemind wemind
Head of the HH relhead hhdrel
Union member lumember a_unmem
More than one employer i39 phmemprs
Weeks looking or on layoff i43wk lkweeks
Weeks looking in one strech i44 lkstrch
Note: Change in survey methodology in 1988
123
Appendix Table 3- Demographic
characteristics of the March CPS
sample: rotation groups 1-4 from 1979
to 2007
Demographic characteristic Percent
in the
sample
male 47.7
manufacturing job** 12.7
white 85.9
unemployed** 5.3
married 47,9
highschool 66.9
some college 17
in the labor force 49.5
full-time** 78.3
part-time** 18.1
private sector** 67.9
self-employed** 10
imputted wages** 14.7
topcoded wages** 4.1
age <25 33.5
age 25-35 13.4
age 35-45 15.2
age 45-55 13.2
age 55-65 10.6
age 65+ 13.8
union member** 3.4
Note: 1,345,109 obs
** ratio from In the Labor Force group
References
[1] Abraham, Katharine G. and Robert Shimer, (2001). "Changes in Unemploy-
ment Duration and Labor Force Attachment," NBER working paper 8513.
[2] Acemoglu, Daron, (1999). “Changes in Unemployment and Wage Inequality:
An Alternative Theory and Some Evidence,” American Economic Review, 89
(December), 1259—1278.
[3] Acemoglu, Daron, (2002). “Technical Change, Inequality and the Labor Mar-
ket,” Journal of Economic Literature 40 (March), 7-72.
[4] Alvarez, Fernando and Marcelo Veracierto, (1999). "Labor-Market Policies in
an Equilibrium Search Model," NBER Macroeconomics Annual 1999. B. S.
Bernanke and J. J. Rotemberg, Volume 14. Cambridge and London: MIT
Press, 2000, 265-304.
[5] Autor, David H. , Lawrence F. Katz, Melissa S. Kearney, (2008) . "Trends in
U.S. Wage Inequality: Revising the Revisionists," Review of Economics and
Statistics 90:2, 300-323.
[6] Bachmann, Ruediger and Christian Bayer, (2009). "Firm-Speci…c Productiv-
ity Risk over the Business Cycle: Facts and Aggregate Implications," mimeo.
[7] Baker, George, Robert Gibbons and Kevin J. Murphy, (1992). "Subjective
Performance Measures in Optimal Incentive Contracts," mimeo.
[8] Bjelland, Melissa, Bruce Fallick, John Haltiwanger and Erika McEntarfer,
(2008). "Employer-to-employer Flows in the United States: Estimates used
Linked Employer-employee Data," NBER working paper 13867.
[9] Blanchard, Olivier, and John Simon, (2001). "The Long and Large Decline in
U.S. Output Volatility," Brookings Papers on Economic Activity, 1, 135-64.
124
125
[10] Bloom, Nicholas, 2009. The Impact of Uncertainty Shocks, Econometrica, Vol.
77, No. 3 (May, 2009), 623–685.
[11] Card, David and John E. DiNardo, (2002). “Skill-Biased Technological
Change and Rising Wage Inequality: Some Problems and Puzzles,” Jour-
nal of Labor Economics 20 (October): 733-83.
[12] Celik, Sule, Chinhui Juhn, Kristin McCue (2009). "Understanding Earnings
Instability: How Important are Employment Fluctuations and Job Changes?"
mimeo
[13] Chugh, Sanjay, (2009). "Costly External Finance and Labor Market Dynam-
ics," mimeo.
[14] Comin, Diego, Erica L. Groshen and Bess Rabin, (2006). "Turbulent …rms,
turbulent wages?" NBER working paper 12032.
[15] Cooper, Russel, John Haltiwanger, and Jonathan L. Willis, (2007). "Implica-
tions of Search Frictions: Matching Aggregate and Establishment-level Ob-
servations," mimeo.
[16] Cunha, Flavio and James Heckman, (2007). "The Evolution of Inequality,
Heterogeneity and Uncertainty in Labor Earnings in the U.S. Economy," IZA
Discussion Paper No. 3115.
[17] Davis, Steven J. and James A. Kahn, (2008). "Interpreting the Great Moder-
ation: Changes in the Volatility of Economic Activity at the Macro and Micro
Levels," NBER working paper 14048.
[18] Davis, Steven J. , 2008. "The Decline of Job Loss and Why It Matters,"
American Economic Review: Papers & Proceedings 2008, 98:2, 263–267.
[19] Davis, Steven J. , R. Jason Faberman, and John Haltiwanger, (2006a). "The
Flow Approach to Labor Markets: New Data Sources and Micro–Macro
Links," Journal of Economic Perspectives, American Economic Association,
vol. 20(3), 3-26, Summer.
[20] Davis, Steven J. , John Haltiwanger , Ron Jarmin, and Javier Miranda,
(2006b). "Volatility and Dispersion in Business Growth Rates: Publicly
126
Traded versus Privately Held Firms," NBER Working Papers 12354, National
Bureau of Economic Research.
[21] Davis, Steven J. , John Haltiwanger, (1990). Gross Job Creation and De-
struction: Microeconomic Evidence and Macroeconomic Implications, NBER
Macroeconomics Annual 1990, Volume 5.
[22] D. McFadden, (1989). " A Method of Simulated Moments for Estimation of
Discrete Response Models Without Numerical Integration," Econometrica,
57(5):995-1026.
[23] Den Han, Wouter J. and Georg Klatenbrunner, (2005). "Anticipated Growth
and Business Cycles in Matching Models", mimeo.
[24] Dynan, Karen, Elmendorf, Douglas and Daniel E. Sichel, (2008). "The Evolu-
tion of Household Income Volatility," Federal Reserve Board working paper.
[25] Dynan, Karen, Elmendorf, Douglas and Daniel E. Sichel, (2006). "Financial
Innovation and the Great Moderation: What Do Household Data Say?" Fed-
eral Reserve Board working paper.
[26] Fallick, Bruce and Charles A. Fleischman, 2004. "Employer-to-Employer
Flows in the U.S. Labor Market: the Complete Picture of Gross Worker
Flows," Finance and Economics Discussion Series 2004-34, Board of Gov-
ernors of the Federal Reserve System.
[27] Farber, Henry, (2005). "What Do We Know About Job Loss in the US? Ev-
idence from the Displaced Worker Survey, 1984-2004," Working paper 498,
Princeton University.
[28] Farber, Henry, (2008). "Employment Insecurity: The Decline in Worker-Firm
Attachment in the United States," Working paper 530, Princeton University.
[29] Gottschalk, Peter and Robert Mo¢tt (1994), “The Growth of Earnings In-
stability in the U.S. Labor Market?” Brookings Papers on Economic Activity,
1994, 217-272.
[30] Gottschalk, Peter, Erika McEntarfer and Robert Mo¢tt (2008),"Trends in
the Transitory Variance of Male Earnings in the U.S., 1991-2003: Preliminary
Evidence from LEHD data", mimeo
127
[31] Hubbard, Thomas (2000). "The Demand for Monitoring Technologies: the
Case of Trucking," The Quarterly Journal of Economics.
[32] Jacobson, Louis S., Robert J. LaLonde, and Daniel G. Sullivan, (1993). “Earn-
ings Losses of Displaced Workers,” American Economic Review, 83(4): 685–
709.
[33] Jaimovich, Nir and Henry E. Siu, (2007). "The Young, the Old, and the
Restless: Demographics and Business Cycle Volatility," Federal Reserve Bank
of Minneapolis Research Department Sta¤ Report 387.
[34] Kambourov, Gueorgui and Iourii Manovskii, (2008) ."Rising Occupational and
Industry Mobility in the United States: 1968-1997," International Economic
Review, 49 (1) February 2008, pp. 41-79.
[35] Kambourov, Gueorgui and Iourii Manovskii, (2007) ."Occupational Mobility
and Wage Inequality," mimeo. University of Pennsylvania.
[36] Katz, Lawrence F. and David H. Autor, (1999). “Changes in the Wage Struc-
ture and Earnings Inequality,” In O. Ashenfelter and D. Card, eds. Handbook
of Labor Economics, volume 3, North Holland.
[37] Kim, Chang-Jin, and Charles Nelson (1999). "Has the U.S. Economy Become
More Stable? A Bayesian Approach Based on a Markov-Switching Model of
the Business Cycle," Review of Economics and Statistics, 81, 608-16.
[38] Krueger, Dirk and Fabrizio Perri, (2005). "Does Income Inequality Lead to
Consumption Inequality? Evidence and Theory." mimeo
[39] Lazear, Edward and Paul Oyer, (2003). "Internal and External Labor Markets:
A Personnel Economics Approach," NBER working paper 10192.
[40] Lemieux, Thomas (2007). "The changing nature of wage inequality," NBER
working paper 13523.
[41] Lemieux, Thomas, MacLeod, W Bentley and Daniel Parent, (2009a). "Per-
formance Pay and Wage Inequality," Quarterly Journal of Economics, 124(1),
February 2009, 1-49.
128
[42] Lemieux, Thomas, MacLeod W Bentley and Daniel Parent, (2009b). "Perfor-
mance Pay, Wage Flexibility, and Hours of Work," unpublished manuscript,
October 2008.
[43] Lubik, Thomas and Michael Krause, (2003). "The (Ir)relevance of Real Wage
Rigidity in the New Keynesian Model with Search Frictions," Economics
Working Paper Archive 504, The Johns Hopkins University,Department of
Economics
[44] Ljungqvist, Lars and Thomas Sargent, (2004). "European Unemployment and
Turbulence Revisited," Journal of the European Economic Association April–
May 2004 2(2–3):456 – 468.
[45] Lucas, Robert Jr. & Prescott, Edward C., (1974). "Equilibrium Search and
Unemployment," Journal of Economic Theory , Elsevier, vol. 7(2), 188-209,
February.
[46] MacLeod, W. Bentley and Parent, Daniel (1999), “Job Characteristics and
the Form of Compensation,” Research in Labor Economics, Vol. 18, edited by
S.W. Polachek. London: JAI Press, 177-242.
[47] Menkulasi, Jeta, (2009). "Rational Inattention and Changes in Macroeco-
nomic Volatility," job market paper.
[48] Michelacci, Claudio and Vincenzo Quadrini,(2008). "Financial Markets and
Wages," University of Southern California, mimeo.
[49] Mortensen, Dale T & Pissarides, Christopher A, (1994). "Job Creation and
Job Destruction in the Theory of Unemployment," Review of Economic Stud-
ies, vol. 61(3), 397-415, July.
[50] Moscarini, Giuseppe and Kaj Thomsson, (2007). "Occupational and Job Mo-
bility in the US," Scan. Journal of Economics,109(4), 807–836.
[51] Neumark, David and Daiji Kawaguchi, (2001). "Attrition Bias and Economic
Relationships Estimated with Matched CPS Files". NBER working paper
8663.
129
[52] Polivka, Anne E. and Stephen M. Miller (1995). "The CPS After the Redesign:
Refocusing the Economic Lens," BLS working paper.
[53] Shimer, Robert (2005). “Reassessing the Ins and Outs of Unemployment,”
University of Chicago, mimeo.
[54] Shimer, Robert (2003). "The Cyclical Behavior of Equilibrium Unemployment
and Vacancies," mimeo
[55] Schmitt-Grohé, Stephanie and Martín Uribe, (2004). Solving dynamic general
equilibrium models using a second-order approximation to the policy function,
Journal of Economic Dynamics and Control, Volume 28, Issue 4, January 2004,
Pages 755-775
[56] Shin, Donggyun and Gary Solon (2008). "Trends in Men’s Earnings Volatility:
What Does the Panel Study of Income Dynamics show?" NBER Working
Paper 14075.
[57] Stock, James, and Mark Watson, (2003). "Has the Business Cycle Changed?
Evidence and Explanations," Prepared for the Federal Reserve Bank of
Kansas City symposium, "Monetary Policy and Uncertainty," Jackson Hole,
Wyoming, August 28-30.
[58] Storesletten, Kjetil, Chris I Telmer and Amir Yaron, (2004). "Cyclical Dynam-
ics in Idiosyncratic Labor Market Risk," The Journal of Political Economy;
Jun 2004; 112, 3
[59] Tauchen, George, (1986). "Finite State Markov-Chain Approximations to Uni-
variate and Vector Autoregressions," Economics Letters, 1986, 20, 177-181.
doc_664320131.pdf