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201103Efficient Search on the Job and the Business Cycle.pdf
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Efficient Search on the Job and the Business Cycle
Author(s): Guido Menzio and Shouyong Shi
Source:
Journal of Political Economy
, Vol. 119, No. 3 (June 2011), pp. 468-510
Published by: The University of Chicago Press
Stable URL: http://www.jstor.org/stable/10.1086/660864
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468
[Journal of Political Economy, 2011, vol. 119, no. 3]
䉷 2011 by The University of Chicago. All rights reserved. 0022-3808/2011/11903-0003$10.00
Efficient Search on the Job and the Business
Cycle
Guido Menzio
University of Pennsylvania and National Bureau of Economic Research
Shouyong Shi
University of Toronto and CEMA-CUFE
The paper develops a model of directed search on the job in which
transitions of workers between unemployment and employment and
across employers are driven by heterogeneity in the quality of firm-
worker matches. The equilibrium is such that the agents’ value and
policy functions are independent of the endogenous distribution of
workers across employment states. Hence, the model can be solved
outside of the steady state and used to measure the effect of cyclical
productivity shocks on the labor market. Productivity shocks are found
to generate large fluctuations in workers’ transitions, unemployment,
and vacancies when matches are experience goods, but not when
matches are inspection goods.
We are grateful to the editor, Robert Shimer, and two referees for their enlightening
comments. We have also benefited from the insights of Mike Elsby, Martin Gervais, Marcus
Hagedorn, Bob Hall, Nir Jaimovich, Dale Mortensen, Giuseppe Moscarini, Toshihiko Mu-
koyama, Thijs van Rens, Ludo Visschers, Randy Wright, and seminar participants at many
conferences and universities. We thank Frank Diebold, Jason Faberman, Giuseppe Mos-
carini, Eva Nagypa´l, David Neumark, and Daniel Polsky for generously sharing their data
with us. Menzio gratefully acknowledges the financial support and the hospitality of the
Hoover Institution. Shi gratefully acknowledges the financial support from the Social
Sciences and Humanities Research Council of Canada and from the Bank of Canada
Fellowship.
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efficient job search 469
TABLE 1
Summary Statistics, Quarterly U.S. Data
xuvh
ue
h
eu
h
ee
p
SD(x)/SD(p) 9.56 10.9 5.96 5.48 5.98 1
Autocorr(x) .872 .909 .822 .698 .597 .760
Corr(7, x):
u 1 ⫺.902 ⫺.916 .778 ⫺.634 ⫺.283
v . . . 1 .902 ⫺.778 .607 .423
h
ue
... ... 1 ⫺.677 .669 .299
h
eu
... ... ... 1 ⫺.301 ⫺.528
h
ee
. . . . . . . . . . . . 1 .208
p ... ... ... ... ... 1
Note.—The seasonally adjusted unemployment rate, u, is constructed by the Bureau
of Labor Statistics (BLS) from the Current Population Survey (CPS). The seasonally ad-
justed Help-Wanted Advertising Index, v, is constructed by the Conference Board. The
UE and EU rates, and , are constructed from the seasonally adjusted unemployment
ue eu
hh
rate and the short-term unemployment rate as explained in App. B. The EE rate, , is
ee
h
constructed by Nagypa´l (2007) from the CPS microdata as explained in App. B. The
variables u, v, , , and are quarterly averages of monthly series. Average labor
ue eu ee
hh h
productivity, p, is seasonally adjusted real average output per worker in the nonfarm
business sector constructed by the BLS. The series for u, v, , , and p cover the period
ue eu
hh
1951(I)–2006(II). The series for covers the period 1994(I)–2006(II). The standard
ee
h
deviation of is expressed relative to the standard deviation of p over the period 1994(I)–
ee
h
2006(II), and the correlation of with u, v,,,andp refers to the period 1994(I)–
ee ue eu
hhh
2006(II). All variables are reported in logs as deviations from a Hodrick-Prescott (HP)
trend with smoothing parameter 1,600.
I. Introduction
In the U.S. labor market, workers move frequently between employment
and unemployment and across different employers. On average, the
rate at which unemployed workers move into employment (henceforth,
the UE rate) is 42 percent a month, the rate at which employed workers
move into unemployment (the EU rate) is 2.6 percent a month, and
the rate at which workers move from one employer to the other (the
EE rate) is 2.9 percent a month. These transition rates are not only
large but also very volatile at the business cycle frequency (relative to
labor productivity), thus contributing to the large volatility of unem-
ployment and vacancies. As documented in table 1, the UE, EU, and
EE rates are five times as volatile as labor productivity, and the unem-
ployment and vacancy rates are more than 10 times as volatile as labor
productivity. Moreover, the cyclical fluctuations in the UE, EU, and EE
rates display a clear pattern of correlations with the cyclical fluctuations
in unemployment and vacancies. As documented in table 1, the UE and
EE rates are strongly negatively correlated with unemployment and pos-
itively correlated with vacancies, and the EU rate is strongly positively
correlated with unemployment and negatively correlated with vacancies.
This paper proposes a model of directed search on the job in which
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470 journal of political economy
the workers’ transitions between employment and unemployment and
across different employers are driven by heterogeneity in the quality of
different firm-worker matches. Like models of random search on the
job (e.g., Burdett and Mortensen 1998; Postel-Vinay and Robin 2002),
our model can account for the frequency and pattern of the transition
of individual workers across employment states. Unlike models of ran-
dom search on the job, our model can be easily solved in and out of
the steady state, and hence, it can be used to study the behavior of
workers’ transitions, unemployment, and vacancies over the business
cycle.
In this paper, we use our model to measure the response of the labor
market to cyclical fluctuations in aggregate productivity. We find that
this response critically depends on whether the quality of a firm-worker
match is observed before or after the match is created. If the quality is
observed after the match is created (i.e., if matches are experience
goods), aggregate productivity shocks generate large fluctuations in un-
employment, vacancies, and workers’ transition rates. If the quality is
observed before the match is created (i.e., if matches are inspection
goods), the effect of aggregate productivity shocks on the labor market
is negligible.
In our model, the search process is directed—as in Shimer (1996)
and Moen (1997)—rather than random—as in Mortensen (1982) and
Pissarides (1985). On one side of the market, firms choose how many
and what type of vacancies to create. On the other side of the market,
workers choose what type of vacancies to search. The type of a vacancy
is defined by the conditions under which it hires a worker and by the
value of the employment contract that it offers to a new hire. Workers
and vacancies searching for each other are brought into contact by a
constant returns to scale meeting function. Upon meeting, a worker
and a firm observe a signal about the idiosyncratic productivity (i.e.,
quality) of their match. If the signal meets the conditions specified by
the vacancy’s type, the worker and the firm begin to produce and,
eventually, observe the actual quality of their match. If the signal does
not meet those conditions, the worker returns to his previous employ-
ment position. Depending on the informativeness of the signal, the
model captures different views about the matching process. If the signal
is completely uninformative, a match is an experience good. If the signal
is perfectly informative, a match is an inspection good. If the signal
contains some but not all information, a match is partly an inspection
and partly an experience good.
In the theoretical part of the paper, we formulate the social planner’s
problem and characterize its solution. Then we prove that there exists
a unique equilibrium for the market economy. This equilibrium is block
recursive in the sense that the agents’ value and policy functions depend
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efficient job search 471
on the aggregate state of the economy only through the realization of
the aggregate shocks, and not through the entire distribution of workers
across employment states (i.e., unemployment and employment in dif-
ferent matches). Because of this property, we can solve our model with
heterogeneous agents and aggregate shocks as easily as one would solve
a representative agent model. Moreover, we prove that the equilibrium
is efficient in the sense that it decentralizes the social planner’s allo-
cation. Because of this property, we can characterize the behavior of
the economy using the first-order conditions of the planner’s problem.
The equilibrium is block recursive because the search process is di-
rected. In fact, with directed search, workers in different employment
states choose to search for different types of vacancies. Workers in low-
value employment states (i.e., unemployment and employment in low-
quality matches) choose to search for vacancies that offer a low value
but are easy to find (because the number of vacancies per applicant is
high). Workers in high-value employment states (i.e., employment in
high-quality matches) choose to search for vacancies that offer a high
value but are hard to find. As a result of this self-selection process, a
firm that opens a particular type of vacancy knows that it will meet only
one type of worker. Hence, the firm’s expected value from meeting a
worker does not depend on the distribution of workers across employ-
ment states, and because of firms’ free entry, the probability that the
firm meets an applicant must have the same property. In turn, the fact
that the meeting probabilities are independent of the distribution of
workers across employment states is sufficient to guarantee that the
agents’ value and policy functions will also be independent of the
distribution.
In the quantitative part of the paper, we consider two versions of the
model that, a priori, provide an equally plausible description of the
labor market. Specifically, we consider a version of the model in which
matches are experience goods and a version in which matches are in-
spection goods. We calibrate the parameters of these two versions of
the model using data on the frequency at which workers move between
employment and unemployment and across different employers, as well
as data on the relationship between tenure and the frequency at which
workers leave their jobs.
Given the calibrated parameter values, we simulate the two versions
of the model to measure the effect of aggregate productivity shocks on
the labor market. When matches are experience goods, we find that
the fluctuations in unemployment, vacancies, and workers’ transition
rates generated by productivity shocks display the same pattern of co-
movement as in the data. Moreover, we find that the volatility of un-
employment, vacancies, and workers’ transition rates generated by pro-
ductivity shocks accounts for a large fraction of the empirical volatility
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