I present a matching model with heterogeneous workers, firms, and worker-fim
matches. The model generalizes the seminal Jovanovic (1979) model to the case of
heterogeneous agents. The equilibrium wage is linear in a person-specific component,
a firm-specific component, and a match specific component that varies with tenure.
Under certain conditions, the equilibrium wage takes a simpler structure where the
match specific component does not vary with tenure. I discuss fixed- and mixedeffect
methods for estimating wage models with this structure on longitudinal linked
employer-employee data. The fixed effect specification relies on restrictive identification
conditions, but is feasible for very large databases. The mixed model requires less
restrictive identification conditions, but is feasible only on relatively small databases.
Both the fixed and mixed models generate empirical person, firm, and match effects
with characteristics that are consistent with predictions from the matching model; the
mixed model moreso than the fixed model. Shortcomings of the fixed model appear to
be artifacts of the identification conditions.
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Agent Heterogeneity and Learning: An Application to Labor Markets
October 2002
Working Paper Number:
tp-2002-20
I develop a matching model with heterogeneous workers, rms, and worker-firm
matches, and apply it to longitudinal linked data on employers and employees. Workers
vary in their marginal product when employed and their value of leisure when unemployed.
Firms vary in their marginal product and cost of maintaining a vacancy. The
marginal product of a worker-firm match also depends on a match-specific interaction
between worker and rm that I call match quality. Agents have complete information
about worker and rm heterogeneity, and symmetric but incomplete information about
match quality. They learn its value slowly by observing production outcomes. There
are two key results. First, under a Nash bargain, the equilibrium wage is linear in a
person-specific component, a firm-specific component, and the posterior mean of beliefs
about match quality. Second, in each period the separation decision depends only on
the posterior mean of beliefs and person and rm characteristics. These results have
several implications for an empirical model of earnings with person and rm eects.
The rst implies that residuals within a worker-firm match are a martingale; the second
implies the distribution of earnings is truncated.
I test predictions from the matching model using data from the Longitudinal
Employer-Household Dynamics (LEHD) Program at the US Census Bureau. I present
both xed and mixed model specifications of the equilibrium wage function, taking
account of structural aspects implied by the learning process. In the most general
specification, earnings residuals have a completely unstructured covariance within a
worker-firm match. I estimate and test a variety of more parsimonious error structures,
including the martingale structure implied by the learning process. I nd considerable
support for the matching model in these data.
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Firm Dynamics and Assortative Matching
May 2014
Working Paper Number:
CES-14-25
I study the relationship between firm growth and the characteristics of newly hired workers. Using Census microdata I obtain a novel empirical result: when a given firm grows faster it hires workers with higher past wages. These results suggest that productive, fast-growing firms tend to hire more productive workers, a form of positive assortative matching. This contrasts with prior research that has found negligible or negative sorting between workers and firms. I present evidence that this difference arises because previous studies have focused on cross-sectional comparisons across firms and industries, while my results condition on firm characteristics (e.g. size, industry, or firm fixed effects). Motivated by the empirical findings I develop a search model with heterogeneous workers and firms. The model is the first to study worker-firm sorting in an environment with worker heterogeneity, firm productivity shocks, multi-worker firms, and search frictions. Despite this richness the model is tractable, allowing me to characterize assortative matching, compositional dynamics and other properties analytically. I show that the model reproduces the positive firm growth-quality of hires correlation when worker and firm types are strong complements in production (i.e. the production function is strictly log-supermodular).
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Displaced workers, early leavers, and re-employment wages
November 2002
Working Paper Number:
tp-2002-18
In this paper, we lay out a search model that takes explicitly into account the
information flow prior to a mass layoff. Using universal wage data files that allow
us to identify individuals working with healthy and displacing firms both at
the time of displacement as well as any other time period, we test the predictions
of the model on re-employment wage differentials. Workers leaving a "distressed"
firm have higher re-employment wages than workers who stay with the
distressed firm until displacement. This result is robust to the inclusion of controls
for worker quality and unobservable firm characteristics.
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Is it Who You Are, Where You Work, or With Whom You Work? Reassessing the Relationship Between Skill Segregation and Wage Inequality
June 2002
Working Paper Number:
tp-2002-10
In a recent paper, Kremer & Maskin (QJE, forthcoming) develop an assignment model in
which increases in the dispersion and mean of the skill distribution can lead simultaneously
to increases in wage inequality and skill segregation. They then present evidence that,
concurrent with rising wage inequality, wage segregation increased for production workers in
the United States between 1975 and 1986. My paper argues that relying on wages as a proxy
for skill may be problematic. Using a newly developed longitudinal dataset linking virtually
the entire universe of workers in the state of Illinois to their employers, I decompose wages
into components due, not only to person and firm heterogeneity, but also to the characteristics
of their co-workers. Such "co-worker effects" capture the impact of a weighted sum of the
characteristics of all workers in a firm on each individual employee's wage. While rising wage
segregation can result from greater skill segregation, it may also be due to changes in the
variance of co-worker effects in the economy, or to changes in the covariance between the
person, firm, and co-worker components of wages.
Due to the limited availability of demographic information on workers, I rely on the
person specific component of wages to proxy for co-worker "skills." Because these person
effects are unknown ex ante, I implement an iterative estimation approach where they are
first obtained from a preliminary regression that excludes any role for co-workers. Because
virtually all person and firm effects are identified, the approach yields consistent estimates
of the co-worker parameters. My estimates imply that a one standard deviation increase
in both a firm's average person effect and experience level is associated, on average, with
wage increases of 3% to 5%. Firms that increase the wage premia they pay workers appear
to do so in conjunction with upgrading worker quality. Interestingly, the average effect
masks considerable variation in the relative importance of co-workers across industries. After
allowing the co-worker parameters to vary across 2 digit industries, I find that industry
average co-worker effects explain 26% of observed inter-industry wage differentials. Finally,
I decompose the overall distribution of wages into components due to persons, firms, and coworkers.
While co-worker effects do indeed serve to exacerbate wage inequality, the tendency
for high and low skilled workers to sort non-randomly into firms plays a considerably more
prominent role.
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Modeling Endogenous Mobility in Wage Determiniation
June 2015
Working Paper Number:
CES-15-18
We evaluate the bias from endogenous job mobility in fixed-effects estimates of worker- and
firm-specific earnings heterogeneity using longitudinally linked employer-employee data from the LEHD infrastructure file system of the U.S. Census Bureau. First, we propose two new residual diagnostic tests of the assumption that mobility is exogenous to unmodeled determinants of earnings. Both tests reject exogenous mobility. We relax the exogenous mobility assumptions by modeling the evolution of the matched data as an evolving bipartite graph using a Bayesian latent class framework. Our results suggest that endogenous mobility biases estimated firm effects toward zero. To assess validity, we match our estimates of the wage components to out-of-sample estimates of revenue per worker. The corrected estimates attribute much more of the variation in revenue per worker to variation in match quality and worker quality than the uncorrected estimates.
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Abandoning the Sinking Ship: The Composition of Worker Flows Prior to Displacement
August 2002
Working Paper Number:
tp-2002-11
declines experienced by workers several years before displacement occurs. Little attention, however,
has been paid to other changes in compensation and employment in firms prior to the actual
displacement event. This paper examines changes in the composition of job and worker flows
before displacement, and compares the "quality" distribution of workers leaving distressed firms to
that of all movers in general.
More specifically, we exploit a unique dataset that contains observations on all workers over
an extended period of time in a number of US states, combined with survey data, to decompose
different jobflow statistics according to skill group and number of periods before displacement.
Furthermore, we use quantile regression techniques to analyze changes in the skill profile of workers
leaving distressed firms. Throughout the paper, our measure for worker skill is derived from
person fixed effects estimated using the wage regression techniques pioneered by Abowd, Kramarz,
and Margolis (1999) in conjunction with the standard specification for displaced worker studies
(Jacobson, LaLonde, and Sullivan 1993).
We find that there are significant changes to all measures of job and worker flows prior to
displacement. In particular, churning rates increase for all skill groups, but retention rates drop
for high-skilled workers. The quantile regressions reveal a right-shift in the distribution of worker
quality at the time of displacement as compared to average firm exit flows. In the periods prior
to displacement, the patterns are consistent with both discouraged high-skilled workers leaving the
firm, and management actions to layoff low-skilled workers.
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A Formal Test of Assortative Matching in the Labor Market
November 2009
Working Paper Number:
CES-09-40
We estimate a structural model of job assignment in the presence of coordination frictions due to Shimer (2005). The coordination friction model places restrictions on the joint distribution of worker and firm effects from a linear decomposition of log labor earnings. These restrictions permit estimation of the unobservable ability and productivity differences between workers and their employers as well as the way workers sort into jobs on the basis of these unobservable factors. The estimation is performed on matched employer-employee data from the LEHD program of the U.S. Census Bureau. The estimated correlation between worker and firm effects from the earnings decomposition is close to zero, a finding that is often interpreted as evidence that there is no sorting by comparative advantage in the labor market. Our estimates suggest that his finding actually results from a lack of sufficient heterogeneity in the workforce and available jobs. Workers do sort into jobs on the basis of productive differences, but the effects of sorting are not visible because of the composition of workers and employers.
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Estimating the Relationship between Employer-Provided Health Insurance, Worker Mobility, and Wages
September 2002
Working Paper Number:
tp-2002-23
In this paper, a joint model of wages, hazard of a job ending, and
probability of holding employer-provided health insurance is estimated,
taking account of unobservable person and job characteristics. A unique
data source, the 1990 and 1996 SIPP Panels linked to SSA administrative
job histories, enables the identification of random person and job effects
and the correlation of these effects across the three equations. The explicit
modeling of this correlation produces consistent estimates of the
effect of tenure on wages and the effect of health insurance on mobility.
Substantial levels of job-lock and significant annual returns to seniority
are found. Increasing the job-specific probability of obtaining employerprovided
health insurance from 60% to 63%, or increasing the job-specific
hourly wage rate by $.80, are both associated with an equivalent decrease
in the hazard of the job ending. However, the dollar value of the wage
benefit is substantially higher.
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Pay, Employment, and Dynamics of Young Firms
July 2019
Working Paper Number:
CES-19-23
Why do young firms pay less? Using confidential microdata from the US Census Bureau, we find lower earnings among workers at young firms. However, we argue that such measurement is likely subject to worker and firm selection. Exploiting the two-sided panel nature of the data to control for relevant dimensions of worker and firm heterogeneity, we uncover a positive and significant young-firm pay premium. Furthermore, we show that worker selection at firm birth is related to future firm dynamics, including survival and growth. We tie our empirical findings to a simple model of pay, employment, and dynamics of young firms.
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The Alpha Beta Gamma of the Labor Market
April 2022
Working Paper Number:
CES-22-10
Using a large panel dataset of US workers, we calibrate a search-theoretic model of the labor market, where workers are heterogeneous with respect to the parameters governing their employment transitions. We first approximate heterogeneity with a discrete number of latent types, and then calibrate type-specific parameters by matching type-specific moments. Heterogeneity is well approximated by 3 types: as, 's and ?s. Workers of type a find employment quickly because they have large gains from trade, and stick to their jobs because their productivity is similar across jobs. Workers of type ? find employment slowly because they have small gains from trade, and are unlikely to stick to their job because they keep searching for jobs in the right tail of the productivity distribution. During the Great Recession, the magnitude and persistence of aggregate unemployment is caused by ?s, who are vulnerable to shocks and, once displaced, they cycle through multiple unemployment spells before finding stable employment.
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