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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Sorting Between and Within Industries: A Testable Model of Assortative Matching
January 2017
Working Paper Number:
CES-17-43
We test Shimer's (2005) theory of the sorting of workers between and within industrial sectors based on directed search with coordination frictions, deliberately maintaining its static general equilibrium framework. We fit the model to sector-specific wage, vacancy and output data, including publicly-available statistics that characterize the distribution of worker and employer wage heterogeneity across sectors. Our empirical method is general and can be applied to a broad class of assignment models. The results indicate that industries are the loci of sorting-more productive workers are employed in more productive industries. The evidence confirm that strong assortative matching can be present even when worker and employer components of wage heterogeneity are weakly correlated.
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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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Distribution Preserving Statistical Disclosure Limitation
September 2006
Working Paper Number:
tp-2006-04
One approach to limiting disclosure risk in public-use microdata is to release multiply-imputed,
partially synthetic data sets. These are data on actual respondents, but with confidential data
replaced by multiply-imputed synthetic values. A mis-specified imputation model can invalidate
inferences because the distribution of synthetic data is completely determined by the model used
to generate them. We present two practical methods of generating synthetic values when the imputer
has only limited information about the true data generating process. One is applicable when
the true likelihood is known up to a monotone transformation. The second requires only limited
knowledge of the true likelihood, but nevertheless preserves the conditional distribution of the confidential
data, up to sampling error, on arbitrary subdomains. Our method maximizes data utility
and minimizes incremental disclosure risk up to posterior uncertainty in the imputation model and
sampling error in the estimated transformation. We validate the approach with a simulation and
application to a large linked employer-employee database.
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Job Referral Networks and the Determination of Earnings in Local Labor Markets
December 2010
Working Paper Number:
CES-10-40
Referral networks may affect the efficiency and equity of labor market outcomes, but few studies have been able to identify earnings effects empirically. To make progress, I set up a model of on-the-job search in which referral networks channel information about high-paying jobs. I evaluate the model using employer-employee matched data for the U.S. linked to the Census block of residence for each worker. The referral effect is identified by variations in the quality of local referral networks within narrowly defined neighborhoods. I find, consistent with the model, a positive and significant role for local referral networks on the full distribution of earnings outcomes from job search.
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Ranking Firms Using Revealed Preference
January 2017
Working Paper Number:
CES-17-61
This paper estimates workers' preferences for firms by studying the structure of employer-toemployer transitions in U.S. administrative data. The paper uses a tool from numerical linear algebra to measure the central tendency of worker flows, which is closely related to the ranking of firms revealed by workers' choices. There is evidence for compensating differential when workers systematically move to lower-paying firms in a way that cannot be accounted for by layoffs or
differences in recruiting intensity. The estimates suggest that compensating differentials account
for over half of the firm component of the variance of earnings.
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Modeling Labor Markets with Heterogeneous Agents and Matches
May 2002
Working Paper Number:
tp-2002-19
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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Wage Dispersion, Compensation Policy and the Role of Firms
November 2005
Working Paper Number:
tp-2005-04
Empirical work in economics stresses the importance of unobserved firm- and person-level characteristics
in the determination of wages, finding that these unobserved components account for the overwhelming
majority of variation in wages. However, little is known about the mechanisms sustaining these wage di'er-
entials. This paper attempts to demystify the firm-side of the puzzle by developing a statistical model that
enriches the role that firms play in wage determination, allowing firms to influence both average wages as
well as the returns to observable worker characteristics.
I exploit the hierarchical nature of a unique employer-employee linked dataset for the United States,
estimating a multilevel statistical model of earnings that accounts for firm-specific deviations in average
wages as well as the returns to components of human capital - race, gender, education, and experience -
while also controlling for person-level heterogeneity in earnings. These idiosyncratic prices reflect one aspect
of firm compensation policy; another, and more novel aspect, is the unstructured characterization of the
covariance of these prices across firms.
I estimate the model's variance parameters using Restricted (or Residual) Maximum Likelihood tech-
niques. Results suggest that there is significant variation in the returns to worker characteristics across
firms. First, estimates of the parameters of the covariance matrix of firm-specific returns are statistically
significant. Firms that tend to pay higher average wages also tend to pay higher than average returns to
worker characteristics; firms that tend to reward highly the human capital of men also highly reward the
human capital of women. For instance, the correlation between the firm-specific returns to education for
men and women is 0.57. Second, the firm-specific returns account for roughly 9% of the variation in wages
- approximately 50% of the variation in wages explained by firm-specific intercepts alone. The inclusion of
firm-specific returns ties variation in wages, otherwise attributable to firm-specific intercepts, to observable
components of human capital.
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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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Total Error and Variability Measures for the Quarterly Workforce Indicators and LEHD Origin Destination Employment Statistics in OnTheMap
September 2020
Working Paper Number:
CES-20-30
We report results from the first comprehensive total quality evaluation of five major indicators in the U.S. Census Bureau's Longitudinal Employer-Household Dynamics (LEHD) Program Quarterly Workforce Indicators (QWI): total flow-employment, beginning-of-quarter employment, full quarter employment, average monthly earnings of full-quarter employees, and total quarterly payroll. Beginning-of-quarter employment is also the main tabulation variable in the LEHD Origin-Destination Employment Statistics (LODES) workplace reports as displayed in On-TheMap (OTM), including OnTheMap for Emergency Management. We account for errors due to coverage; record-level non response; edit and imputation of item missing data; and statistical disclosure limitation. The analysis reveals that the five publication variables under study are estimated very accurately for tabulations involving at least 10 jobs. Tabulations involving three to nine jobs are a transition zone, where cells may be fit for use with caution. Tabulations involving one or two jobs, which are generally suppressed on fitness-for-use criteria in the QWI and synthesized in LODES, have substantial total variability but can still be used to estimate statistics for untabulated aggregates as long as the job count in the aggregate is more than 10.
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Earnings Inequality and Mobility Trends in the United States: Nationally Representative Estimates from Longitudinally Linked Employer-Employee Data
January 2017
Working Paper Number:
CES-17-24
Using earnings data from the U.S. Census Bureau, this paper analyzes the role of the employer in explaining the rise in earnings inequality in the United States. We first establish a consistent frame of analysis appropriate for administrative data used to study earnings inequality. We show that the trends in earnings inequality in the administrative data from the Longitudinal Employer-Household Dynamics Program are inconsistent with other data sources when we do not correct for the presence of misused SSNs. After this correction to the worker frame, we analyze how the earnings distribution has changed in the last decade. We present a decomposition of the year-to-year changes in the earnings distribution from 2004-2013. Even when simplifying these flows to movements between the bottom 20%, the middle 60% and the top 20% of the earnings distribution, about 20.5 million workers undergo a transition each year. Another 19.9 million move between employment and nonemployment. To understand the role of the firm in these transitions, we estimate a model for log earnings with additive fixed worker and firm effects using all jobs held by eligible workers from 2004-2013. We construct a composite log earnings firm component across all jobs for a worker in a given year and a non-firm component. We also construct a skill-type index. We show that, while the difference between working at a low-or middle-paying firm are relatively small, the gains from working at a top-paying firm are large. Specifically, the benefits of working for a high-paying firm are not only realized today, through higher earnings paid to the worker, but also persist through an increase in the probability of upward mobility. High-paying firms facilitate moving workers to the top of the earnings distribution and keeping them there.
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