In this paper we provide the exact formulas for the direct least squares estimation of statistical models that include both person and firm effects. We also provide an algorithm for determining the estimable functions of the person and firm effects (the identifiable effects). The computational techniques are also directly applicable to any linear two-factor analysis of covariance with two high-dimension non-orthogonal factors. We show that the application of the exact solution does not change the substantive conclusions about the relative importance of person and firm effects in the explanation of log real compensation; however, the correlation between person and firm effects is negative, not weakly positive, in the exact solution. We also provide guidance for using the methods developed in earlier work to obtain an accurate approximation.
-
Mixed-Effects Methods For Search and Matching Research
September 2023
Working Paper Number:
CES-23-43
We study mixed-effects methods for estimating equations containing person and firm effects. In economics such models are usually estimated using fixed-effects methods. Recent enhancements to those fixed-effects methods include corrections to the bias in estimating the covariance matrix of the person and firm effects, which we also consider.
View Full
Paper PDF
-
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.
View Full
Paper PDF
-
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.
View Full
Paper PDF
-
Unlocking the Information in Integrated Social Data
May 2002
Working Paper Number:
tp-2002-21
View Full
Paper PDF
-
The Measurement of Human Capital in the U.S. Economy
April 2002
Working Paper Number:
tp-2002-09
We develop a new approach to measuring human capital that permits the distinction of both observable
and unobservable dimensions of skill by associating human capital with the portable part
of an individual's wage rate. Using new large-scale, integrated employer-employee data containing
information on 68 million individuals and 3.6 million firms, we explain a very large proportion
(84%) of the total variation in wages rates and attribute substantial variation to both individual
and employer heterogeneity. While the wage distribution remained largely unchanged between
1992-1997, we document a pronounced right shift in the overall distribution of human capital.
Most workers entering our sample, while less experienced, were otherwise more highly skilled, a
difference which can be attributed almost exclusively to unobservables. Nevertheless, compared
to exiters and continuers, entrants exhibited a greater tendency to match to firms paying below
average internal wages. Firms reduced employment shares of low skilled workers and increased
employment shares of high skilled workers in virtually every industry. Our results strongly suggest
that the distribution of human capital will continue to shift to the right, implying a continuing
up-skilling of the employed labor force.
View Full
Paper PDF
-
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.
View Full
Paper PDF
-
The Relation among Human Capital, Productivity and Market Value: Building Up from Micro Evidence
December 2002
Working Paper Number:
tp-2002-14
This paper investigates and evaluates the direct and indirect contribution of human capital
to business productivity and shareholder value. The impact of human capital may occur in two ways:
the specific knowledge of workers at businesses may directly increase business
performance, or a skilled workforce may also indirectly act as a complement to improved
technologies, business models or organizational practices. We use newly created firm-level
measures of workforce human capital and productivity to examine links between those measures
and the market value of the employing firm. The new human capital measures come from an
integrated employer-employee data base under development at the US Census Bureau. We link
these data to financial information from Compustat at the firm level, which provides measures of
market value and tangible assets. The combination of these two sources permits examination of
the link between human capital, productivity, and market value. There is a substantial positive
relation between human capital and market value that is primarily related to the unmeasured
personal characteristics of the employees, which are captured by the new measures.
View Full
Paper PDF
-
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.
View Full
Paper PDF
-
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.
View Full
Paper PDF
-
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.
View Full
Paper PDF