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.
-
Computing Person and Firm Effects Using Linked Longitudinal Employer-Employee Data
March 2002
Working Paper Number:
tp-2002-06
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.
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
-
NOISE INFUSION AS A CONFIDENTIALITY PROTECTION MEASURE FOR GRAPH-BASED STATISTICS
September 2014
Working Paper Number:
CES-14-30
We use the bipartite graph representation of longitudinally linked em-ployer-employee data, and the associated projections onto the employer and em-ployee nodes, respectively, to characterize the set of potential statistical summar-ies that the trusted custodian might produce. We consider noise infusion as the primary confidentiality protection method. We show that a relatively straightfor-ward extension of the dynamic noise-infusion method used in the U.S. Census Bureau's Quarterly Workforce Indicators can be adapted to provide the same confidentiality guarantees for the graph-based statistics: all inputs have been modified by a minimum percentage deviation (i.e., no actual respondent data are used) and, as the number of entities contributing to a particular statistic increases, the accuracy of that statistic approaches the unprotected value. Our method also ensures that the protected statistics will be identical in all releases based on the same inputs.
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
-
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
-
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
-
Male Earnings Volatility in LEHD before, during, and after the Great Recession
September 2020
Working Paper Number:
CES-20-31
This paper is part of a coordinated collection of papers on prime-age male earnings volatility. Each paper produces a similar set of statistics for the same reference population using a different primary data source. Our primary data source is the Census Bureau's Longitudinal Employer-Household Dynamics (LEHD) infrastructure files. Using LEHD data from 1998 to 2016, we create a well-defined population frame to facilitate accurate estimation of temporal changes comparable to designed longitudinal samples of people. We show that earnings volatility, excluding increases during recessions, has declined over the analysis period, a finding robust to various sensitivity analyses. Although we find volatility is declining, the effect is not homogeneous, particularly for workers with tenuous labor force attachment for whom volatility is increasing. These 'not stable' workers have earnings volatility approximately 30 times larger than stable workers, but more important for earnings volatility trends we observe a large increase in the share of stable employment from 60% in 1998 to 67% in 2016, which we show to largely be responsible for the decline in overall earnings volatility. To further emphasize the importance of not stable and/or low earning workers we also conduct comparisons with the PSID and show how changes over time in the share of workers at the bottom tail of the cross-sectional earnings distributions can produce either declining or increasing earnings volatility trends.
View Full
Paper PDF
-
An Economist's Primer on Survey Samples
September 2000
Working Paper Number:
CES-00-15
Survey data underlie most empirical work in economics, yet economists typically have little familiarity with survey sample design and its effects on inference. This paper describes how sample designs depart from the simple random sampling model implicit in most econometrics textbooks, points out where the effects of this departure are likely to be greatest, and describes the relationship between design-based estimators developed by survey statisticians and related econometric methods for regression. Its intent is to provide empirical economists with enough background in survey methods to make informed use of design-based estimators. It emphasizes surveys of households (the source of most public-use files), but also considers how surveys of businesses differ. Examples from the National Longitudinal Survey of Youth of 1979 and the Current Population Survey illustrate practical aspects of design-based estimation.
View Full
Paper PDF
-
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.
View Full
Paper PDF
-
U.S. Long-Term Earnings Outcomes by Sex, Race, Ethnicity, and Place of Birth
May 2021
Working Paper Number:
CES-21-07R
This paper is part of the Global Income Dynamics Project cross-country comparison of earnings inequality, volatility, and mobility. Using data from the U.S. Census Bureau's Longitudinal Employer-Household Dynamics (LEHD) infrastructure files we produce a uniform set of earnings statistics for the U.S. From 1998 to 2019, we find U.S. earnings inequality has increased and volatility has decreased. The combination of increased inequality and reduced volatility suggest earnings growth differs substantially across different demographic groups. We explore this further by estimating 12-year average earnings for a single cohort of age 25-54 eligible workers. Differences in labor supply (hours paid and quarters worked) are found to explain almost 90% of the variation in worker earnings, although even after controlling for labor supply substantial earnings differences across demographic groups remain unexplained. Using a quantile regression approach, we estimate counterfactual earnings distributions for each demographic group. We find that at the bottom of the earnings distribution differences in characteristics such as hours paid, geographic division, industry, and education explain almost all the earnings gap, however above the median the contribution of the differences in the returns to characteristics becomes the dominant component.
View Full
Paper PDF