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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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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Estimating Measurement Error in SIPP Annual Job Earnings: A Comparison of Census Bureau Survey and SSA Administrative Data
July 2011
Working Paper Number:
CES-11-20
We quantify sources of variation in annual job earnings data collected by the Survey of Income and Program Participation (SIPP) to determine how much of the variation is the result of measurement error. Jobs reported in the SIPP are linked to jobs reported in an administrative database, the Detailed Earnings Records (DER) drawn from the Social Security Administration's Master Earnings File, a universe file of all earnings reported on W-2 tax forms. As a result of the match, each job potentially has two earnings observations per year: survey and administrative. Unlike previous validation studies, both of these earnings measures are viewed as noisy measures of some underlying true amount of annual earnings. While the existence of survey error resulting from respondent mistakes or misinterpretation is widely accepted, the idea that administrative data are also error-prone is new. Possible sources of employer reporting error, employee under-reporting of compensation such as tips, and general differences between how earnings may be reported on tax forms and in surveys, necessitates the discarding of the assumption that administrative data are a true measure of the quantity that the survey was designed to collect. In addition, errors in matching SIPP and DER jobs, a necessary task in any use of administrative data, also contribute to measurement error in both earnings variables. We begin by comparing SIPP and DER earnings for different demographic and education groups of SIPP respondents. We also calculate different measures of changes in earnings for individuals switching jobs. We estimate a standard earnings equation model using SIPP and DER earnings and compare the resulting coefficients. Finally exploiting the presence of individuals with multiple jobs and shared employers over time, we estimate an econometric model that includes random person and firm effects, a common error component shared by SIPP and DER earnings, and two independent error components that represent the variation unique to each earnings measure. We compare the variance components from this model and consider how the DER and SIPP differ across unobservable components.
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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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Downward Nominal Wage Rigidity in the United States:
New Evidence from Worker-Firm Linked Data
February 2019
Working Paper Number:
CES-19-07
This paper examines the extent and consequences of Downward Nominal Wage Rigidity (DNWR) using administrative worker-firm linked data from the Longitudinal Employer Household Dynamics (LEHD) program for a large representative U.S. state. Prior to the Great Recession, only 7-8% of job stayers are paid the same nominal hourly wage rate as one year earlier - substantially less than previously found in survey-based data - and about 20% of job stayers experience a wage cut. During the Great Recession, the incidence of wage cuts increases to 30%, followed by a large rise in the proportion of wage freezes to 16% as the economy recovers. Total earnings of job stayers exhibit even fewer zero changes and a larger incidence of reductions than hourly wage rates, due to systematic variations in hours worked. The results are consistent with concurrent findings in the literature that reductions in base pay are exceedingly rare but that firms use different forms of non-base pay and variations in hours worked to flexibilize labor cost. We then exploit the worker-firm link of the LEHD and find that during the Great Recession, firms with indicators of DNWR reduced employment by about 1.2% more per year. This negative effect is driven by significantly lower hiring rates and persists into the recovery. Our results suggest that despite the relatively large incidence of wage cuts in the aggregate, DNWR has sizable allocative consequences.
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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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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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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.
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Hours Off the Clock
January 2017
Working Paper Number:
CES-17-44
To what extent do workers work more hours than they are paid for? The relationship
between hours worked and hours paid, and the conditions under which employers can demand more hours 'off the clock,' is not well understood. The answer to this question impacts worker welfare, as well as wage and hour regulation. In addition, work off the clock has important implications for the measurement and cyclical movement of productivity and wages. In this paper, I construct a unique administrative dataset of hours paid by employers linked to a survey of workers on their reported hours worked to measure work off the clock. Using cross-sectional variation in local labor markets, I find only a small cyclical component to work off the clock. The results point to labor hoarding rather than efficiency wage theory, indicating work off the clock cannot explain the counter-cyclical movement of productivity. I find workers employed by small firms, and in industries with a high rate of wage and hour violations are associated with larger differences in hours worked than hours paid. These findings suggest the importance of tracking hours of work for enforcement of labor regulations.
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Spillovers from Immigrant Diversity in Cities
November 2015
Working Paper Number:
CES-15-37
Using comprehensive longitudinal matched employer-employee data for the U.S., this paper provides new evidence on the relationship between productivity and immigration spawned urban diversity. Existing empirical work has uncovered a robust positive correlation between productivity and immigrant diversity, supporting theory suggesting that diversity acts as a local public good that makes workers more productive by enlarging the pool of knowledge available to them, as well as by fostering opportunities for them to recombine ideas to generate novelty. This paper makes several empirical and conceptual contributions. First, it improves on existing empirical work by addressing various sources of potential bias, especially from unobserved heterogeneity among individuals, work establishments, and cities. Second, it augments identification by using longitudinal data that permits examination of how diversity and productivity co-move. Third, the paper seeks to reveal whether diversity acts upon productivity chiefly at the scale of the city or the workplace. Findings confirm that urban immigrant diversity produces positive and nontrivial spillovers for U.S. workers. This social return represents a distinct channel through which immigration generates broad-based economic benefits.
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Are the Lasting Effects of Employee-Employer Separations induced by Layoff and Disability Similar? Exploring Job Displacement using Survey and Administrative Data
October 2005
Working Paper Number:
tp-2005-03
This paper integrates the existing literatures on displacement and health by examining the enduring
effects of job dislocations that are induced by firm and individual shocks to employment. A joint estimation of
hourly wage rates and weekly hours illuminates the disparities in these economic outcomes
that exist between those who have reestablished themselves in the workplace subsequent to a layoff and
those who have returned to work following the onset of a disability relative to those with uninterrupted
job histories. As an extension of these ideas, employment transitions and workplace adjustments are
modeled to capture spousal reactions to these shocks. Multiple indicators of health from the Survey of
Income and Program Participation and Social Security Administrative benefits records are incorporated
into the analyses of those with impairments that prompted job loss. These measures allow knowledge
to be gleaned regarding the qualitative di'erences in the lasting impacts of job cessation resulting from
medically diagnosed illnesses as compared to estimates uncovered using survey data sources alone. By
considering time durations following these periods of separation in light of these indicators of well-being,
a more comprehensive understanding of the long-run repercussions of employee-employer separation is
acquired.
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