We propose a framework to identify and estimate earnings distributions and worker composition on matched panel data, allowing for two‐sided worker‐firm unobserved heterogeneity and complementarities in earnings. We introduce two models: a static model that allows for nonlinear interactions between workers and firms, and a dynamic model that allows, in addition, for Markovian earnings dynamics and endogenous mobility. We show that this framework nests a number of structural models of wages and worker mobility. We establish identification in short panels, and develop tractable two‐step estimators where firms are classified in a first step. Applying our method to Swedish administrative data, we find that log‐earnings are approximately additive in worker and firm heterogeneity. Our estimates imply the presence of strong sorting patterns between workers and firms, and a small contribution of firms—net of worker composition—to earnings dispersion. In addition, we document that wages have a direct effect on mobility, and that, beyond their dependence on the current firm, earnings after a job move also depend on the previous employer.

Using this panel data, we provide two empirical findings on the role that firms play in the wage determination in the U.S. The first finding is that idiosyncratic productivity shocks to a firm transmit significantly to the earnings of its workers. Controlling for time-invariant firm and worker heterogeneity through a difference-indifferences strategy, we estimate that a 10 percent increase in the value added of a firm leads to a 1.4 percent increase in the earnings of incumbent workers. The second finding is that little of the variation in earnings is due to workers being employed in different firms. Estimating a two-way (worker and firm) fixed effect model, we find that firm effects explain no more than 3 percent of the variation in workers' earnings. To interpret these two findings, we develop a model of the labor market where multiple employers compete with one another for workers who have heterogeneous preferences over non-wage job characteristics or amenities. These heterogeneous preferences give rise to imperfect competition and rents. The model suggests a significant amount of rents and imperfect competition in the U.S. labor market. Workers are, on average, willing to pay 14 percent of their wage to stay in the current jobs. Comparing these worker rents to those earned by employers suggests that total rents are divided relatively equally between firms and workers. The model also reveals that the finding of small firm effects do not imply that labor markets are competitive or that rents are negligible. Instead, firm effects are small because productive firms tend to have good amenities, which pushes down the wages that these firms have to pay. As a result, firms contribute much less to earnings inequality than what is predicted by the variance of firm productivity only.

We quantify the importance of imperfect competition in the US labor market by estimating the size of labor market rents earned by American firms and workers. We construct a matched employer-employee panel dataset by combining the universe of US business and worker tax records for the period 2001–2015. Using this panel data, we identify and estimate an equilibrium model of the labor market with two-sided heterogeneity where workers view firms as imperfect substitutes because of heterogeneous preferences over nonwage job characteristics. The model allows us to draw inference about imperfect competition, worker sorting, compensating differentials, and rent sharing. (JEL D24, H24, H25, J22, J24, J31, J42)

We study panel data estimators based on a discretization of unobserved heterogeneity when individual heterogeneity is not necessarily discrete in the population. We focus on two-step grouped-fixed effects estimators, where individuals are classified into groups in a first step using kmeans clustering, and the model is estimated in a second step allowing for group-specific heterogeneity. We analyze the asymptotic properties of these discrete estimators as the number of groups grows with the sample size, and we show that bias reduction techniques can improve their performance. In addition to reducing the num-ber of parameters, grouped fixed-effects methods provide effective regularization. When allowing for the presence of time-varying unobserved heterogeneity, we show they enjoy fast rates of convergence depending of the underlying dimension of heterogeneity. Finally, we document the finite sample properties of two-step grouped fixedeffects estimators in two applications: a structural dynamic discrete choice model of migration, and a model of wages with worker and firm heterogeneity.JEL codes: C23, C38.

Many studies use matched employer-employee data to estimate a statistical model of earnings determination where log-earnings are expressed as the sum of worker effects, firm effects, covariates, and idiosyncratic error terms. Estimates based on this model have produced two influential yet controversial conclusions. First, firm effects typically explain around 20% of the variance of log-earnings, pointing to the importance of firm-specific wage-setting for earnings inequality. Second, the correlation between firm and worker effects is often small and sometimes negative, indicating little if any sorting of highwage workers to high-paying firms. The objective of this paper is to assess the sensitivity of these conclusions to the biases that arise because of limited mobility of workers across firms. We use employer-employee data from the US and several European countries while taking advantage of both fixed-effects and random-effects methods for bias-correction. We find that limited mobility bias is severe and that bias-correction is important. Once one corrects for limited mobility bias, firm effects dispersion matters less for earnings inequality and worker sorting becomes always positive and typically strong.