This paper examines how employer- and worker-specific productivity shocks transmit to earnings and employment. We develop an equilibrium search model and characterize the optimal contract offered by firms. Risk-neutral firms provide partial insurance against shocks to risk-averse workers and offer contingent contracts, where payments are backloaded in good times and frontloaded in bad times. The model is estimated on matched employer-employee data from Sweden. Firms absorb persistent worker and firm shocks, with respective passthrough values of 26 and 10 percent. We evaluate the effects of redistributive policies and find that 30 percent of government insurance is undone by crowding out firm insurance.

We study discrete panel data methods where unobserved heterogeneity is revealed in a first step, in environments where population heterogeneity is not discrete. We focus on two‐step grouped fixed‐effects (GFE) estimators, where individuals are first classified into groups using kmeans clustering, and the model is then estimated allowing for group‐specific heterogeneity. Our framework relies on two key properties: heterogeneity is a function—possibly nonlinear and time‐varying—of a low‐dimensional continuous latent type, and informative moments are available for classification. We illustrate the method in a model of wages and labor market participation, and in a probit model with time‐varying heterogeneity. We derive asymptotic expansions of two‐step GFE estimators as the number of groups grows with the two dimensions of the panel. We propose a data‐driven rule for the number of groups, and discuss bias reduction and inference.

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.

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.

Many studies use matched employer-employee data to estimate a statistical model of earnings determination with worker and firm fixed effects. Estimates based on this model have produced influential yet controversial conclusions. 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 United States 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.