This paper analyzes the allocation of workers to firms in an economy with search friction and sorting. We present a model with two sided heterogeneity, training costs, on-the-job search and vacancy creation. We provide a constructive proof for the non-parametric identification of the model, and evaluate the properties of the associated estimator with a Monte-Carlo simulation. Finally we estimate the model using GMM on the matched employer-employee data from Sweden to decompose the sources of income inequality and quantify the output loss due to search frictions.

We use population panel data on firms and workers in Norway to estimate how a firm's output, use of input factors, and payment to labor change in response to exogenous changes in revenues due to shifts in its product demand or productivity. These estimates allow us to draw causal inferences about how firms change the way they produce as they grow and why larger firms have lower labor shares. We develop and estimate a model to quantify the relative importance of three sources for variation in labor shares across firms: i) the shape of the labor supply curve facing the firm, ii) differences in the returns to scale between labor and other inputs, and iii) heterogeneity across firms in the output elasticities of input factors. We employ instrument variable strategies to isolate plausibly exogenous sources of variation in the revenues of firms. We compare these instrumental variable estimates to OLS estimates and document the biases that arise when using cross-sectional data to draw conclusions about how firms grow and why larger firms have lower labor shares.

Variational inference is a popular machine learning method in a variety of fields, including natural language processing and computer vision. In this paper we evaluate its performance to estimate models of earnings dynamics. We focus on models with a Markovian, conditionally Gaussian persistent component and an additive transitory component. We parameterize the data-generating processes to match estimates from the earnings literature while allowing for nonlinearities, non-Gaussianity, serial correlation in transitory shocks, and time-invariant latent heterogeneity. We implement a range of variational posterior families leading to differentiable objective functions. The results highlight that variational posterior choice is crucial: independent (also known as mean-field) approximations systematically underperform, while richer families provide more reliable inference. We find that the persistent component process is generally well recovered, but that the kurtosis of transitory shocks tends to be understated. Finally, applying the estimator to the Panel Study of Income Dynamics (PSID) from 1980 to 1990, we find the presence of nonlinearities in the conditional volatility and persistence of earnings.

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. Es- timates 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 high-wage workers to high-paying firms. The objective of this paper is to assess the sensi- tivity 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 matter less for earnings inequality and worker sorting becomes always positive and typically strong.

This paper examines how employer and worker specific productivity shocks transmit to wages and employment. I characterize the optimal contract in an equilibrium directed-search model. I provide conditions for identification. I estimate the model on Swedish matched employer-employee data.

We develop two-step and iterative panel data estimators based on a discretization of unobserved heterogeneity. We view discrete estimators as approximations, and study their properties in environments where population heterogeneity is individual-specific and un-restricted. Two applications suggest computational and statistical advantages of the method.

The paper uses the universe of tax record from the Internal Revenue Services to evaluate the size of rents captured by worker and firms in the U.S. labor market. Within a structural model where firms have wage-setting power we show that the size of rents is linked to the pass-trhough of firm shocks to employees' earnings. Our estimates suggets that workers are willing to pay 17% of their earnings to keep their current job versus moving to their second best.

We propose a framework to estimate earnings distributions and worker and firm unobserved heterogeneity while allowing for complementarities and rich mobility and wage dynamics. We estimate our model on Swedish data. We find that log-addivity provides a good approximation for earnings. We find strong sorting, small firm effects and evidence of endogenous mobility.

Proving the folk theorem in a game with three or more players usually requires imposing restrictions on the dimensionality of the stage-game payoffs. We show that all players having different discount factors can substitute for such restrictions.

We develop an equilibrium search model with all the characteristics of the the Canadian welfare system and the Self Sufficiency Program. In this experiment, a group of lone mothers on income assistance for longer than 12 months are offered a wage premium if they find a full-time job within a year. Using the SSP experimental data and Labor Force Survey data we estimate a model with endogenous search effort, full time and part time work, heterogeneity in disutility of work and match heterogeneity. We extend the classical firm-worker wage bargaining problem to work in the presence of non-convex budget sets introduced by non-linear policies. The model is then used to quantify the crowding out effects associated with extending the SSP program to all women in the economy.