Identifying Uncertainty, Learning about Productivity, and Human Capital Acquisition: A Reassessment of Labor Market Sorting and Firm Monopsony Power

We examine the empirical content of a large class of dynamic matching models of the labor market with ex-ante heterogeneous firms and workers, symmetric uncertainty and learning about workers’ productivity, and firms’ monopsony power. We allow workers’ human capital, acquired before and after entry into the labor market, to be general across firms to varying degrees. Such a framework nests and extends known models of worker turnover across firms, occupational choice, wage growth, wage differentials across occupations, firms, and industries, and wage dispersion across workers and over the life cycle. We establish intuitive conditions under which the model primitives are semiparametrically identified solely from data on workers’ wages and jobs, despite the dynamics of these models giving rise to complex patterns of selection based on endogenously time-varying observable and unobservable characteristics of workers and firms. By relying on this identification argument, we develop a constructive estimator of the model primitives, which builds on common methods for mixture and extremal quantile regression models and displays standard properties. Through the lens of this framework, we investigate how well typical empirical wage measures of matching assortativeness and firms’ wage-setting power detect the degrees of sorting and monopsony power in the labor market, respectively. We show that usual measures of sorting severely understate its importance because they ignore the option value of worker human capital and the information about worker productivity acquired through employment, in terms of higher future wages and improved future sorting, which is priced into current wages thus depressing them. We also demonstrate how the markdown of wages relative to output largely overstates firms’ labor market power by ignoring that this option value, which captures future returns from acquired human capital and information, generally lowers wages. We find evidence of both of these features in U.S. data by documenting a strong degree of labor market sorting once appropriately measured and, correspondingly, a lower degree of firm monopsony power than typically documented.