Identifying Equilibrium Models of Labor Market Sorting

Does the market allocate the right workers to the right jobs? Since observable (to economists) variables account for only a small fraction of the wage variance in the data, to answer this question it is essential to study assortative matching between employers and employees based on their unobserved characteristics. This paper enables this line of research. We show theoretically that all parameters of the classic model of sorting based on absolute advantage in Becker (1973) with search frictions can be identified using only matched employer-employee data on wages and labor market transitions. In particular, these data are sufficient to assess whether matching between workers and firms is assortative, whether sorting is positive or negative, and to measure the potential effect on output from moving any given worker to any given employer in the economy. We provide computational algorithms that implement our identification strategy given the limitations of the available data sets. Finally, we extend our identification and implementation strategies to the commonly used class of models of sorting based on comparative advantage and provide a test that discriminates between these models.