The Macroeconomics of Sorting and Turnover in a Dynamic Assignment Model\

We build a tractable assignment model to characterize the matching and separation patterns of CEOs and their employers. Managers learn about their own type by observing a sequence of public signals (productivity shocks). The sorting is ex ante perfect across managers of a given cohort who are not currently matched (either because they were unmatched in the previous period or because they decided to split from their previous match), but is not typically so ex post. Moreover, in the special case with frictionless matching, perfect ex ante sorting occurs across managers of a given cohort regardless of their assignment history. We calibrate the model to match empirical targets from a large matched employer-employee dataset covering the Danish labor force between 2000 and 2009. We have a particular interest in the degree of complementarity between the attributes of the manager and those of the firm in the production function and our results fill a gap in the literature on the aggregate effects of a particular form of misallocation, mismatch, the size of which depends critically on this elasticity. Moreover, in ongoing work our model connects turnover to systematic differences in the cross-sectional size distribution of firms across countries at different income levels, which has been shown to be correlated with aggregate TFP in earlier work.