A Tale of Two C(...)s: Competence and Complementarity

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. The sorting is ex ante perfect across managers of a given cohort whose most recent assignment is the same, but is not typically so ex post. Moreover, if matching is costless, perfect \textit{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 exploit the non-monotonicity of executive compensation in the employer type - the firm's productivity, that is - to parameterize the model. We have a particular interest in the degree of complementarity between the characteristics 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, namely mismatch, which depend critically on this elasticity. What's more, our theory is a natural building block for a dynamic theory of entrepreneurship.