Dynamic Sorting

We introduce a novel assignment model to understand patterns of firm growth and entrepreneurial (managerial) turnover. The economy is endowed with a measure of en- trepreneurs who are distinct in two dimensions: they vary in their skill e to operate a given technology and in their ability to innovate, q. In addition, the economy is populated by an endogenous distribution of firms with exogenous entry and exit. High-q entrepreneurs are more likely to grow their form than a low-q manager. The entrepreneurs’ e and q attributes are not perfectly correlated, in general, and the planner faces an assignment trade-off between maximizing current output and fostering innovation. Since entry and exit are exogenous, our theory emphasizes survivor growth over selection to account for the life cycle of firms. The model makes sharp predictions for the handover of firms from relatively "innovative" entrepreneurs to more "efficient" managers. In an extension we characterize the effects on optimal matching introduced by match-specific capital, learn- ing about managerial types, financial constraints, and contractual frictions.