Limit your applications : dealing with congested markets in the matching procedure

Abstract

We study congested matching markets, such as the PhD academic job market, and consider alternative mechanisms that could be implemented by a social planner. Building on the Gale and Shapley algorithm, we analyse (i) a procedure accounting for a limit in the number of applications PhD graduates can submit (PhD-LIMIT), and (ii) a procedure accounting for a limit in the number of applications universities can evaluate (UNI-LIMIT). We find that the PhD-LIMIT procedure improves the matching outcome and is preferable to a UNI-LIMIT procedure. The optimal limit in the number of applications balances the trade-off between being unmatched and gaining a better match in the aggregate, and the benefit can be considerable if the graduates' preferences over the positions are not very correlated. Overall, we suggest a direction to improve the matching market for PhD candidates by improving the outcome of their matches and lowering the hiring costs for universities.