Limit your applications. Dealing with congested markets in the matching procedure

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.