Truncation in the Matching Markets and Market Ineffciency

In this paper, we study the Ph.D academic job market. Based on the Gale and Shapley algorithm, we analyse whether a social planner can improve market efficiency by truncation, i.e., exogenously imposing a limit on the number of possible applications. Using simulations, we derive the optimal truncation level which balances the trade-off between being unmatched and gaining a better match in the aggregate. When graduates apply to their most preferred positions, we find that aggregate efficiency can be improved by limiting the number of applications. In particular, the limit can be considerable if the graduates' preferences over the positions are not very correlated. The derived limit is still the best one when graduates respond strategically (applying to universities which are at least individually most preferred at the expenses of those most preferred commonly) in a conservative sense: given the strategic behaviour of the graduates, the market efficiency can be further improved by choosing an even lower limit on the number of applications. Overall, this paper suggests a direction to improve the matching market for Ph.D. candidates by improving the quality of their matches and lowering the hiring costs for universities.