Regulating Matching Markets with Distributional Constraints

Distributional constraints arise naturally in many matching markets, requiring the number of matches of specific types to satisfy predetermined bounds. This article reviews recent developments in the design and analysis of matching markets under such constraints. We discuss existing theoretical and empirical approaches. We then describe the results of [Ikegami et al. 2025], which develops a new framework for matching markets with distributional constraints and applies it to the Japan Residency Matching Program. The analysis illustrates how data can be used to evaluate regulatory instruments and to construct subsidy schemes that implement constrained-efficient outcomes.