Regulating Matching Markets with Constraints: Data-driven Taxation

Abstract

Real-world matching markets often restrict the number of matches for a specific group or type of agents. In fact, in a medical residency match, a policymaker often needs to guarantee the number of doctors working in rural areas to achieve the minimum standards for health care. Toward the goal, this paper proposes a tax scheme to regulate matching outcomes so that the policymaker meets the upper and lower bound constraints on the number of matches. First, we describe a transferable utility matching model with unobserved heterogeneity in preferences; the model allows us to estimate the preferences of agents using observed data on matching, i.e., who is matched with whom. Then, we prove that there is a unique social welfare maximizing tax scheme that satisfies the constraints. We also show that the tax scheme can be obtained by solving a convex programming problem. Furthermore, we numerically evaluate our method in an artificial matching market with regional constraints.