  This paper develops a framework to conduct a counterfactual analysis to
regulate matching markets with regional constraints that impose lower and upper
bounds on the number of matches in each region. Our work is motivated by the
Japan Residency Matching Program, in which the policymaker wants to guarantee
the least number of doctors working in rural regions to achieve the minimum
standard of service. Among the multiple possible policies that satisfy such
constraints, a policymaker wants to choose the best. To this end, we develop a
discrete choice model approach that estimates the utility functions of agents
from observed data and predicts agents' behavior under different counterfactual
policies. Our framework also allows the policymaker to design the
welfare-maximizing tax scheme, which outperforms the policy currently used in
practice. Furthermore, a numerical experiment illustrates how our method works.
