A Matching Estimator Based on a Bilevel Optimization Problem

This paper proposes a novel matching estimator where neighbors used and weights are endogenously determined by optimizing a covariate balancing criterion. The estimator is based on finding, for each unit that needs to be matched, sets of observations such that a convex combination of them has the same covariate values as the unit needing matching or with minimized distance between them. We implement the proposed estimator with data from the National Supported Work Demonstration, finding outstanding performance in terms of covariate balance. Monte Carlo evidence shows that our estimator performs well in designs previously used in the literature.