A matching estimator based on a bi-level optimization problem

This paper proposes a matching estimator where the size of the weights and the number of neighbors are endogenously determined from the solution of a bi-level optimization problem. The first level problem minimizes the distance between the characteristics of an individual and a convex combination of characteristics of individuals belonging to the corresponding counterfactual set, and with the second level we choose a solution point of the first level that minimizes the sum of the distances between the characteristics of the individual under analysis and those from the counterfactuals employed in the optimal convex combination. We show that this estimator is consistent and asymptotically normal. Finally we study its behavior in finite samples by performing Monte Carlo experiments with designs based on the related literature. In terms of bias, standard deviation and mean square error, we find significant improvements using our estimator in comparison to the simple matching estimator, widely employed in the literature.