Asymptotic properties of an optimization-based matching estimator for average treatment effects

Abstract:
This paper investigates  the  asymptotic  properties  of  a  novel  matching  estimator  for  the average treatment effects of binary programs.  In order to impute the  missing potential outcome for each unit, this approach employs both a number of neighbors and a  weighting scheme that are endogenously determined by solving a nested pair of optimization  problems associated with an individual covariate balancing criterion.  Under mild conditions, our  main contributions are:  (i) the asymptotic normality and a consistent estimator of the conditional  variance of the estimators for the ATE and ATT, (ii) the conditional bias of the estimator for the  ATE is “O_p(n^{-2/n})”, where “n” is the sample size and “d” is the dimension of continuous covariate, and  (iii) general conditions under  which  the  estimator  of  the  ATT  do  attain squar{n}-consistency. Save particular cases, the order of convergence in (ii) cannot be achieved by the conditional bias of any nonparametric “matching estimator” for the ATT, neither by k-NN matching estimators.

Posted on Jun 29, 2016 in Optimization and Equilibrium, Seminars