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.
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