Model averaging in semiparametric estimation of treatment effects

Abstract

In the practice of program evaluation, choosing the covariates and the functional form of the propensity score is an important choice that the researchers make when estimating treatment effects. This paper proposes a data-driven way of averaging the estimators over the candidate specifications in order to resolve the issue of specification uncertainty in the propensity score weighting estimation of the average treatment effects for treated (ATT). The proposed averaging procedures aim to minimize the estimated mean squared error (MSE) of the ATT estimator in a local asymptotic framework. We formulate model averaging as a statistical decision problem in a limit experiment, and derive an averaging scheme that is Bayes optimal with respect to a given prior for the localization parameters. Analytical comparisons of the Bayes asymptotic MSE show that the averaging estimator outperforms post model selection estimators and the estimators in any of the candidate models. Our Monte Carlo studies confirm these theoretical results and illustrate the size of the MSE gains from averaging. We apply the averaging procedure to evaluate the effect of the labor market program analyzed in LaLonde (1986).Keywords: Treatment effects, Propensity score, Model averaging, Limit experiment.JEL Classification: C13, C21, C52. * We thank Debopam Bhattacharya, Irene Botosaru, Xiaohong Chen, Christian Hansen, Yuichi Kitamura, Frank Kleibergen, Michael Lechner, Simon Lee, Richard Smith, and Frank Windmeijer for valuable comments and discussions. We thank an associate editor and three referees for their thorough reading and constructive comments on an earlier draft. We also thank the seminar participants at AMES 2013, University of Bristol, University of British Columbia, Brown University, the Cemmap/PEPA workshop on Program Evaluation, University of Groningen, University of Sankt Gallen, Tilburg University, Toulouse School of Economics, and Yale Econometrics Lunch for their helpful comments. All remaining errors are ours. Financial support from the ESRC through the ESRC Centre for Microdata Methods and Practice (CeMMAP) (grant number RES-589-28-0001) is gratefully acknowledged.