Uniformly Semiparametric Efficient Estimation of Treatment Effects With a Continuous Treatment

Abstract

This article studies identification, estimation, and inference of general unconditional treatment effects models with continuous treatment under the ignorability assumption. We show identification of the parameters of interest, the dose–response functions, under the assumption that selection to treatment is based on observables. We propose a semiparametric two-step estimator, and consider estimation of the dose–response functions through moment restriction models with generalized residual functions that are possibly nonsmooth. This general formulation includes average and quantile treatment effects as special cases. The asymptotic properties of the estimator are derived, namely, uniform consistency, weak convergence, and semiparametric efficiency. We also develop statistical inference procedures and establish the validity of a bootstrap approach to implement these methods in practice. Monte Carlo simulations show that the proposed methods have good finite sample properties. Finally, we apply the proposed methods to estimate the unconditional average and quantile effects of mothers’ weight gain and age on birthweight. Supplementary materials for this article are available online.

• Birthweight
• Dose–response function
• Ignorability
• Semiparametric estimation and inference

Additional information

Notes on contributors

Antonio F. Galvao

Antonio F. Galvao is Associate Professor, Department of Economics, University of Iowa, Iowa City, IA 52242 (E-mail: [email protected]). Liang Wang is PhD Student, Department of Economics, University of Wisconsin-Milwaukee, Milwaukee, WI 53201 (E-mail: [email protected]). The authors express their appreciation to Sergio Firpo, Carlos Flores, Alfonso Flores-Lagunes, Zhengyuan Gao, Chuan Goh, Roger Koenker, Carlos Lamarche, Ying-Ying Lee, Marcelo Medeiros, Marcelo Moreira, Cristine Pinto, Alexandre Poirier, Suyong Song, Elie Tamer, Zhijie Xiao, Ting Zhang, and participants in the seminars at the University of Wisconsin Madison, University of Iowa, University of Illinois at Urbana-Champaign, University of Wisconsin-Milwaukee, PUC-Rio, Central Bank of Brazil, and the 2013 Latin American Workshop in Econometrics for useful comments and discussions regarding this article. The authors also thank the editor and three anonymous referees for their careful reading and comments to improve the article. Computer programs to replicate the numerical analyses are available from the authors. All the remaining errors are ours.

Liang Wang

Antonio F. Galvao is Associate Professor, Department of Economics, University of Iowa, Iowa City, IA 52242 (E-mail: [email protected]). Liang Wang is PhD Student, Department of Economics, University of Wisconsin-Milwaukee, Milwaukee, WI 53201 (E-mail: [email protected]). The authors express their appreciation to Sergio Firpo, Carlos Flores, Alfonso Flores-Lagunes, Zhengyuan Gao, Chuan Goh, Roger Koenker, Carlos Lamarche, Ying-Ying Lee, Marcelo Medeiros, Marcelo Moreira, Cristine Pinto, Alexandre Poirier, Suyong Song, Elie Tamer, Zhijie Xiao, Ting Zhang, and participants in the seminars at the University of Wisconsin Madison, University of Iowa, University of Illinois at Urbana-Champaign, University of Wisconsin-Milwaukee, PUC-Rio, Central Bank of Brazil, and the 2013 Latin American Workshop in Econometrics for useful comments and discussions regarding this article. The authors also thank the editor and three anonymous referees for their careful reading and comments to improve the article. Computer programs to replicate the numerical analyses are available from the authors. All the remaining errors are ours.