Covariate Distribution Balance via Propensity Scores

31 Pages Posted: 18 Oct 2018 Last revised: 18 Feb 2019

See all articles by Pedro H. C. Sant'Anna

Pedro H. C. Sant'Anna

Vanderbilt University - College of Arts and Science - Department of Economics

Xiaojun Song

Peking University - Guanghua School of Management

Qi Xu

Vanderbilt University - College of Arts and Science - Department of Economics

Date Written: February 15, 2019

Abstract

The propensity score plays an important role in causal inference with observational data. However, it is well documented that under slight model misspecifications, propensity score estimates based on maximum likelihood can lead to unreliable treatment effect estimators. To address this practical limitation, this article proposes a new framework for estimating propensity scores that mimics randomize control trials (RCT) in settings where only observational data is available. More specifically, given that in RCTs the joint distritbution of covariates are balanced between treated and not-treated groups, we propose to estimate the propensity score by maxizing the covariate distribution balance. The proposed propensity score estimators, which we call the integrated propensity score (IPS), are data-driven, do not rely on tuning parameters such as bandwidths, admit an asymptotic linear representation, and can be used to estimate many different treatment effect measures in a unified manner. We derive the asymptotic properties of inverse probability weighted estimators for the average, distributional and quantile treatment effects based on the IPS and illustrate their relative performance via Monte Carlo simulations and three empirical applications. An implementation of the proposed methods is provided in the new package \texttt{IPS} for \texttt{R}.

Keywords: Causal inference; Empirical process; Inverse probability weighting; Minimum distance; Quantile treatment effects; Treatment effect heterogeneity.

Suggested Citation

Sant'Anna, Pedro H. C. and Song, Xiaojun and Xu, Qi, Covariate Distribution Balance via Propensity Scores (February 15, 2019). Available at SSRN: https://ssrn.com/abstract=3258551 or http://dx.doi.org/10.2139/ssrn.3258551

Pedro H. C. Sant'Anna (Contact Author)

Vanderbilt University - College of Arts and Science - Department of Economics ( email )

Box 1819 Station B
Nashville, TN 37235
United States

HOME PAGE: http://https://sites.google.com/site/pedrohcsantanna/

Xiaojun Song

Peking University - Guanghua School of Management ( email )

Peking University
Beijing, Beijing 100871
China

Qi Xu

Vanderbilt University - College of Arts and Science - Department of Economics ( email )

Box 1819 Station B
Nashville, TN 37235
United States

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