Treatrew: A User-Written Command for Estimating Average Treatment Effects by Reweighting on the Propensity Score

Abstract

Reweighting is a popular statistical technique to deal with inference in the presence of a nonrandom sample, and various reweighting estimators have been proposed in the literature. This article presents the user-written command treatrew, which implements reweighting on the propensity-score estimator as proposed by Rosenbaum and Rubin (1983, Biometrika 70: 41–55) in their seminal article. The main contribution of this command lies in providing analytical standard errors for the average treatment effects in the whole population, in the subpopulation of the treated, and in that of the untreated. Standard errors are calculated using the approximation suggested by Wooldridge (2010, 920–930, Econometric Analysis of Cross Section and Panel Data [MIT Press]), but bootstrapped standard errors can also be easily computed. Because an implementation of this estimator with analytic standard errors and nonnormalized weights is missing in Stata, this article and the accompanying ado-file aim to provide the community with an easy-to-use method for reweighting on the propensity-score. The estimator proves to be a valuable tool for estimating average treatment effects under selection on observables.