Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score

Abstract

We are interested in estimating the average effect of a binary treatment on a scalar outcome. If assignment to the treatment is exogenous or unconfounded, that is, independent of the potential outcomes given covariates, biases associated with simple treatmentcontrol average comparisons can be removed by adjusting for differences in the covariates. Rosenbaum and Rubin (1983) show that adjusting solely for differences between treated and control units in the propensity score removes all biases associated with differences in covariates. Although adjusting for differences in the propensity score removes all the bias, this can come at the expense of efficiency, as shown by Hahn (1998), and Robins, Mark, and Newey (1992. We show that weighting by the inverse of a nonparametric estimate of the propensity score, rather than the true propensity score, leads to an efficient estimate of the average treatment effect. We provide intuition for this result by showing that this estimator can be interpreted as an empirical likelihood estimator that efficiently incorporates the information about the propensity score.

The neurocognitive effects of aripiprazole: an open-label comparison with olanzapine

“…To address the effects of attrition, we first examined group differences in dropout (i.e., subjects with baseline plus at least one postbaseline assessment) using chi-square analyses. In response to the differential dropout rates, the data were then reanalyzed using propensity score weighting (Hirano et al 2003;Rosenbaum and Rubin 1983).…”

Radius matching on the propensity score with bias adjustment: tuning parameters and finite sample behaviour

“…observables, whereas curse of dimensionality problems related to an entirely non-parametric estimation are avoided. Popular classes of propensity score methods include direct matching (Rubin 1974;Rosenbaum and Rubin 1983), kernel matching (Heckman et al 1998a), radius matching (Rosenbaum and Rubin 1985;Dehejia and Wahba 1999), inverse probability weighting (Horvitz and Thompson 1952;Hirano et al 2003), inverse probability tilting (Graham et al 2012) and doubly robust estimation (Robins et al 1992). Huber et al (2013), henceforth referred to as HLW13, assess the finite sample properties of a broad range of different (classes of) estimators of the average treatment effect on the treated (ATET) by constructing a-what they call-Empirical Monte Carlo Study (EMCS) which is based on empirical labour market data from Germany.…”

Using Propensity Score Analysis for Making Causal Claims in Research Articles

“…The appropriate way to select covariates to be included in PSA is to identify the related confounding variables from theory to existing literature (Brookhart et al 2006;Greenland 2007). PSA performs better when the researcher includes as many theoretically important covariates as possible in the analysis, and therefore, if any theoretically identified covariate cannot be included in PSA because it is immeasurable, researchers should address the concern for any causal claims related to the treatment effects (Dehejia and Wahba 2002;Hirano et al 2003).…”

“…The concept and effectiveness of PSA are discussed at length in the literature (e.g., Abadie and Imbens 2006;Dehejia and Wahba 2002;Gu and Rosenbaum 1993;Heckman et al 1998;Hill and Reiter 2006;Hirano et al 2003;McCandless et al 2008;Rosenbaum 1987;Rubin and Thomas 1996). Here, only a primer of PSA is introduced.…”