Efficient estimation of average treatment effects using the estimated propensity score

Keisuke Hirano, Guido W. Imbens, Geert Ridder

Research output: Contribution to journalArticle

810 Scopus citations

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 treatment-control 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), Heckman, Ichimura, and Todd (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.

Original languageEnglish (US)
Pages (from-to)1161-1189
Number of pages29
JournalEconometrica
Volume71
Issue number4
DOIs
StatePublished - Jan 1 2003

All Science Journal Classification (ASJC) codes

  • Economics and Econometrics

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