Efficient Semiparametric Estimation of Multi-valued Treatment Effects

A large fraction of the literature on program evaluation focuses on efficient estimation of binary treatment effects under the assumption of unconfoundedness. In practice, however, treatments are frequently multi-valued and available econometric techniques in this literature cannot be applied directly. This paper studies the efficient estimation of a large class of multi-valued treatment effects as implicitly defined by a collection of possibly over-identified non-smooth moment conditions when treatment assignment is assumed to be ignorable. We propose two estimators, one based on an inverse probability weighting scheme and the other based on the efficient in‡fluence function of the model, and provide a set of sufficient conditions that ensure root-N consistency, asymptotic normality and efficiency of these estimators. Under

mild assumptions, these conditions are satisfied for the marginal mean treatment effect and marginal quantile treatment effect, two estimands of particular importance

for empirical applications. Furthermore, based on these large sample results, other important population parameters of interest may be efficiently estimated by means of

transformations of the two estimators considered. Using this idea, previous results for average and quantile treatments effects may be seen as particular cases of the methods proposed here when treatment is assumed to be dichotomous. We illustrate the procedures presented in this paper by studying the effect of maternal smoking intensity during pregnancy on birth weight. Our main findings suggest the presence of approximately homogeneous, non-linear treatment effects concentrated on the first 10 cigarettes-per-day smoked during pregnancy.

For more information, contact Frank Schorfheide.