In this paper we study doubly robust estimators of various average treatment effects under unconfoundedness. We unify and extend much of the recent literature by providing a very general identification result which covers binary and multi-valued treatments; unnormalized and normalized weighting;...

We consider nonparametric identification and estimation in a nonseparable model where a continuous regressor of interest is a known, deterministic, but kinked function of an observed assignment variable. This design arises in many institutional settings where a policy variable (such as weekly...

Matching estimators are widely used in statistical data analysis. However, the distribution of matching estimators has been derived only for particular cases (Abadie and Imbens, 2006). This article establishes a martingale representation for matching estimators. This representation allows the...

Traditional instrumental variable estimators do not generally estimate effects for the treated population but for the unobserved population of compliers. They do identify effects for the treated when there is one-sided perfect non-compliance. However, this property is lost when covariates are...