Estimating the distribution of treatment effects

In this paper we show that the distribution of treatment effects is point identi ed in a model where the outcome equation is of unrestricted form and the selection equation contains more than one unobservable. This is different and economically better motivated than the treatment e ffect on the distribution, usually the quantiles, which is commonly analyzed in the literature. Our key identifying assumption in the selection equation is a linear random coeffcients structure and the assumption that the instruments are continuously distributed. This allows point identi cation of the entire distribution of treatment e ffects under conditions on unobserved heterogeneity that unlike the case of additively separable/monotonic scalar unobservables have a clear economic interpretation in terms of unobserved heterogeneity. Also, we obtain results on the distribution of treatment eff ects without invoking any scalar monotonicity assumption in the outcome equation. Moreover, the identi cation is constructive and suggests estimators of various quantities of interest by sample counterparts.