Seminar

Estimating Treatment Effects with a Nonparametric Random Coefficients Selection Equation

Eric Gautier (CREST)

October 12, 2012, 13:45–15:00

Toulouse

Room MF 323

Decision Mathematics Seminar

Abstract

In this paper we study a binary treatment model where the outcome equation is of unrestricted form, and the selection equation contains multiple unobservables that enter through a nonparametric random coefficients specification. This specification is flexible because it allows for complex unobserved heterogeneity of economic agents and non-monotone selection into treatment. Employing continuous instruments, we establish that both the marginal conditional distributions of Y0 and Y1, the outcome for the untreated, respectively treated, given first stage random coefficients, are identified. We can thus identify an average treatment effect, conditional on first stage unobservables called UCATE, which yields most treatment effects parameters that depend on averages, like ATE and ATT. Moreover, we provide sharp bounds on the variance, the joint distribution of Y0, Y1 and the distribution of treatment effects. When the outcomes are continuously distributed, we provide novel and weak conditions that allow to point identify the conditional distribution of Y0, Y1, given the unobservables. This allows to derive every treatment effect parameter, e.g. the distribution of treatment effects and the proportion of individuals who benefit from treatment. Finally, we present estimators together with their rates of convergence and we evaluate them in a simulation study.