Identification and Estimation of Triangular Models with a Binary Treatment

Abstract

I study the identification and estimation of a nonseparable triangular model with an endogenous binary treatment. Unlike other studies, I do not impose rank invariance or rank similarity on the unobservable of the outcome equation. Instead, I achieve identification using continuous variation of the instrument and a shape restriction on the distribution of the unobservables, which is modeled with a copula. The latter captures the endogeneity of the model and is one of the components of the marginal treatment effect, making it informative about the effects of extending the treatment to untreated individuals. The estimation is a multi-step procedure based on rotated quantile regression. Finally, I use the estimator to revisit the effects of Work First Job Placements on future earnings.

Keywords: Copula, endogeneity, policy analysis, quantile regression, unconditional distributional effects

JEL Classification: C31, C36