Abstract: I study the identification and estimation of a nonseparable triangular model with an
endogenous binary treatment. I impose neither rank invariance nor rank similarity on
the unobservable term of the outcome equation. Identification is achieved by 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
