Conditional independence of treatment assignment from potential outcomes is a commonly used but nonrefutable assumption. We derive identified sets for various treatment effect parameters under nonparametric deviations from this conditional independence assumption. These deviations are defined...

We analyze identification of nonseparable models under three kinds of exogeneity assumptions weaker than full statistical independence. The first is based on quantile independence. Selection on unobservables drives deviations from full independence. We show that such deviations based on quantile...

Given a set of baseline assumptions, a breakdown frontier is the boundary between the set of assumptions which lead to a specific conclusion and those which do not. In a potential outcomes model with a binary treatment, we consider two conclusions: First, that ATE is at least a specific value...

We analyze identification of nonseparable models under three kinds of exogeneity assumptions weaker than full statistical independence. The first is based on quantile independence. Selection on unobservables drives deviations from full independence. We show that such deviations based on quantile...

Continuous treatments (e.g., doses) arise often in practice. Methods for estimation and inference for quantile treatment effects models with a continuous treatment are proposed. Identification of the parameters of interest, the dose-response functions and the quantile treatment effects, is...