In this paper, we investigate what can be learned about average counterfactual outcomes when it is assumed that treatment response functions are smooth. The smoothness conditions in this paper amount to assuming that the differences in average counterfactual outcomes are bounded under different...

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...

We provide an overidentification test for a nonparametric treatment model where individuals are allowed to select into treatment based on unobserved gains. Our test can be used to test the validity of instruments in a framework with essential heterogeneity (Imbens and Angrist 1994). The...

This paper examines identification power of the instrument exogeneity assumption in the treatment effect model. We derive the identification region: The set of potential outcome distributions that are compatible with data and the model restriction. The model restrictions whose identifying power...

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 (e.g., nonnegative) and second that the...

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...

This paper asks which aspects of a structural Nonparametric Instrumental Variables Regression (NPIVR) can be identified well and which ones cannot. It contributes to answering this question by characterizing the identified set of linear continuous functionals of the NPIVR under norm constraints....

This paper explores semi-monotonicity constraints in the distribution of potential outcomes, first, conditional on an instrument, and second, in terms of the response function. The imposed assumptions are strictly weaker than traditional instrumental variables assumptions and can be gainfully...

This paper discusses the nonparametric identification of causal direct and indirect effects of a binary treatment based on instrumental variables. We identify the indirect effect, which operates through a mediator (i.e. intermediate variable) that is situated on the causal path between the...

This paper discusses the nonparametric identi.cation of causal direct and indirect effects of a binary treatment based on instrumental variables. We identify the indirect effect, which operates through a mediator (i.e. intermediate variable) that is situated on the causal path between the...