Identifying treatment effects on categorical outcomes in IV models

Abstract

This paper provides a nonparametric framework for causal inference with categorical outcomes under binary treatment and binary instrument settings. I decompose the observed joint probability of outcomes and treatment into marginal probabilities of potential outcomes and treatment, and association parameters that capture selection bias due to unobserved heterogeneity. Under a novel identifying assumption \emph{association similarity}, which requires the dependence between unobserved factors driving treatment and potential outcomes to be invariant across treatment states, I achieve point identification of the full distribution of potential outcomes. Recognizing that this assumption may be strong in some contexts, I propose two weaker alternatives: monotonic association, which restricts the direction of selection heterogeneity, and bounded association, which constrains its magnitude. These relaxed assumptions deliver sharp partial identification bounds that nest point identification as a special case and facilitate transparent sensitivity analysis. I illustrate the framework in an empirical application, estimating the causal effect of private health insurance on health outcomes.