Identifying treatment effects on categorical outcomes in IV models

Abstract

This paper studies population treatment effects when the outcome is unordered categorical, the treatment is binary, and the instrument is binary. I introduce an assumption called association similarity. For each instrument value, association similarity requires the odds-ratio association between potential treatment and potential outcome to be the same whether the outcome is evaluated under treatment or under no treatment. Under association similarity and a testable categorywise dominance condition, the full potential-outcome distributions are point identified. The identification is constructive and allows estimation using sample frequencies. I also consider weaker restrictions on departures from association similarity that lead to sharp partial identification. I illustrate the method with an application about the effect of insurance on health outcomes.