On Causal Inference for Ordinal Outcomes

Abstract

This dissertation studies the problem of causal inference for ordinal outcomes. Chapter 1 focuses on the sharp null hypothesis of no treatment effect on all experimental units, and develops a systematic procedure for closed-form construction of sequences of alternative hypotheses in increasing orders of their departures from the sharp null hypothesis. The resulted construction procedure helps assessing the powers of randomization tests with ordinal outcomes. Chapter 2 proposes two new causal parameters, i.e., the probabilities that the treatment is beneficial and strictly beneficial for the experimental units, and derives their sharp bounds using only the marginal distributions, without imposing any assumptions on the joint distribution of the potential outcomes. Chapter 3 generalizes the framework in Chapter 2 to address noncompliance.