Treatment Effect Heterogeneity and Statistical Decision-making in the Presence of Interference

Abstract

This dissertation consists of three chapters that generally focus on the design of welfare-maximizing treatment assignment rules in heterogeneous populations with interactions. In the first two chapters, I focus on an important pre-step in the design of treatment assignment rules: inference for heterogeneous treatment effects in populations with interactions. In the final chapter, I and my co-authors study treatment assignment rules in the presence of social interaction in heterogeneous populations. In chapter one, I argue that statistical inference of heterogeneous treatment effects (HTEs) across predefined subgroups is complicated when economic units interact because treatment effects may vary by pretreatment variables, post-treatment exposure variables (that measure the exposure to other units’ treatment statuses), or both. It invalidates the standard hypothesis testing technique used to infer HTEs. To address the problem, I develop statistical methods (asymptotic and bootstrap) to infer HTEs and disentangle the drivers of treatment effects heterogeneity in populations where units interact. Specifically, I incorporate clustered interference into the potential outcomes model and propose kernel-based test statistics for the null hypotheses of (a) no HTEs by treatment assignment (or post-treatment exposure variables) for all pretreatment variables values; and (b) no HTEs by pretreatment variables for all treatment assignment vectors. To disentangle the source of heterogeneity in treatment effects, I recommend a multiple-testing algorithm. In addition, I prove the asymptotic properties of the proposed test statistics via a modern poissonization technique. As a robust alternative to the inferential methods I propose in chapter one, in chapter two, I design randomization tests of heterogeneous treatment effects (HTEs) when units interact on a single network. My modeling strategy allows network interference into the potential outcomes framework using the concept of network exposure mapping. I consider three null hypotheses that represent different notions of homogeneous treatment effects, but due to nuisance parameters and the multiplicity of potential outcomes, the hypotheses are not sharp. To address the issue of multiple potential outcomes, I propose a conditional randomization inference method that expands on existing methods. Additionally, I consider two techniques that overcome the nuisance parameter issue. I show that my conditional randomization inference method, combined with either of the proposed techniques for handling nuisance parameters, produces asymptotically valid p-values. Chapter three is based on a joint paper with Young Ki Shin and Seungjin Han. We study treatment assignment rules in the presence of social interaction in heterogeneous populations. We construct an analytical framework under the anonymous interaction assumption, where the decision problem becomes choosing a treatment fraction. We propose a multinomial empirical success (MES) rule that includes the empirical success rule of Manski (2004) as a special case. We investigate the non-asymptotic bounds of the expected utility based on the MES rule.