Distributions of Treatment Effects in Switching Regimes Models: Partial Identification, Confidence Sets, and an Application

Abstract

This dissertation studies the distributions of treatment effects in switching regimes models (SRMs). First, we propose a general class of SRMs and provide simple estimators of average treatment effects. Second, we establish sharp bounds on the joint distribution of potential outcomes and the distribution of treatment effects in parametric and semi-parametric SRMs. Lastly, we apply our models to study the effect of accelerated underwriting on firm’s performance. The dissertation consists of four chapters. In Chapter One, we review the literature of treatment effect studies and selection models. In Chapter Two, we introduce a general class of SRMs via a copula approach. Specifically, we model the joint distribution of each outcome error and the selection error via Normal mean-variance mixture copulas. We extend Heckman's two-step estimation procedure to the new class of models. We include additional correction terms in the second step to account for skewness in the outcome errors. We construct simple estimators of average treatment effects and establish their asymptotic properties. Simulation results confirm the importance of accounting for skewness in the outcome errors. In Chapter Three, we establish sharp bounds on the joint distribution of potential outcomes and the distribution of treatment effects in parametric and semiparametric SRMs. Our results for parametric SRMs with normal mean-variance mixture errors extend some existing results for Gaussian SRMs and our results for semiparametric SRMs supplement the point identification results of Heckman (1990). Compared with the corresponding sharp bounds when selection is random, we observe that self selection tightens the bounds on the joint distribution of the potential outcomes and the distribution of treatment effects. In Chapter Four, we apply our econometric models to study the impact of accelerated underwriting of seasoned equity offerings (SEOs) on a firm's performance one year after the issuance. Our initial results indicate that the private information in a firm's choice of flotation methods has a significant positive impact on its operating performance measured by return on assets, and this significance can not be captured through conventional sample selection models.