UC Irvine

This dissertation comprises three chapters that expand upon Bayesian econometrics and game theory. Chapter 1 integrates heteroskedasticity into various models including regression discontinuity design, the Rubin causal (Roy-type) model, propensity score matching, and inverse probability weighting within a Bayesian framework. The practical adequacy of our modeling techniques is assessed through formal Bayesian model comparisons. Simulation studies evaluate the impact of neglected heteroskedasticity and the efficacy of our proposed methods, while their practical applicability is examined through three applications. Specifically, we investigate the impact of academic probation on subsequent academic performance, the effect of Medigap on healthcare expenditures, and the influence of COVID-19 vaccination on mental well-being. These applications highlight the consequences of misspecification and underscore the importance of addressing risks associated with omitted heteroskedasticity. Chapter 2 introduces a Bayesian treatment model that incorporates self-selection and multiple outcomes. We discuss marginal likelihood estimation for formal model comparison and validate our approach through simulation results. We then apply the model to two datasets, examining the influence of insurance on healthcare utilization. In particular, we analyze the impact of Medigap policies on healthcare expenditure using 1987 National Medical Expenditure Survey (NMES) data and the effect of types of private insurance on healthcare utilization using 1996 Medical Expenditure Panel Survey (MEPS) data. Our analysis indicates weak evidence supporting selection bias in both applications. In Chapter 3, we delve into the analysis of a price signaling game that integrates consumer learning. The chapter delineates the perfect Bayesian equilibrium for sellers and employs the undefeated equilibrium refinement to determine optimal choices. Furthermore, our analysis encompasses comparative statics, examining how variations in the probability of type revelation, initial customer review scores, and the quality of both high and low-quality seller products impact the expected return for sellers. Collectively, these chapters offer methodological advancements in Bayesian econometrics and game theory, and provide insights into real-world phenomena across various industries.