Essays in Bayesian Econometrics

Abstract

This thesis comprises three chapters in Bayesian econometrics. Although the chapters are independent, the unifying theme is that Bayesian inference is semiparametric. That is, the econometric model is either 1. indexed by finite- and infinite-dimensional parameters, or 2. interest is a finite-dimensional transformation of an infinite-dimensional parameter. All chapters are solo-authored. Chapter 1 proposes Bayesian inference for conditional moment equality models. The framework starts with a prior for a conditional distribution and reports a marginal posterior for an estimand that minimizes the distance of the conditional moments to zero. The key theoretical result is a Bernstein-von Mises theorem, establishing asymptotic normality of the minimum distance posterior. Chapter 2 presents a new approach to Bernstein-von Mises theory for partially linear regression models. The idea is to embed an adaptive parametrization of the regression function within a (quasi-)likelihood model, enabling verification of the Bernstein-von Mises theorem using ordinary expansions of the log-likelihood function. The new parametrization alleviates some smoothness restrictions that are encountered in the original parametrization of the model. Chapter 3 introduces a Bayesian inference framework for a linear index threshold-crossing binary choice model subject to a median independence restriction. The proposal exploits an observational equivalence between the model and a probit model with nonparametric heteroskedasticity. This leads to a computationally attractive Bayesian inference procedure in which a Gaussian process forms a conditionally conjugate prior for the natural logarithm of the skedastic function.