Essays on Bayesian semiparametric models

This thesis contains three essays on Bayesian semiparametric models. The material in Chapter 2 is based on lecture notes prepared for a graduate course in modern Bayesian econometrics. This chapter gives an introduction to Bayesian analysis of semiparametric models. The chapter contains a discussion of how to assign prior distributions to infinite dimensional parameters and how to compute their posterior distribution.; Chapter 3 takes up Bayesian semiparametric inference in the Roy selection model. Current semiparametric procedures for selection models typically focus on estimating mean regressions. While these approaches achieve great generality by avoiding specifying the error distribution of the model, they do so at a cost; no estimate of the error distribution or, more importantly, of the earnings distributions at various values of the covariates is achieved. A definite advantage of the Bayesian procedures suggested in chapter 3 is the relative ease with which various predictive distributions can be derived, without restricting the error distribution to belong to a known parametric family. The proposed procedure assigns a Dirichlet process mixture prior to the underlying error density of the model.; Chapter 4 deals with a class of linear fixed effects panel models. The basic statistical problem in a fixed effects panel model is how to remove a set of nuisance parameters (the fixed effects) in a way that ensures "good" inferences for the parameters of interest, the regression slopes. A popular method to remove fixed effects is to first difference the data and then apply either GLS or use the first differenced likelihood function to estimate the regression slopes. However, one may ask what principle in inference underlies this approach. Chapter 4 gives the answer: Under a specific prior a Bayesian is always lead to base inference about the regression slopes on the first differenced likelihood function. It is shown that using a uniform independent prior for the fixed effects leads to the first differenced likelihood. It is also shown how two existing panel estimators for the model under normality can be interpreted as modes of the marginal posteriors that arise after uniform integration of the fixed effects.