Three essays on Bayesian inference in econometrics with an application to estimating the returns to schooling quality

This dissertation consists of three essays in econometrics, with a large emphasis on Bayesian econometrics. The last two chapters in the dissertation, joint work with Arnold Zellner, describe the theory and application of the Bayesian Method of Moments (BMOM). This approach is particularly useful when there is difficulty in specifying a prior distribution or a likelihood function, and thus traditional Bayesian techniques can not be applied. Given a set of moment conditions from a model, a proper maximum entropy post-data density can be derived which satisfies the imposed moment side conditions and enables one to compute finite sample moments, confidence intervals, or virtually any other statistic of interest. Model selection techniques via posterior odds and an average log odds or cross entropy criterion are also introduced as procedures to determine the set of moment conditions that are most favored by the data.;The first essay is original work which examines the economic returns to high school quality. Both Bayesian and non-Bayesian techniques are employed, and a variety of generalizations upon past work on this topic are discussed. I estimate the marginal effect of quality on earnings nonparametrically using local polynomial regression and examine if the linearity assumption often encountered in the literature is appropriate. Further, I describe Bayesian procedures for estimating econometric models in the presence of selection bias, and examine the role of self-selection into higher education on estimated returns to high school quality. I find small returns to typical proxies for high school quality such as teacher education, school enrollment, and starting teacher salary.