This chapter serves as an introduction to Bayesian econometrics. Bayesian regression analysis has grown in a spectacular fashion since the publication of books by Zellner (1971) and Leamer (1978). Application to routine data analysis has also expanded enormously, greatly aided by revolutionary advances in computer hardware and software technology. In the light of such major developments, a single chapter can never do adequate justice to the many facets of this subject. This chapter therefore has the very modest goal of providing a rough road map to the major ideas and developments in Bayesian econometrics. Despite this modest objective some parts are still quite technical.
The Bayesian approach, unlike the likelihood or frequentist or classical approach presented in previous chapters, requires the specification of a probabilistic model of prior beliefs about the unknown parameters, given an initial specification of a model. Many researchers are uncomfortable about this step, both philosophically and practically. This has traditionally been the basis of the concern that the Bayesian approach is subjective rather than objective. It will be shown that in large samples the role of the prior may be negligible, that relatively uninformative priors can be specified, and that there are methods available for studying the sensitivity of inferences to priors. Therefore, the charge of subjectivity may not always be as serious as many claim.
Bayesian approaches play a potentially large role in applied microeconometrics, especially when dealing with complex models that lack analytically tractable likelihood functions.