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A Bayesian analysis of a nonidentified model is always possible if a proper prior on all the parameters is specified. There is, however, no Bayesian free lunch. The “price” is that there exist quantities about which the data are uninformative, i.e., their marginal prior and posterior distributions are identical. In the case of improper priors the analysis is problematic—resulting posteriors can be improper. This study investigates both proper and improper cases through a series of examples.

This volume in the Econometric Exercises series contains questions and answers to provide students with useful practice, as they attempt to master Bayesian econometrics. In addition to many theoretical exercises, this book contains exercises designed to develop the computational tools used in modern Bayesian econometrics. The latter half of the book contains exercises that show how these theoretical and computational skills are combined in practice, to carry out Bayesian inference in a wide variety of models commonly used by econometricians. Aimed primarily at advanced undergraduate and graduate students studying econometrics, this book may also be useful for students studying finance, marketing, agricultural economics, business economics or, more generally, any field which uses statistics. The book also comes equipped with a supporting website containing all the relevant data sets and MATLAB computer programs for solving the computational exercises.

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This paper develops new Bayesian methods for semiparametric inference in the partial linear Normal regression model: y=zβ+f(x)+var epsilon where f(.) is an unknown function. These methods draw solely on the Normal linear regression model with natural conjugate prior. Hence, posterior results are available which do not suffer from some problems which plague the existing literature such as computational complexity. Methods for testing parametric regression models against semiparametric alternatives are developed. We discuss how these methods can, at some cost in terms of computational complexity, be extended to other models (e.g. qualitative choice models or those involving censoring or truncation) and provide precise details for a semiparametric probit model. We show how the assumption of Normal errors can easily be relaxed

"It is difficult for me to tone down the missionary zeal acquired in youth, but perhaps the good battle is justified since there are still many heathens."I. J. Good (1976, p. 126) T he "heathens" to whom I. J. Good refers are the non-Bayesians of the world and they are my targeted audience as well. Specifically, I plan to discuss, in as simple and nontechnical a fashion as possible, the subjectivist-Bayesian attitude toward model building in econometrics and to contrast it with the standard frequentist attitude. Most of the issues I raise are familiar to statisticians but not to economists. Rather than give the suspicious reader a menu of Bayesian techniques, I hope to create an interest in acquiring a taste for the Bayesian cuisine by recommending five pragmatic principles.While neither the Bayesian nor the non-Bayesian flocks are homogeneous with respect to the beliefs of their own members, I believe the "within-group" differences

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