Applications of Bayesian inference in econometrics.

Abstract

This study proposes the application of the Bayesian st and point and approach to economics and econometric methods employed in economic research. The focus of this study is in demonstrating the usefulness and applicability of Bayesian methods in econometrics and economic theory. (By Bayesian methods, we mean methods representing the Bayesian st and point as well as techniques that follow from the application of Bayes's theorem). In Chapter I, the philosophical basis of the Bayesian st and point, which is distinct from Bayesian techniques derived from the Bayes theorem, is discussed. A brief review of Bayesian inference is given in Chapter II. The first application considered is in the context of the linear regression model, where Bayesian inference is applied in the context of estimation. A multivariate transformation is proposed that yields the induced prior on the reparametrized parameter vector. Using this induced prior, the posterior distribution of the shrinkage coefficients of the Bayes estimator is derived. Using this posterior distribution, a new estimator is proposed which enables us to evaluate the Bayes estimator in a novel way in Chapter III. The ridge regression estimator is seen to be a special case of the Bayes estimator. More general models are considered in Chapter IV, such as models with autocorrelation and models with errors in measurement. In the context of these models, the analysis developed in Chapter III is generalized to these models. Chapters V and VI discuss applications of Bayesian methods in economic theory. Models which try to capture uncertainty in decision making or which try to model the expectations of individual agents provide a favorable setting for the Bayesian approach. In Chapter V, a simple duopoly model is considered. Each firm is assumed to have prior knowledge on the production decision of the rival in each time period. A Bayesian solution is derived in the context of the duopoly model. In addition, a Bayesian expectations scheme is developed on the lines of the adaptive expectations scheme. This draws upon the work of Turnovsky (1974) but provides a different interpretation of the formation of expectations and differs in the statistical representation of the expectations formation. (Abstract shortened with permission of author).