Bayesian applications in econometrics

Abstract

The thesis considers several related aspects of Bayesian inference in econometrics. Particular attention is given to model-comparisons, distributed lags, and the sampling properties of estimators.

In Chapter III the natural-conjugate Bayes (β˜) and Ordinary Least Squares (βˆ) estimators for the linear model are compared, and a condition is derived and investigated under which β˜ is preferred to βˆ in terms of matrix mean squared error. In a limiting case a test statistic is obtained and shown to be related to another well-known test. Two observable substitute statistics are shown to be consistent but upward-biased. The bias is studied in a limited Monte Carlo experiment.

Bayesian inferential methods are advocated in Chapter IV for the seasonal adjustment of economic time-series. This is motivated by Chapter III and the application in Chapter VIII. A well-known classical procedure is shown to be a special case of the Bayesian method.

Bayesian analyses of distributed lag models are surveyed in Chapter V, and Chapter VI considers the problem of discriminating between a Koyck distributed lag model and a regression model with autocorrelated disturbances. A Monte Carlo study compares several interpretations of an ad hoc rule-of-thumb proposed by Griliches with Bayesian Posterior Odds analysis, and the latter is found to be generally superior to the former.

Chapters VII and VIII present a Bayesian interpretation of the Almon estimator, treating theoretical results and an application to some New Zealand data. The theory generalizes that of Zellner and Williams, special attention being paid to: prior information; unknown lags; model comparisons; and autocorrelation. Although the methodological problems associated with the classical Almon estimator are overcome, the computational cost is increased substantially.

The evidence presented suggests that several econometric problems may be handled more satisfactorily by Bayesian methods than by classical methods.