Bayesian Testing Procedure Research Articles

It is an honour to present this paper at St John's College, Cambridge, Sir Harold Jeffreys' college. As you all probably know, Sir Harold has made outstanding, pioneering contributions to the development of Bayesian statistical methodology and applications of it to many problems. In appreciation of his great work, our NBER-NSF Seminar on Bayesian Inference has recently published a book (Zellner, 1980a) honouring him. Jeffreys (1967) set a fine example for us by emphasizing both theory and applications in his work. It is this theme, the interaction between theory and application in Bayesian econometrics, that I shall emphasize in what follows. The rapid growth of Bayesian econometrics from its practically non-existent state in the early 1960s to the present (Zellner, 1981) has involved work on Bayesian inference and decision techniques, applications of them to econometric problems and development of Bayesian computer programs.? Selected applications include Geisel (1970, 1975) who used Bayesian prediction and odds ratios to compare the relative performance of simple Keynesian and Quantity of Money Theory macroeconomic models. Peck (1974) utilized Bayesian estimation techniques in an analysis of investment behaviour of firms in the electric utility industry. Varian (1975) developed and applied Bayesian methods for real estate tax assessment problems. Flood and Garber (1980a, b) applied Bayesian methods in study of monetary reforms using data from the German and several other hyperinflations. Evans (1978) employed posterior odds ratios in a study to determine which of three alternative models best explains the German hyperinflation data. Cooley and LeRoy (1981), Shiller (1973), Zellner and Geisel (1970), and Zellner and Williams (1973) employed a Bayesian approach in study of time series models for US money demand, investment and personal consumption data. Production function models have been analysed from the Bayesian point of view by Sankar (1969), Rossi (1980) and Zellner and Richard (1973). Tsurumi (1976) and Tsurumi and Tsurumi (1981) used Bayesian techniques to analyse structural change problems. Reynolds (1980) developed and applied Bayesian estimation and testing procedures in an analysis of survey data relating to health status, income and other variables. Litterman (1980) has formulated a Bayesian vector autoregressive model that he employed (and is employing) to generate forecasts of major US macroeconomic variables that compare very

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