[The widespread use of prior information in formulating, estimating, and using econometric models is reviewed. Attempts to avoid the use of prior information by formulating multivariate statistical VAR and ARMA time series models for economic time series data have resulted in heavily over-parametrized models. A simple demand, supply, and entry model is presented to contrast models utilizing prior information provided by economic theory and other sources with multivariate statistical time series models. Formal Bayesian methods for incorporating prior information in econometric estimation, testing, and prediction are presented. A number of published applied Bayesian studies are cited in which Bayesian methods have proved to be effective. It is concluded that wise use of the Bayesian approach will produce improved econometric results.]

USUAL SPECIFYING ASSUMPTIONS for simultaneous equation econometric models imply strong inequality constraints on structural parameters which are formally similar to those encountered in connection with the classical errors-in-the-variables model.2 To illustrate, consider the following simple simultaneous equation model for two endogenous variables, Y,, and Y2t, say price and quantity, respectively:

SINCE KOYCK'S pioneering work, distributed lag models have come to play an important role in econometrics and much work has been done to develop methods for analyzing them-see e.g. Koyck [15], Klein [12], Solow [20], Fuller and Martin [5], Malinvaud [18], Hannan [9], Liviatan [17], Amemiya and Fuller [1], Zellner and Park [25], Thornber [21], Waud [23], Dhrymes [3], and Griliches [7]. In the present paper we present maximum likelihood and Bayesian estimation procedures for estimating the parameters of a typical distributed lag model under four alternative sets of assumptions regarding disturbance terms' properties. Then these procedures and assumptions are employed in analyses of a sample of United States quarterly consumption data to illustrate their application and to show the sensitivity of inferences to the assumptions made about disturbance terms' properties. We also compute posterior probabilities associated with four alternative models. The plan of the paper is as follows. In Section 2, the model to be analyzed is described and alternative assumptions about disturbance terms are introduced. Section 3 contains a discussion of maximum likelihood techniques and application of them in the analysis of U.S. quarterly consumption data. Then in Sections 4 and