Use of Prior Information in the Analysis and Estimation of Cobb-Douglas Production Function Models

Abstract

IN ANALYSES OF PRODUCTION-FUNCTION MODELS employing aggregate time-series data, it is often difficult to obtain precise estimates of parameters because input variables are usually highly intercorrelated. For example, in the case of a CobbDouglas (CD) production function with neutral technical change, the labor, capital, and time-trend variables are frequently highly intercorrelated, a fact that may lead to imprecise parameter estimates and, as will be seen below with U.S. data, highly implausible point estimates for certain parameters. It is generally recognized that introduction of prior information is one possible way of dealing with the above problems-sometimes referred to as multicollinearity problems. Another course of action in dealing with these problems is to extend the data base-say, by combining cross-section data with the available timeseries data. In both approaches, or in a combination of them, additional information is added to the information in the aggregate time-series sample in an attempt to improve the quality of inferences. In the present paper, we review a sampling-theory analysis of the CD production function put forward by Morishima and Saito [3], in which nondata-based prior information was added to aggregate time-series information in order to deal with what appears to be a multicollinearity problem. Then we turn to an analysis of the Morishima-Saito (MS) production function problem, using the. Bayesian approach in which nondata-based prior information is introduced by use of prior probability density functions (pdf's) for the parameters. By the use of prior pdf's in the Bayesian approach, it will be seen that prior information can be introduced in a rather flexible manner, and posterior pdf's for parameters of interest, that reflect both sample and prior information, can be readily computed. In particular, we wish to assess how sensitive inferences about the technical-change parameter and other parameters are to the form and manner in which prior information is introduced. The plan of the paper is as follows. In Section 2, we state the problem and review some sampling-theory results. We then present Bayesian analyses of the problem in Section 3 and provide a summary of results and some concluding remarks in Section 4.