On the Empirical Relevance of the CES Production Function

W ITH the pathbreaking article by Arrow, Al Chenery, Minhas and Solow [1] introducing the constant elasticity of substitution (CES) production function, interest in production theory has multiplied. No longer is the Cobb-Douglas function the workhorse for neoclassical theory; rather, the role of the production function has been examined anew in the theory of the firm, in growth theory, and in the theory of international trade. This re-examination has taken the form (1) of theoretical analysis of the role of the elasticity of substitution, (2) of empirical estimation of the elasticity, and (3) of the introduction of new forms for the production relation, e.g., Zellner and Revankar [14] and Revankar [8]. Unfortunately, knowledge about the appropriate micro-economic or macro-economic production function seems further away now than before 1961, the year of the ACMS article [1]. Nerlove [7, p. 58] reports that "even slight variations in the period or concepts tend to produce drastically different estimates of the elasticity [of substitution] " and he presents a summary of empirical studies of the CES production function to support his conclusion. In this paper it is first shown that Nerlove's conclusion on the definition of time periods is an inappropriate interpretation of previous estimates (however, part of the difficulty was outside Nerlove's control); that in fact changes in period do not produce significantly different estimates of the elasticity. To demonstrate this contention, estimates of the elasticity from the factor demand equation for labor for two consecutive years are obtained. However, evidence of serial correlation leads to a correction of the labor and wage rate variables for quality variation in the workers over states. Since this correction does not remove the serial correlation, the estimation is then undertaken using the efficient estimation technique of Zellner [12] and the results suggest that use of different time periods does not produce different estimates of the elasticity. Second, the estimates of the elasticity are constrained to be equal for the two years and the efficient estimation techniques are again used with the labor quality correction included. A test on the null hypothesis that the elasticity of substitution equals one for each industry indicates that the elasticity does not in general depart significantly from one. This conclusion from estimates of the labor demand equation supports a similar conclusion of Griliches [3, p. 292] based upon least squares regressions for two-digit manufacturing industries. However, he uses a smaller sample (only 1958 data) than here, and his estimates are biased toward one because labor quality variation was not included in his two-digit industry estimates (he only considers labor quality variation in his estimates for manufacturing as a whole). Third, direct estimates of the CES production function are obtained for each industry using Kmenta's approximation [5]. Again, using efficient estimation and correcting for labor quality differences across states, the elasticity of substitution is not in general significantly different from one. It is incidentally shown that returns to scale can be accepted as being equal to unity for most industries.