Constant Elasticity Of Substitution Production Function Research Articles

On Estimation of the CES Production Function

THE ORIGINAL SPECIFICATION of the constant-elasticity-of-substitution (CES) production function by Arrow, Chenery, Minhas, and Solow [1] was restricted to the case of constant returns to scale. With this restriction it is possible to estimate the elasticity of substitution from the marginal productivity condition by regressing the value of production per worker on wage rate (both variables measured in logarithms). If, however, the CES production function is generalized to allow for the possibility of non-constant returns to scale, this method of estimation is no longer feasible. The purpose of this paper is to consider estimation procedures applicable to the generalized version of the CES function under various circumstances. An obvious starting point is to consider estimates obtained by fitting the production function to observations on output and inputs alone. These estimates are consistent if the input variables are non-stochastic or, if stochastic, independent of the disturbance in the production function. The CES function can be written in the form

Efficiency Differences and Factor Intensities in the CES Production Function: An Interpretation

IN THIEIR celebrated article on the constantelasticity-of-substitution (CES) production function, Arrow, Cheney, Minhas, and Solow (1961) estimate factor-neutral efficiency differences between U.S. and Japanese manufacturing industries. They note that there is some slight indication... that the American advantage in efficiency tends to be least in capital-intensive (p. 247). Elsewhere, I have suggested that these factor-neutral differences may be due to differences in factor quality or to the role of capital invested in skills and, if the latter, should indeed be smallest in the least labor-intensive (most capital-intensive) industries (Kenen, 1965, p. 456). A formal demonstration follows: Consider the constant-cost CES production function:

A Measure of the Change in Relative Exploitation of Capital and Labor

BY exploitation, we mean that a factor of production is receiving less than its marginal revenue product. Relative exploitation connotes that the marginal rate of technical substitution of two factors is not equal to the ratio of their scarcity prices. Hence, either both factors may be exploited, but in different degrees, or one factor may be exploited while the other is not. In the present paper, a measure of the change in relative exploitation of capital and labor is presented together with empirical results for three two-digit industries (machinery except electric, primary metal industries, and electric and gas utilities), where the observations are drawn from the period, 1948-1960. Knowledge of variations in relative exploitation is useful in quantifying and explaining the sources of change in the distribution of income between the factors of production. This, in itself, is sufficient justification for focusing on the change in relative exploitation rather than the level. Although there may be more intrinsic interest in a measure of the level of exploitation as defined above, the framework used below does not lend itself to such a measure. The paper is laid out in the following manner. An elementary model of exploitation within a constant elasticity of substitution (CES) framework is presented first. This is followed by an econometric specification of one of the equations which must be tested in order to derive the required measure, while the succeeding section is devoted to the direct estimation method of the second required equation, the CES production function. Next, the empirical results for three selected industries are presented and discussed. The subsequent section contains the quantification of the changes in relative exploitation. In a later section, some problems with the framework and measuring procedures are discussed.

A Short Review of the SMAC Production-Function

The constant elasticity of substitution production-function or the SMAC production-function has been introduced in economic analysis very recently. Even in this short span of time it has been found very useful and has gained a great deal of popularity. Its practical and theoretical importance is all the greater since the two production-functions which have been studied and used in empirical analysis for a long time, namely the Cobb-Douglas production-function and the Leontief type of fixed input-coefficient production-function, become a particular case of this new production-function. A brief review of the theoretical and empirical work done on this new production-function is given in this article.