T. Krishna Kumar

Nonlinear Estimation of the CES Production Function: Sampling Distributions and Tests in Small Samples

Over the past decade the parameters of the CES production function have been estimated from a variety of regression forms by a variety of regression techniques. One method of attack has been to estimate the CES parameters through the direct application of nonlinear regression procedures to the production function itself. Notable in this regard are Bodkin and Klein [1], Kumar and Asher [7], and Weitzman [11]. Despite the growing use of the nonlinear methods, little has been discovered about their econometric properties. Attempts have been made to fill the enormous void between

On Estimating the Elasticity of Factor Substitution by Nonlinear Least Squares

After briefly reviewing the recent history of estimating the elasticity of factor substitution by nonlinear least squares from the CES production function, this note activates the elasticity estimates generated by a previous Monte Carlo study and processes them to yield relative frequency distributions of the elasticity estimator. The note then deals with the issue of estimating the ‘location parameter’ of the underlying sampling distribution. Mean, mode and median are compared as estimators of the ‘location parameter’. It is shown that all the estimators are biased, and biased towards unity — the Cobb-Donglas function. Among all these point estimators median estimator is shown to have the least percent bias. The paper highlights the limitations of CES production function specification and Nonlinear Least Squares estimation of the elasticity of factor substitution. But if one must use CES specification and NLS estimation it shows how to cumulate evidence from comparable studies.