On Estimating the Elasticity of Factor Substitution by Nonlinear Least Squares

Abstract

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.

All this time the Guard was looking at her, first through a telescope, then through a microscope, and then through an opera-glass. At last he said, “You’re travelling the wrong way,” and shut up the window, and went away.

Lewis Carroll

Through the Looking-Glass