A semiparametric estimator of the Zellner production function for corn: fitting the univariate primal

Abstract

Recent developments in production agriculture have resurrected interest in the primal production approach. This study develops a semi-parametric procedure for estimation of the Zellner production function for a single input.

Notes

¹ This represents a slight modification from Zellner's original two variable specification:

Here we implicitly set the scale variable v ₂ to 1.

² This nonparametric estimator follows Härdle's (1990) definition of a nonparametric regression estimator. The bivariate Gaussian kernel is similar to the multivariate normal distribution function

where A represents some positive definite symmetric matrix. This study sets A to be the observed covariance between phosphorous and potash. The nonparametric regression is then a weighted average response across observations.

³ Using the Zellner production function as the first equation and differentiating the production function with respect to nitrogen to derive the second equation yields

where x ₁ and y are the average nitrogen applied and corn yield respectively, and p ₁ and p_y are the prices of nitrogen and corn respectively. This system can be solved using Gauss--Seidel to yield estimates parameters a and b.