A Nonparametric Kernel Representation of the Agricultural Production Function: Implications for Economic Measures of Technology

The issue of production function estimation has received recent attention, particularly in agricultural economics with the advent of precision farming. Yet, the evidence to date is far from unanimous on the proper form of the production function. This paper reexamines the use of the primal production function framework using nonparametric regression techniques. Specifically, the paper demonstrates how a nonparametric regression based on a kernel density estimator can be used to estimate a production function using data on corn production from Illinois and Indiana. Nonparametric results are compared to common parametric specifications using the Nadaraya-Watson kernel regression estimator. The parametric and nonparametric forms are also compared in terms of describing the true technology of the firm by obtaining measures of the elasticity of scale and the marginal physical product through nonparametric estimation of the gradient of the production surface. Finally, the elasticities of substitution are compared between both parametric and nonparametric representations.