Estimating production functions with damage control inputs: an application to Korean vegetable production

Abstract

This thesis focuses on the use of chemicals for pest control in Korean cucumber production. The empirical issue addressed is whether estimating crop production functions consistent with the economic theory of damage control inputs makes significant differences in estimates of chemical productivity and the impact of chemicals on production risk. A distinguishing aspect of this analysis is that biotic factors related to pest damage are explicitly included in estimating production functions for Korean cucumbers. The first objective of this paper is to determine whether the pest control inputs are risk increasing or risk decreasing. The estimation results show that insecticide is risk decreasing and fungicide is risk increasing for all the functional forms, regardless of the functional form with and without a damage abatement function. Risk decreasing means that if insecticide use increases, the variability of output decreases. These results imply that policy makers and regulators should be cautious about assuming pesticides reduce risk. The risk impact of different types of pesticides is an empirical issue. The second objective is to determine how the form of the damage abatement function affects the marginal productivity of pest control inputs. For insecticide, the exponential and logistic are almost same as the conventional production function at the mean. The Weibull and Pareto are lower than with a conventional production function. For fungicide, the logistic and exponential are higher than with a conventional production function, while the Pareto and Weibull are lower than with a conventional production function. These results are generally consistent with Lichtenberg and Zilberman's theory that a conventional production function overestimates the marginal productivity of damage control inputs such as pesticides. The third objective is the derivation of the optimal use of pest controls inputs in Korean cucumber production. Assuming expected profit maximization, the optimal use of insecticide and fungicide is lower for all evaluated functional forms than the current mean. Furthermore, the optimal use of insecticide and fungicide with all damage abatement functions is substantially smaller than with a conventional production function, which is consistent with Lichtenberg and Zilberman's theory.