Mathematical Model of Channel Catfish Foodfish Production in Multiple-Batch

Abstract

Market size requirements for catfish change periodically, and catfish farmers must adjust quickly. Data from catfish pond studies at the University of Arkansas at Pine Bluff (UAPB) were used to develop mathematical models of catfish foodfish in multiple-batch culture across a variety of management alternatives. Two different functional forms (Cobb–Douglas and a modified translog) were each developed into average and stochastic frontier models. Inefficiency terms were found to be non-significant in the frontier models, thus making the average and frontier models equivalent. In the average regression models, the modified translog form demonstrated superior statistical values as compared to the Cobb–Douglas form, but the latter resulted in lower prediction error and was validated with the Chow test when used to predict observations from commercial catfish farms. This approach appears to have merit from the perspective of its statistical properties, and represents a step towards development of a model that could be used for farm management purposes.

Keywords:

• average and stochastic frontier production models
• channel catfish foodfish
• functional forms
• multiple-batch
• size at harvest

ACKNOWLEDGMENTS

The authors thank Nathan Stone and Kehar Singh for helpful comments and suggestions on an earlier version of this manuscript. Thanks are also due to those individuals who conducted the catfish production studies that generated the data used in this analysis.