Economies of scale for data envelopment analysis with a Kansas farm application

Abstract

Estimation of cost functions can provide useful economic information to producers, economists, and policy makers. From the estimation of a cost function, it is possible to calculate cost efficiency, economies of scope, and economies of scale. Economic theory specifies the cost function as a frontier since firms cannot operate at lower cost than the cost minimizing input/output bundle. However, traditional parametric estimation techniques often violate economic theory using two sided-error systems. The stochastic frontier method has allowed the estimation of a frontier but continues to restrict the technology through functional assumption. Nonparametric frontier estimation is an alternative approach to estimate a cost frontier by enveloping the data which by its construct, conforms to economic theory. This research expands the economic information available by deriving multi-product scale economies and product-specific scale economies from the nonparametric approach. It also tests its ability to accurately recover these important economic measures under different assumptions of the cost function, and cost inefficiency distributions. Next, this new method is compared to other methods used to estimate cost functions and associated economic measures including a two-sided error system, stochastic frontier method, and an OLS model restricting the errors to take on only positive values. Finally, the nonparametric approach with the new measures is applied to a sample of Kansas farms. The nonparametric approach is able to closely estimate economies of scale and scope from estimation of a cost frontier. Comparison reveals that the nonparametric approach is closer to the “true” economic measures than some parametric methods and that it is better able to extrapolate out of sample when there are no zero output firms. Finally, the nonparametric approach shows that potential cost savings from economies of scale and economies of scope exist for small Kansas farms. However, cost savings from economies of scale become exhausted when farms exceed gross annual revenues of $500k, while economies of scope also diminish as farms grow larger. Results also show from annual frontier estimations that estimates of economies of scale, scope, and cost efficiency have remained relatively stable from 2002 to 2011.