A Comparison of Parametric and Nonparametric Estimation Methods for Cost Frontiers and Economic Measures

This research examines the robustness of four different estimation approaches to evaluate their ability to estimate a “true” cost frontier and associated economic measures. The manuscript evaluates three parametric methods including a two-sided error system, OLS with only positive errors, and the stochastic frontier method. The fourth method is the nonparametric DEA method augmented to calculate multi-product and product-specific economies of scale. The robustness of the four estimation methods is examined using simulated data sets from two different distributions and two different observation quantity levels. The theoretical condition of curvature for the estimated cost functions was checked for the input price, and output quantity matrices. Calculation of the Eigenvalues revealed that all three parametric estimation methods violated curvature of either the price or quantity matrix, or both. Calculation of the estimated economic efficiency measures shows the parametric methods to be susceptible to distributional assumptions. However, the DEA method in all three simulations is fairly robust in estimating the “true” cost frontier and associated economic measures while maintaining curvature of the cost function.