A simulation study of Data Envelopment Analysis and parametric frontier models in the presence of heteroscedasticity

This paper studies the effects of heteroscedasticity on the following five types of estimators: (1) Data Envelopment Analysis (DEA) per se as well as DEA joined to regression forms, (2) Corrected Ordinary Least Squares based on maximum residual (COLS-R), (3) Corrected Ordinary Least Squares based on moments of residuals (COLS-M), (4) Maximum Likelihood Estimation (MLE), and (5) Goal Programming with one-sided deviations as in Aigner and Chu (A&C). This is accomplished with simulated data in an experiment designed around a single output–single input production function which is piecewise Cobb–Douglas. Robustness of results is confirmed with another experiment employing a shifted smooth Cobb–Douglas production function. The model has a composed error term consisting of two components – one for measurement error and the other for inefficiency. The simulation results indicate that heteroscedasticity does not have an adverse impact on DEA-based estimators and that DEA-based estimators are the best estimators of efficient output even under heteroscedasticity.