## Simulation studies of efficiency, returns to scale and misspecification with nonlinear functions in DEA.(English)Zbl 0864.90013

Summary: Using statistically designed experiments, 12,500 observations are generated from a “4-pieced Cobb-Douglas function” exhibiting increasing and decreasing returns to scale in its different pieces. Performances of DEA and frontier regressions represented by COLS (corrected ordinary least squares) are compared at sample sizes of $$n=50, 100, 150$$ and 200. Statistical consistency is exhibited, with performances improving as sample sizes increase. Both DEA and COLS generally give good results at all sample sizes. In evaluating efficiency, DEA generally shows superior performance, with BCC models being best (except at “corner points”), followed by the CCR model and then by COLS, with log-linear regressions performing better than their translog counterparts at almost all sample sizes. Because of the need to consider locally varying behavior, only the CCR and translog models are used for returns to scale, with CCR being the better performer. An additional set of 7,500 observations were generated under conditions that made it possible to compare efficiency evaluations in the presence of collinearity and with model misspecification in the form of added and omitted variables. Results were similar to the larger experiment: the BCC model is the best performer. However, COLS exhibited surprisingly good performances – which suggests that COLS may have previously unidentified robustness properties – while the CCR model is the poorest performer when one of the variables used to generate the observations is omitted.

### MSC:

 91B38 Production theory, theory of the firm 91B06 Decision theory 91B82 Statistical methods; economic indices and measures