Accuracy of Deterministic Nonparametric Frontier Models with Undesirable Outputs

The accuracy of deterministic nonparametric frontier models with desirable outputs has been extensively investigated. However, research on the models’ accuracy in the presence of undesirable outputs is almost nonexistent, though applications in this regard are abundant. This paper evaluates the accuracy of seven representative deterministic nonparametric frontier models in dealing with undesirable outputs. The experimental design employs Monte Carlo simulation and translog production functions across a wide range of settings. We find that the integration of undesirable outputs lowers model accuracy. All seven models display robust performance under different returns-to-scale assumptions. Outputs correlation has a positive effect on model performance. Using a large sample can improve the models’ accuracy except for the range-adjusted measure model. The models’ accuracy is most sensitive to noise at low noise levels. Endogeneity has a negative effect on the models’ accuracy, but depreciation of accuracy is minor at low to medium endogeneity levels. Heteroskedasticity leads to improved performance. Overall, the experimental results support the usage of the by-production approach and strongly disfavor the range-adjusted measure approach and the hyperbolic approach. The directional distance function method has an edge for large samples, if the objective is to identify top and bottom units. Another approach, treating undesirable outputs as inputs, is dominated by other methods. The ranking of the methods is generally robust to the variations of returns-to-scale, sample size, noise, outputs correlation, endogeneity, and heteroskedasticity. We also show that the slacks-based measure under the by-production framework has better performance than the Färe–Grosskopf–Lovell index proposed in literature.