Statistical Inference of DEA Model of Environmental Efficiency Considering Undesirable Outputs

There has been considerable theoretical and application of data envelopment analysis (DEA) directed to environmental efficiency measurement due to its capability of accounting for undesirable outputs. However, once statistical noise as well as environmental effects considered, these methods might fail to provide an appropriate estimates as the non-stochastic nature of deterministic DEA-based model. At present an approach for accounting for environmental effects as well as for overcoming the inherent dependency among decision-making units (DMUs). In this paper, a novel bootstrap approach is developed for obtaining the estimates of efficiency scores, the standard errors and the confidence intervals and a three-stage strategy which incorporates stochastic frontier analysis (SFA) and general multivariate regression is adapted for obtaining the adjusted estimates for efficiency measures. This approach not only can allow statistical noise and inherent dependency to be investigated simultaneously, but also can further enhance the statistical foundation of DEA analysis with the case of undesirable outputs. A simulation study illustrates the usefulness and effectiveness of our methodology for statistical inference of DEA-based efficiency evaluation with undesirable outputs.