Asymptotics and Consistent Bootstraps for DEA Estimators in Non-parametric Frontier Models

Non-parametric data envelopment analysis (DEA) estimators based on linear programmingmethods have been widely applied in analyses of productive efficiency. Thedistributions of these estimators remain unknown except in the simple case of one inputand one output, and previous bootstrap methods proposed for inference have notbeen proven consistent, making inference doubtful.Non-parametric data envelopment analysis (DEA) estimators based on linear programmingmethods have been widely applied in analyses of productive efficiency. Thedistributions of these estimators remain unknown except in the simple case of one inputand one output, and previous bootstrap methods proposed for inference have notbeen proven consistent, making inference doubtful. This paper derives the asymptoticdistribution of DEA estimators under variable returns-to-scale. This result is thenused to prove that two different bootstrap procedures (one based on sub-sampling, theother based on smoothing) provide consistent inference. The smooth bootstrap requiressmoothing the irregularly-bounded density of inputs and outputs as well as smoothingof the DEA frontier estimate. Both bootstrap procedures allow for dependence of theinefficiency process on output levels and the mix of inputs in the case of input-orientedmeasures, or on inputs levels and the mix of outputs in the case of output-orientedmeasures.