Estimating output targets to evaluate output-specific efficiencies: A statistical framework

This paper presents a statistical framework for estimating output-specific efficiencies for the 2-output case based upon a data envelopment analysis (DEA) frontier estimate. The key to this approach are estimated output targets, which are used to identify proper reference points for efficiency comparisons. Being usually unobserved, output targets of firms are modelled as missing data and estimated jointly with output-specific efficiencies. The involved likelihood function is analytically intractable, so a data augmented Bayesian approach is proposed for estimation and adapted to the present purpose. Some implementation issues are discussed leading to an empirical Bayes setup with data informed priors. A proof of scale invariance is provided.