Nonparametric Productivity Analysis with Undesirable Outputs: Reply

Hailu and Veeman (2001) (henceforth HV) use both primal nonparametric (DEA) and dual nonparametric frontiers that include undesirable outputs. The dual frontier provides the tightest nonparametric outer-bound to the unknown underlying technology while the DEA frontier provides the tightest innerbound to the technology (Varian, Banker and Maindiratta, Chavas and Cox). All previous nonparametric analyses incorporating undesirable outputs had been based on the DEA model, and HV highlighted the limitations of this one-sided approach by confronting the results from the DEA model with those from the dual model. The DEA model was found to be very poor in terms of discriminating between observations. As indicated in HV, this is a problem that has also been noted by several other researchers in the conventional productivity literature. Before I provide specific responses to some of the comments by Fare and Grosskopf (FG), I would like to make the following general remarks. First, HV use input-based measures and a variable returns-to-scale formulation of the DEA model. However, FG support their arguments using output-possibility frontiers, output-based measures and constant returnsto-scaleassumptionsthatwerenotusedinHV. It is well known that a DEA model with constant returns to scale has different characteristics and provides different results compared to those with variable returns. Second, and more importantly, it should be noted that the DEA model with constant returns to scale does not qualify as the inner nonparametric bound that is the subject of HV’s article. Third, the major difference between the weakly disposable and HV DEA frontiers becomes irrelevant for measures of efficiency that explicitly penalize extrabadoutput.InFG’sfigure1,forexample, the area east of line bc is irrelevant in the HV