Alternative treatments of congestion in DEA: A rejoinder to Cooper, Gu, and Li

This paper is a response to Cooper, W.W., B. Gu, and S. Li: 'Comparisons and Evaluations of Alternative Approaches to the Treatment of Congestion in DEA', European Journal of Operational Research (this issue), who claim that the standard FGL procedure by Färe, Grosskopf, and Lovell for dealing with congestion in DEA can (i) fail to identify congestion when it is present, and (ii) identify congestion when it is not present. We clarify the notion of congestion, and its relationship to structural efficiency and free disposability respectively, to point out that the FGL approach was originally intended for measuring structural efficiency, i.e. the influence of congestion on the efficiency of a particular production unit, not for identifying occurrence of congestion in any feasible production vector. Moreover, we point out that the result of Cooper et al. partially arises from ignorance of some key maintained assumptions underlying the FGL approach. Further, we present some counter-examples which demonstrate that the alternative approach advocated by Cooper et al. can equally fail in identification of congestion. Finally, some remarks on the influence of sampling error and errors-in-variables on the two-stage DEA approaches are presented.