Conditional nonparametric frontier models for convex and non convex technologies: A unifying approach

The explanation of productivity differentials is very important to identify the economic conditions that create inefficiency and to improve managerial performance. In literature two main approaches have been developed: one-stage approaches and twostage approaches. Daraio and Simar (2003) propose a full nonparametric methodology based on conditional FDH and conditional order-m frontiers without any convexity assumption on the technology. On the one hand, convexity has always been assumed in mainstream production theory and general equilibrium. On the other hand, in many empirical applications, the convexity assumption can be reasonable and sometimes natural. Leading by these considerations, in this paper we propose a unifying approach to introduce external-environmental variables in nonparametric frontier models for convex and non convex technologies. Developing further the work done in Daraio and Simar (2003) we introduce a conditional DEA estimator, i.e., an estimator of production frontier of DEA type conditioned to some external-environmental variables which are neither inputs nor outputs under the control of the producer. A robust version of this conditional estimator is also proposed. These various measures of efficiency provide also indicators of convexity. Illustrations through simulated and real data (mutual funds) examples are reported. ∗This paper has been prepared within the AQuaMethPSR Project under the PRIME Network of Excellence supported by the European Commission, 6th Framework Programme. Previous versions of this paper were presented at the 4 International DEA Symposium, Birmingham, 4-7 September 2004 and at the First Italian Congress in Econometrics and Empirical Economics, 24-25 January 2005. We would like to thank conferences participants for helpful comments. The usual disclaimers apply. †Work partially supported by the Italian Registry of ccTLD .it. ‡Research support from the “Interuniversity Attraction Pole”, Phase V (No. P5/24) from the Belgian Government (Belgian Science Policy) is acknowledged.