Identification and Use of Efficient Faces and Facets in DEA

This paper provides an outline of possible uses of complete information on the facial structure of a polyhedral empirical production possibility set obtained by DEA. It is argued that an identification of all facets can be used for a characterization of basic properties of the empirical production frontier. Focus is on the use of this type of information for (i) the specification of constraints on the virtual multipliers in a cone-ratio model, (ii) a characterization of the data generation process for the underlying observed data set, and (iii) the estimation of isoquants and relevant elasticities of substitution reflecting the curvature of the frontier. The relationship between the so-called FDEF approach and the cone-ratio model is explored in some detail. It is demonstrated that a decomposition of the facet generation process followed by the use of one of the available (exponential) convex hull algorithms allows for an explicit identification of the facial structure of the possibility set in fairly large DEA data sets. It is a main point to be made that the difficulties encountered for an identification of all facets in a DEA-possibility set can be circumvented in a number of empirical data sets and that this type of information can be used for a characterization of the structural properties of the frontier.