What Is the Economic Meaning of FDH?

The central feature of the FDH model is the lack of convexity for its production possibility set, TF. Starting with n observed (distinct) decision making units DMU k , each defined by an input-output vector p k =[y k -x k ], domination is defined by ordinary vector inequalities. DMU k is said to dominate DMU j if p k ≥ p j , p k ≠ p j . The FDH production possibility set TF consists of the observed DMU j together with all input-output vectors p=[y k ,−x k ] with y ≥ 0, x ≥ 0, y ≠ 0, x ≠ 0 which are dominated by at least one of the observed DMU j . DMU k is defined as “FDH efficient” if no DMU j dominates it. In the BCC (or variable return to scale) DEA model the production possibility set TB consists of the observed DMU k together with all input-output vectors dominated by any convex combination of them and DMU k is DEA efficient if it is not dominated by any p in TB. In the DEA model, economic meaning is established by the introduction of (non negative) multiplier (price) vectors w=[u,v]. If DMU k is undominated (in TB) then there exists a positive multiplier vector w for which (a) w T p k =u T y k − v T x k ≥ w T p for every p ∈ TB. In everyday language, the net return (or profit) for DMU k relative to the given multiplier vector w is at least as great as that for any production possibility p. On the other hand, if DMU k is FDH but not DEA efficient then it is proved that there exists no positive multiplier vector >w for which (a) holds, i.e. for any positive w there exists at least one DMU j for which w T p j > w T p k . Since, therefore, FDH efficiency does not guarantee price efficiency what is its economic significance? Without economic significance, how can FDH be considered as being more than a mathematical system however logically soundly it may be conceived? Copyright Kluwer Academic Publishers 1999