Explicit Construction and Analysis of Some Efficient Empirical Production Functions in Data Envelopment Analysis

摘要

In contrast to classical econometric work which only tests data for consistency with a special class of production functions, new theory and explicit construction by Data Envelopment Analysis of the empirical Pareto-Koopmans efficient production function is developed for data sets which satisfy two conditions met in all previous real applications of DEA known to the authors. The construction requires no additional computation beyond that of the DEA tests. In section 2, we bring forth the differences in key preoccupations of research in economic production theory with those of DEA by references to papers of Hanoch and Rothschild (1972), of Diewert and Parkan (1983) and, in still another direction by Fare, Grosskopf and Lovell (1985) and Debreu (1951). In section 3, we develop basic concepts of and theorems for geometric elucidation and analysis of the empirical efficient production functions of DEA including a new lemma on optimal solutions to the general linear programming problem (for arbitrary ordered fields of scalars). Then, restricting ourselves to two conditions on empirical data which have held in every DEA application we have made, we show that the mathematical structure of the efficient empirical function is so simplified that it is available immediately in analytic form without further computational work on top of the DEA tests. The efficient empirical production is then, moreover, piece-wise linear and continuous from piece to piece.