A Generalized Distance Function and the Analysis of Production Efficiency

A generalization of Shephard’s distance functions is proposed, extending the usefulness of distance functions in economic analysis. Applications to efficiency measurements and productivity analysis are presented. New indexes of productivity and technical, allocative, and scale efficiency are proposed and analyzed. Interpretation of these indexes in terms of ray-average cost, ray-average revenue, and cost-to-revenue ratio is discussed.

[1]  Lawrence J. Lau,et al.  Profit Functions of Technologies with Multiple Inputs and Outputs , 1972 .

[2]  D. Luenberger.  New optimality principles for economic efficiency and equilibrium , 1992 .

[3]  Walter Diewert,et al.  Exact and superlative index numbers , 1976 .

[4]  L. R. Christensen,et al.  MULTILATERAL COMPARISONS OF OUTPUT, INPUT, AND PRODUCTIVITY USING SUPERLATIVE INDEX NUMBERS* , 1982 .

[5]  M. Farrell.  The Measurement of Productive Efficiency , 1957 .

[6]  W. Briec.  A Graph-Type Extension of Farrell Technical Efficiency Measure , 1997 .

[7]  R. R. Russell,et al.  Measures of technical efficiency , 1985 .

[8]  L. R. Christensen,et al.  THE ECONOMIC THEORY OF INDEX NUMBERS AND THE MEASUREMENT OF INPUT, OUTPUT, AND PRODUCTIVITY , 1982 .

[9]  R. Shepherd.  Theory of cost and production functions , 1970 .

[10]  R. Färe,et al.  Benefit and Distance Functions , 1996 .

[11]  P. Bauer.  Recent developments in the econometric estimation of frontiers , 1990 .

[12]  D. Luenberger.  Benefit functions and duality , 1992 .

[13]  R. Färe,et al.  Productivity Growth, Technical Progress, and Efficiency Change in Industrialized Countries , 1994 .

[14]  J. Aczél,et al.  Lectures on Functional Equations and Their Applications , 1968 .

[15]  S. Malmquist.  Index numbers and indifference surfaces , 1953 .

[16]  G. Debreu.  The Coefficient of Resource Utilization , 1951 .

[17]  R. Färe,et al.  Profit, Directional Distance Functions, and Nerlovian Efficiency , 1998 .

[18]  C. Lovell,et al.  A survey of frontier production functions and of their relationship to efficiency measurement , 1980 .

[19]  Lawrence M. Seiford,et al.  Recent developments in dea : the mathematical programming approach to frontier analysis , 1990 .

[20]  R. Banker,et al.  NONPARAMETRIC ANALYSIS OF TECHNICAL AND ALLOCATIVE EFFICIENCIES IN PRODUCTION , 1988 .

[21]  Jean-Paul Chavas,et al.  Applied Production Analysis: A Dual Approach , 1988 .

[22]  S. Ray,et al.  PRODUCTIVITY GROWTH, TECHNICAL PROGRESS AND EFFICIENCY CHANGE IN INDUSTRIALIZED COUNTRIES: COMMENT , 1997 .