Scale, Indivisibilities and Production Function in Data Envelopment Analysis

This paper critically re-examines the concept of returns to scale vis-a-vis economies of scale since the writings of Adam Smith by relating the former to the concept of production unit and the latter to the concept of firm. Though to date some valuable progress has been made exploring the economic theory underlying DEA models, these developments have remained in their infancy and have not found enough application. An attempt is made here to examine the DEA model of efficiency measurement and its application from an economic viewpoint. We show here that the presence of indivisibilities in all multi-stage production processes makes the technology structure non-convex, and therefore, the standard convex DEA production models (e.g., CCR and BCC) fail to exhibit increasing returns due to indivisibilities. However, the non-convex technology embedded in FDH model helps revealing process indivisibilities arising from task-specific processes whereas a homogeneous characterization of production function fails to do so.

[1]  James E. Storbeck,et al.  Efficiency gains from regionalization: economic development in China revisited , 2000 .

[2]  L. E. Fouraker,et al.  The Theory of Monopolistic Competition , 1933 .

[3]  Gang Yu,et al.  Estimating returns to scale in DEA , 1997 .

[4]  N. Kaldor,et al.  The Equilibrium of the Firm , 1934 .

[5]  Thomas M. Mitchell,et al.  Output scaling in a cost function setting , 1992 .

[6]  P. S. Florence,et al.  The structure of competitive industry , 1932 .

[7]  Philippe Vanden Eeckaut,et al.  Non-parametric efficiency, progress and regress measures for panel data: Methodological aspects☆ , 1995 .

[8]  Jati K. Sengupta,et al.  Efficiency Measurement in Nonmarket Systems Through Data Envelopment Analysis , 1987 .

[9]  Joan V. Robinson.  Economics of imperfect competition , 1969 .

[10]  E. Chamberlin.  Proportionality, Divisibility and Economies of Scale , 1948 .

[11]  A. Charnes,et al.  Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis , 1984 .

[12]  Thomas Mitchell,et al.  Homotheticity and Non-Radial Changes , 2001 .

[13]  Rajiv D. Banker,et al.  A note on returns to scale in DEA , 1996 .

[14]  Rolf Färe,et al.  Linear Programming Models for Firm and Industry Performance , 1992 .

[15]  R. Robert Russell,et al.  Microeconomics: A Synthesis of Modern and Neoclassical Theory , 1979 .

[16]  H. Scarf.  Production Sets with Indivisibilities Part I: Generalities , 1981 .

[17]  Hirofumi Fukuyama,et al.  Returns to Scale and Scale Elasticity in Farrell, Russell and Additive Models , 2001 .

[18]  Production and distribution theories : the formative period , 1942 .

[19]  Sten Thore,et al.  Economies of scale in the US computer industry: An empirical investigation using data envelopment analysis , 1996 .

[20]  John C. Panzar,et al.  Economies of Scale in Multi-Output Production , 1977 .

[21]  Kristiaan Kerstens,et al.  Estimating returns to scale using non-parametric deterministic technologies: A new method based on goodness-of-fit , 1999, Eur. J. Oper. Res..

[22]  A. Marshall.  Principles of Economics , .

[23]  篠原 正明,et al.  William W.Cooper,Lawrence M.Seiford,Kaoru Tone 著, DATA ENVELOPMENT ANALYSIS : A Comprehensive Text with Models, Applications, References and DEA-Solver Software, Kluwer Academic Publishers, 2000年, 318頁 , 2002 .

[24]  R. Banker,et al.  A Comparative Application of Data Envelopment Analysis and Translog Methods: An Illustrative Study of Hospital Production , 1986 .

[25]  Boaz Golany,et al.  Restricted best practice selection in DEA: An overview with a case study evaluating the socio-economic performance of nations , 1997, Ann. Oper. Res..

[26]  Hollis B. Chenery,et al.  Engineering Production Functions , 1949 .

[27]  Ury Passy,et al.  Lower Bound Restrictions on Intensities in Data Envelopment Analysis , 2001 .

[28]  Abraham Charnes,et al.  Measuring the efficiency of decision making units , 1978 .

[29]  Herbert E. Scarf,et al.  Neighborhood Systems for Production Sets with Indivisibilities , 1986 .

[30]  R. Grabowski,et al.  An analysis of optimal scale and factor intensity in Nepalese agriculture: an application of a ray–homothetic production function , 1986 .

[31]  W. Cooper,et al.  Data Envelopment Analysis: A Comprehensive Text with Models, Applications, References and DEA-Solver Software , 1999 .

[32]  Robert M. Thrall,et al.  What Is the Economic Meaning of FDH? , 1999 .

[33]  Paul A. Samuelson.  Economics: An Introductory Analysis , 1948 .

[34]  Rolf Färe,et al.  Estimation of returns to scale using data envelopment analysis: A comment , 1994 .

[35]  R. Färe,et al.  Intertemporal Production Frontiers: With Dynamic DEA , 1996 .

[36]  Kaoru Tone,et al.  A SIMPLE CHARACTERIZATION OF RETURNS TO SCALE IN DEA , 1996 .

[37]  Rolf Färe,et al.  AN INTERMEDIATE INPUT MODEL OF DAIRY PRODUCTION USING COMPLEX SURVEY DATA , 1995 .

[38]  Rolf Färe,et al.  Scale economies and duality , 1986 .

[39]  K. Arrow,et al.  Capital-labor substitution and economic efficiency , 1961 .

[40]  Toshiyuki Sueyoshi,et al.  Measuring efficiencies and returns to scale of Nippon telegraph & telephone in production and cost analyses , 1997 .

[41]  P. Samuelson,et al.  Foundations of Economic Analysis. , 1948 .

[42]  Kristiaan Kerstens,et al.  Returns to Scale on Nonparametric Deterministic Technologies: Simplifying Goodness-of-Fit Methods Using Operations on Technologies , 2000 .

[43]  R. Grabowski,et al.  Returns to scale in agriculture: An empirical investigation of Japanese experience , 1986 .

[44]  Henry Tulkens,et al.  On FDH efficiency analysis: Some methodological issues and applications to retail banking, courts, and urban transit , 1993 .

[45]  O. Williamson,et al.  The firm as a nexus of treaties , 1992 .

[46]  Kaoru Tone,et al.  A slacks-based measure of super-efficiency in data envelopment analysis , 2001, Eur. J. Oper. Res..

[47]  Finn R. Førsund,et al.  On the calculation of the scale elasticity in DEA models , 1996 .

[48]  R. Färe,et al.  The measurement of efficiency of production , 1985 .

[49]  B. Gold.  Changing Perspectives on Size, Scale, and Returns: An Interpretive Survey , 1981 .

[50]  T. Koopmans.  Three Essays on the State of Economic Science , 1958 .

[51]  Rajiv D. Banker,et al.  Estimation of returns to scale using data envelopment analysis , 1992 .

[52]  F. Førsund,et al.  Generalised Farrell Measures of Efficiency: An Application to Milk Processing in Swedish Dairy Plants , 1979 .

[53]  R. Färe,et al.  Returns to scale in U.S. surface mining of coal , 1985 .

[54]  Per Joakim Agrell,et al.  A Dual Approach to Nonconvex Frontier Models , 2001 .

[55]  B. Mandelbrot.  When Can Price Be Arbitraged Efficiently? A Limit to the Validity of the Random Walk and Martingale Models , 1971 .

[56]  Kaoru Tone,et al.  On Returns to Scale under Weight Restrictions in Data Envelopment Analysis , 2001 .

[57]  Aubrey Silberston,et al.  Economies of Scale in Theory and Practice , 1972 .

[58]  G. Hanoch,et al.  Homotheticity in joint production , 1970 .

[59]  Herbert E. Scarf,et al.  The Allocation of Resources in the Presence of Indivisibilities , 1994 .

[60]  Biresh K. Sahoo.  A comparative application of data envelopment analysis and frontier translog production function for estimating returns to scale and efficiencies , 1999, Int. J. Syst. Sci..

[61]  D. Primont,et al.  Multi-Output Production and Duality: Theory and Applications , 1994 .

[62]  W. Baumol,et al.  Contestable Markets and the Theory of Industry Structure , 1982 .

[63]  Rolf Färe,et al.  Modelling Scale Economies with Ray-Homothetic Production Functions , 1985 .

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

[65]  R. Banker.  Estimating most productive scale size using data envelopment analysis , 1984 .

[66]  H. Scarf.  Production Sets with Indivisibilities-Part II: The Case of Two Activities , 1981 .

[67]  John Haldi,et al.  Economies of Scale in Industrial Plants , 1967, Journal of Political Economy.

[68]  Rajiv D. Banker,et al.  Equivalence and Implementation of Alternative Methods for Determining Returns to Scale in Data Envel , 1996 .