A scale elasticity measure for directional distance function and its dual: Theory and DEA estimation

In this paper we introduce a scale elasticity measure based on directional distance function for multi-output-multi-input technologies and explore its fundamental properties. Specifically, we derive necessary and sufficient condition for equivalence of the scale elasticity measure based on the directional distance function with the input oriented and output oriented scale elasticity measures. We also establish duality relationship between the scale elasticity measure based on the directional distance function with a scale elasticity measure based on the profit function. This theoretical result is valuable for empirical researchers as it provides a testable analytical condition for when (and only when) the alternative primal and dual definitions of scale elasticity for multi-output-multi-input technologies yield equivalent conclusions about economies or diseconomies of scale.

[1]  V. Zelenyuk.  A note on equivalences in measuring returns to scale , 2011 .

[2]  G. Hanoch.  The Elasticity of Scale and the Shape of Average Costs , 1975 .

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

[4]  R. Färe,et al.  Trade Restrictiveness and Efficiency , 2003 .

[5]  Hirofumi Fukuyama,et al.  Returns to scale and scale elasticity in data envelopment analysis , 2000, Eur. J. Oper. Res..

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

[7]  Victor V. Podinovski,et al.  Production , Manufacturing and Logistics A simple derivation of scale elasticity in data envelopment analysis , 2009 .

[8]  Kristiaan Kerstens,et al.  Infeasibility and Directional Distance Functions with Application to the Determinateness of the Luenberger Productivity Indicator , 2009 .

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

[10]  Rolf Färe,et al.  Productivity and Undesirable Outputs: A Directional Distance Function Approach , 1995 .

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

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

[13]  Lennart Hjalmarsson,et al.  Calculation of scale elasticities in DEA models: direct and indirect approaches , 2007 .

[14]  Hirofumi Fukuyama.  Scale characterizations in a DEA directional technology distance function framework , 2003, Eur. J. Oper. Res..

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

[16]  Finn R. Førsund,et al.  Calculating scale elasticity in DEA models , 2004, J. Oper. Res. Soc..

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

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

[19]  Rolf Färe,et al.  Estimating demand with distance functions: Parameterization in the primal and dual , 2008 .

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

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

[22]  Shadow Pricing Market Access: A Trade Benefit Function Approach , 2008 .

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

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

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

[26]  P. Hadjicostas,et al.  Different orders of one-sided scale elasticities in multi-output production , 2010 .

[27]  A. V. Volodin,et al.  Constructions of economic functions and calculations of marginal rates in DEA using parametric optimization methods , 2004, J. Oper. Res. Soc..

[28]  D. Primont,et al.  Directional Duality Theory , 2004 .

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

[30]  Petros Hadjicostas,et al.  One-sided elasticities and technical efficiency in multi-output production: A theoretical framework , 2006, Eur. J. Oper. Res..

[31]  D. Primont,et al.  Directional duality theory Directional duality theory , 2006 .

[32]  William L. Weber,et al.  Characteristics of a Polluting Technology: Theory and Practice , 2002 .

[33]  R. RajivD.BANKE.  Estimating most productive scale size using data envelopment analysis , 2003 .

[34]  R. Shephard.  Cost and production functions , 1953 .

[35]  David G. Luenberger,et al.  Optimality and the Theory of Value , 1994 .