Global and local scale characteristics in convex and nonconvex nonparametric technologies: A first empirical exploration

The purpose of this contribution is to empirically implement and supplement the proposals made by Podinovski (2004b) to explore the nature of both global and local returns to scale in nonconvex nonparametric technologies. In particular, we both propose a simplified method to compute the global returns to scale and employ some secondary data sets to investigate the frequency of the special case of global sub-constant returns to scale. Furthermore, when determining global returns to scale using both convex and nonconvex technologies, we verify how often the resulting information is concordant or conflicting. Finally, besides comparing the FDH and DEA evolution of ray-average productivity for some typical individual observations, we introduce in the literature two original methods for the determination of local returns to scale in nonconvex technologies.

[1]  Douglas D. Evanoff,et al.  Scale Elasticity versus Scale Efficiency in Banking , 1995 .

[2]  Rajiv D. Banker,et al.  Returns to scale in different DEA models , 2004, Eur. J. Oper. Res..

[3]  R. Sickles,et al.  The Relationship Between Stock Market Returns and Technical Efficiency Innovations: Evidence from the US Airline Industry , 1998 .

[4]  Pekka Korhonen,et al.  Non-convex value efficiency analysis and its application to bank branch sales evaluation , 2014 .

[5]  Majid Soleimani-damaneh,et al.  A polynomial-time algorithm to estimate returns to scale in FDH models , 2007, Comput. Oper. Res..

[6]  Ali Emrouznejad,et al.  DEA models for ratio data:convexity consideration , 2009 .

[7]  Kristiaan Kerstens,et al.  Solution Methods for nonconvex Free disposal Hull Models: a Review and some Critical Comments , 2014, Asia Pac. J. Oper. Res..

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

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

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

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

[12]  Stephen Haag,et al.  Assessing the relative efficiency of agricultural production units in the Blackland Prairie, Texas , 1992 .

[13]  Victor V. Podinovski,et al.  Efficiency and Global Scale Characteristics on the “No Free Lunch” Assumption Only , 2004 .

[14]  Giovanni Cesaroni,et al.  Average-cost efficiency and optimal scale sizes in non-parametric analysis , 2015, Eur. J. Oper. Res..

[15]  L. Seiford,et al.  An investigation of returns to scale in data envelopment analysis , 1999 .

[16]  J. Cummins,et al.  Comparison of Frontier Efficiency Methods: An Application to the U.S. Life Insurance Industry , 1998 .

[17]  Hervé Leleu,et al.  A linear programming framework for free disposal hull technologies and cost functions: Primal and dual models , 2006, Eur. J. Oper. Res..

[18]  R. Färe,et al.  Measuring Efficiency in Production: With an Application to Electric Utilities , 1985 .

[19]  Ronald W. Shephard,et al.  The notion of a production function , 1967, Unternehmensforschung.

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

[21]  S. Destefanis The Verdoorn Law: Some Evidence from Non-parametric Frontier Analysis , 2002 .

[22]  Steven T. Hackman,et al.  Production Economics: Integrating the Microeconomic and Engineering Perspectives , 2007 .

[23]  Majid Soleimani-Damaneh,et al.  On the estimation of returns-to-scale in FDH models , 2006, Eur. J. Oper. Res..

[24]  Qi Li,et al.  Nonparametric testing of closeness between two unknown distribution functions , 2009 .

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

[26]  Kaoru Tone,et al.  Decomposing technical efficiency and scale elasticity in two-stage network DEA , 2014, Eur. J. Oper. Res..

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

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

[29]  Yanqin Fan,et al.  On goodness-of-fit tests for weakly dependent processes using kernel method , 1999 .

[30]  V. V. Podinovski On the linearisation of reference technologies for testing returns to scale in FDH models , 2004, Eur. J. Oper. Res..

[31]  Kaoru Tone,et al.  Scale, Indivisibilities and Production Function in Data Envelopment Analysis , 2003 .

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

[33]  Rolf Färe,et al.  The relative efficiency of Illinois electric utilities , 1983 .

[34]  H. Varian The Nonparametric Approach to Production Analysis , 1984 .

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

[36]  R. Färe,et al.  The Structure of Technical Efficiency , 1983 .

[37]  V. V. Podinovski Local and global returns to scale in performance measurement , 2004, J. Oper. Res. Soc..

[38]  Kristiaan Kerstens,et al.  Non-convex Technologies and Cost Functions: Definitions, Duality and Nonparametric Tests of Convexity , 2004 .

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

[40]  Yanqin Fan,et al.  Semiparametric Estimation of Stochastic Production Frontier Models , 1996 .

[41]  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..

[42]  Dominique Deprins,et al.  Measuring Labor-Efficiency in Post Offices , 2006 .

[43]  Lawrence M. Seiford,et al.  A bibliography for Data Envelopment Analysis (1978-1996) , 1997, Ann. Oper. Res..

[44]  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..

[45]  W. Diewert,et al.  Linear Programming Tests of Regularity Conditions for Production Functions , 1983 .

[46]  S. Afriat Efficiency Estimation of Production Function , 1972 .

[47]  D. Prior,et al.  On the determinants of local government performance: A two-stage nonparametric approach , 2007 .

[48]  Giovanni Cesaroni,et al.  A complete FDH efficiency analysis of a diffused production network: the case of the Italian driver and vehicle agency , 2011, Int. Trans. Oper. Res..

[49]  Majid Soleimani-Damaneh,et al.  Stability of the classification of returns to scale in FDH models , 2009, Eur. J. Oper. Res..

[50]  Ali Emrouznejad,et al.  Evaluation of research in efficiency and productivity: A survey and analysis of the first 30 years , 2008 .

[51]  Subhash C. Ray,et al.  Data Envelopment Analysis: Theory and Techniques for Economics and Operations Research , 2004 .