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New Definitions of Economic Cross-efficiency

  • Juan AparicioEmail author
  • José L. Zofío
Chapter
  • 126 Downloads
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 287)

Abstract

Overall efficiency measures were introduced in the literature for evaluating the economic performance of firms when reference prices are available. These references are usually observed market prices. Recently, Aparicio and Zofío (Economic cross-efficiency: Theory and DEA methods. ERIM Report Series Research in Management, No. ERS-2019-001-LIS. Erasmus Research Institute of Management (ERIM). Erasmus University Rotterdam, The Netherlands. http://hdl.handle.net/1765/115479, 2019) have shown that the result of applying cross-efficiency methods (Sexton, T. R., Silkman, R. H., & Hogan, A. J. (1986). Data envelopment analysis: Critique and extensions. In R. H. Silkman (Ed.), Measuring efficiency: An assessment of data envelopment analysis, new directions for program evaluation (Vol. 32, pp. 73–105). San Francisco/London: Jossey-Bass), yielding an aggregate multilateral index that compares the technical performance of firms using the shadow prices of competitors, can be precisely reinterpreted as a measure of economic efficiency. They termed the new approach “economic cross-efficiency.” However, these authors restrict their analysis to the basic definitions corresponding to the Farrell (Journal of the Royal Statistical Society, Series A, General 120, 253–281, 1957) and Nerlove (Estimation and identification of Cobb-Douglas production functions. Chicago: Rand McNally, 1965) approaches, i.e., based on the duality between the cost function and the input distance function and between the profit function and the directional distance function, respectively. Here we complete their proposal by introducing new economic cross-efficiency measures related to other popular approaches for measuring economic performance, specifically those based on the duality between the profitability (maximum revenue to cost) and the generalized (hyperbolic) distance function and between the profit function and either the weighted additive or the Hölder distance function. Additionally, we introduce panel data extensions related to the so-called cost-Malmquist index and the profit-Luenberger indicator. Finally, we illustrate the models resorting to data envelopment analysis techniques—from which shadow prices are obtained and considering a banking industry dataset previously used in the cross-efficiency literature.

Keywords

Data envelopment analysis Overall efficiency Cross-efficiency 

Notes

Acknowledgments

J. Aparicio and J. L. Zofío thank the financial support from the Spanish Ministry of Economy and Competitiveness (Ministerio de Economía, Industria y Competitividad), the State Research Agency (Agencia Estatal de Investigación), and the European Regional Development Fund (Fondo Europeo de Desarrollo Regional) under grant no. MTM2016-79765-P (AEI/FEDER, UE).

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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Center of Operations Research (CIO), Universidad Miguel Hernandez de ElcheElche, AlicanteSpain
  2. 2.Department of EconomicsUniversidad Autónoma de MadridMadridSpain
  3. 3.Erasmus Research Institute of Management, Erasmus UniversityRotterdamThe Netherlands

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