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New Definitions of Economic Cross-efficiency

In: Advances in Efficiency and Productivity II

Author

Listed:
  • Juan Aparicio

    (Center of Operations Research (CIO), Universidad Miguel Hernandez de Elche)

  • José L. Zofío

    (Universidad Autónoma de Madrid
    Erasmus Research Institute of Management, Erasmus University)

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.

Suggested Citation

  • Juan Aparicio & José L. Zofío, 2020. "New Definitions of Economic Cross-efficiency," International Series in Operations Research & Management Science, in: Juan Aparicio & C. A. Knox Lovell & Jesus T. Pastor & Joe Zhu (ed.), Advances in Efficiency and Productivity II, pages 11-32, Springer.
    • Handle: RePEc:spr:isochp:978-3-030-41618-8_2
    DOI: 10.1007/978-3-030-41618-8_2
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    Cited by:

    1. Ebrahimi, Bohlool & Dhamotharan, Lalitha & Ghasemi, Mohammad Reza & Charles, Vincent, 2022. "A cross-inefficiency approach based on the deviation variables framework," Omega, Elsevier, vol. 111(C).
    2. Mocholi-Arce, Manuel & Sala-Garrido, Ramon & Maziotis, Alexandros & Molinos-Senante, Maria, 2024. "The evolution of benchmaking the carbon efficiency drinking water companies in England and Wales," Utilities Policy, Elsevier, vol. 91(C).
    3. Aparicio, Juan & Zofío, José L. & Noonan, Doug & Thompson, Dylan & Woronkowicz, Joanna, 2025. "An innovative approach to efficiency measurement: Combining convexified efficiency analysis trees and data envelopment analysis to benchmark U.S. museums," Socio-Economic Planning Sciences, Elsevier, vol. 102(C).

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