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Bounded directional distance function models

Author

Listed:
  • Jesus T. Pastor

    (Center of Operations Research (CIO), University Miguel Hernandez of Elche (UMH))

  • Juan Aparicio

    (Center of Operations Research (CIO), University Miguel Hernandez of Elche (UMH))

  • Javier Alcaraz

    (Center of Operations Research (CIO), University Miguel Hernandez of Elche (UMH))

  • Fernando Vidal

    (University Miguel Hernandez of Elche (UMH))

  • Diego Pastor

    (University Miguel Hernandez of Elche (UMH))

Abstract

Bounded additive models in data envelopment analysis (DEA) under the assumption of constant returns to scale (CRS) were recently introduced in the literature (Cooper et al. in J Product Anal 35(2):85–94, 2011; Pastor et al. in J Product Anal 40:285–292, 2013; Pastor et al. in Omega 56:16–24, 2015). In this paper, we propose to extend the so far generated knowledge about bounded additive models to the family of directional distance function (DDF) models in DEA, giving rise to a completely new subfamily of bounded or partially-bounded CRS-DDF models. We finally check the new approach on a real agricultural panel data set estimating efficiency and productivity change over time, resorting to the Luenberger indicator in a context where at least one variable is naturally bounded.

Suggested Citation

  • Jesus T. Pastor & Juan Aparicio & Javier Alcaraz & Fernando Vidal & Diego Pastor, 2018. "Bounded directional distance function models," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 26(4), pages 985-1004, December.
    • Handle: RePEc:spr:cejnor:v:26:y:2018:i:4:d:10.1007_s10100-018-0562-7
    DOI: 10.1007/s10100-018-0562-7
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    References listed on IDEAS

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    1. Färe, Rolf & Grosskopf, Shawna, 2010. "Directional distance functions and slacks-based measures of efficiency: Some clarifications," European Journal of Operational Research, Elsevier, vol. 206(3), pages 702-702, November.
    2. Ray, Subhash C & Desli, Evangelia, 1997. "Productivity Growth, Technical Progress, and Efficiency Change in Industrialized Countries: Comment," American Economic Review, American Economic Association, vol. 87(5), pages 1033-1039, December.
    3. B. Hollingsworth & P. Smith, 2003. "Use of ratios in data envelopment analysis," Applied Economics Letters, Taylor & Francis Journals, vol. 10(11), pages 733-735.
    4. Pastor, Jesus T. & Aparicio, Juan & Alcaraz, Javier & Vidal, Fernando & Pastor, Diego, 2015. "An enhanced BAM for unbounded or partially bounded CRS additive models," Omega, Elsevier, vol. 56(C), pages 16-24.
    5. Fried, Harold O. & Lovell, C. A. Knox & Schmidt, Shelton S. (ed.), 1993. "The Measurement of Productive Efficiency: Techniques and Applications," OUP Catalogue, Oxford University Press, number 9780195072181.
    6. Charnes, A. & Cooper, W. W. & Rhodes, E., 1978. "Measuring the efficiency of decision making units," European Journal of Operational Research, Elsevier, vol. 2(6), pages 429-444, November.
    7. Rashidi, Kamran & Farzipoor Saen, Reza, 2015. "Measuring eco-efficiency based on green indicators and potentials in energy saving and undesirable output abatement," Energy Economics, Elsevier, vol. 50(C), pages 18-26.
    8. William Cooper & Jesús Pastor & Fernando Borras & Juan Aparicio & Diego Pastor, 2011. "BAM: a bounded adjusted measure of efficiency for use with bounded additive models," Journal of Productivity Analysis, Springer, vol. 35(2), pages 85-94, April.
    9. William Cooper & Kyung Park & Jesus Pastor, 1999. "RAM: A Range Adjusted Measure of Inefficiency for Use with Additive Models, and Relations to Other Models and Measures in DEA," Journal of Productivity Analysis, Springer, vol. 11(1), pages 5-42, February.
    10. Bert Balk, 2001. "Scale Efficiency and Productivity Change," Journal of Productivity Analysis, Springer, vol. 15(3), pages 159-183, May.
    11. Caves, Douglas W & Christensen, Laurits R & Diewert, W Erwin, 1982. "The Economic Theory of Index Numbers and the Measurement of Input, Output, and Productivity," Econometrica, Econometric Society, vol. 50(6), pages 1393-1414, November.
    12. Olesen, Ole Bent & Petersen, Niels Christian & Podinovski, Victor V., 2015. "Efficiency analysis with ratio measures," European Journal of Operational Research, Elsevier, vol. 245(2), pages 446-462.
    13. Liu, John S. & Lu, Louis Y.Y. & Lu, Wen-Min & Lin, Bruce J.Y., 2013. "Data envelopment analysis 1978–2010: A citation-based literature survey," Omega, Elsevier, vol. 41(1), pages 3-15.
    14. Jesus Pastor & Juan Aparicio & Juan Monge & Diego Pastor, 2013. "Modeling CRS bounded additive DEA models and characterizing their Pareto-efficient points," Journal of Productivity Analysis, Springer, vol. 40(3), pages 285-292, December.
    15. C. Lovell, 2003. "The Decomposition of Malmquist Productivity Indexes," Journal of Productivity Analysis, Springer, vol. 20(3), pages 437-458, November.
    16. R. G. Chambers & Y. Chung & R. Färe, 1998. "Profit, Directional Distance Functions, and Nerlovian Efficiency," Journal of Optimization Theory and Applications, Springer, vol. 98(2), pages 351-364, August.
    17. Chambers, Robert G. & Fare, Rolf & Grosskopf, Shawna, 1996. "Productivity Growth in APEC Countries," Working Papers 197843, University of Maryland, Department of Agricultural and Resource Economics.
    18. Mehdi Toloo & Soroosh Nalchigar & Babak Sohrabi, 2018. "Selecting most efficient information system projects in presence of user subjective opinions: a DEA approach," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 26(4), pages 1027-1051, December.
    19. Kapelko, M. & Horta, I.M. & Camanho, A.S. & Oude Lansink, A., 2015. "Measurement of input-specific productivity growth with an application to the construction industry in Spain and Portugal," International Journal of Production Economics, Elsevier, vol. 166(C), pages 64-71.
    20. Färe, Rolf & Grosskopf, Shawna, 2010. "Directional distance functions and slacks-based measures of efficiency," European Journal of Operational Research, Elsevier, vol. 200(1), pages 320-322, January.
    21. Chambers, Robert G. & Chung, Yangho & Fare, Rolf, 1996. "Benefit and Distance Functions," Journal of Economic Theory, Elsevier, vol. 70(2), pages 407-419, August.
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    2. Tavana, Madjid & Izadikhah, Mohammad & Toloo, Mehdi & Roostaee, Razieh, 2021. "A new non-radial directional distance model for data envelopment analysis problems with negative and flexible measures," Omega, Elsevier, vol. 102(C).
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