[go: up one dir, main page]
More Web Proxy on the site http://driver.im/
IDEAS home Printed from https://ideas.repec.org/p/biw/wpaper/99.html
   My bibliography  Save this paper

On selecting directions for directional distance functions in a non-parametric framework: A review

Author

Listed:
  • Ke Wang
  • Yujiao Xian
  • Chia-Yen Lee
  • Yi-Ming Wei

    (Center for Energy and Environmental Policy Research (CEEP), Beijing Institute of Technology)

  • Zhimin Huang
Abstract
Directional distance function (DDF) has been a commonly used technique for estimating efficiency and productivity over the past two decades, and the directional vector is usually predetermined in the applications of DDF. The most critical issue of using DDF remains that how to appropriately project the inefficient decision-making unit (DMU) onto the production frontier along with a justified direction. This paper provides a comprehensive literature review on the techniques for selecting directional vector of the directional distance function. It begins with a brief introduction of the existing methods around the inclusion of the exogenous direction techniques and the endogenous direction techniques. The former commonly includes arbitrary direction and conditional direction techniques, while the latter involves the techniques for seeking theoretically optimized directions (i.e., direction towards the closest benchmark or indicating the largest efficiency improvement potential) and market-oriented directions (i.e., directions towards cost minimization, profit maximization, or marginal profit maximization benchmarks). The main advantages and disadvantages of these techniques are summarized, and the limitations inherent in the exogenous direction-selecting techniques are discussed. It also analytically argues the mechanism of each endogenous direction technique. The literature review is end up with a numerical example of efficiency estimation for power plants, in which most of the reviewed directions for DDF are demonstrated and their evaluation performance are compared.

Suggested Citation

  • Ke Wang & Yujiao Xian & Chia-Yen Lee & Yi-Ming Wei & Zhimin Huang, 2017. "On selecting directions for directional distance functions in a non-parametric framework: A review," CEEP-BIT Working Papers 99, Center for Energy and Environmental Policy Research (CEEP), Beijing Institute of Technology.
    • Handle: RePEc:biw:wpaper:99
    as

    Download full text from publisher

    File URL: http://ceep.bit.edu.cn/docs/2018-10/20181012074849820360.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Du, Limin & Hanley, Aoife & Zhang, Ning, 2016. "Environmental technical efficiency, technology gap and shadow price of coal-fuelled power plants in China: A parametric meta-frontier analysis," Resource and Energy Economics, Elsevier, vol. 43(C), pages 14-32.
    2. Jose Zofio & Jesus Pastor & Juan Aparicio, 2013. "The directional profit efficiency measure: on why profit inefficiency is either technical or allocative," Journal of Productivity Analysis, Springer, vol. 40(3), pages 257-266, December.
    3. Pathomsiri, Somchai & Haghani, Ali & Dresner, Martin & Windle, Robert J., 2008. "Impact of undesirable outputs on the productivity of US airports," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 44(2), pages 235-259, March.
    4. 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.
    5. 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.
    6. Adler, Nicole & Volta, Nicola, 2016. "Accounting for externalities and disposability: A directional economic environmental distance function," European Journal of Operational Research, Elsevier, vol. 250(1), pages 314-327.
    7. Timo Kuosmanen, 2005. "Weak Disposability in Nonparametric Production Analysis with Undesirable Outputs," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 87(4), pages 1077-1082.
    8. Kumar, Surender, 2006. "Environmentally sensitive productivity growth: A global analysis using Malmquist-Luenberger index," Ecological Economics, Elsevier, vol. 56(2), pages 280-293, February.
    9. Victor V. Podinovski & Finn R. Førsund, 2010. "Differential Characteristics of Efficient Frontiers in Data Envelopment Analysis," Operations Research, INFORMS, vol. 58(6), pages 1743-1754, December.
    10. Murty, Sushama & Russell, R. Robert, 2010. "On modeling pollution-generating technologies," Economic Research Papers 271176, University of Warwick - Department of Economics.
    11. Wang, Ke & Wei, Yi-Ming, 2016. "Sources of energy productivity change in China during 1997–2012: A decomposition analysis based on the Luenberger productivity indicator," Energy Economics, Elsevier, vol. 54(C), pages 50-59.
    12. Rolf Färe & Shawna Grosskopf & Carl A. Pasurka & William L. Weber, 2012. "Substitutability among undesirable outputs," Applied Economics, Taylor & Francis Journals, vol. 44(1), pages 39-47, January.
    13. 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.
    14. Maria Silva Portela & Pedro Borges & Emmanuel Thanassoulis, 2003. "Finding Closest Targets in Non-Oriented DEA Models: The Case of Convex and Non-Convex Technologies," Journal of Productivity Analysis, Springer, vol. 19(2), pages 251-269, April.
    15. Atakelty Hailu & Robert Chambers, 2012. "A Luenberger soil-quality indicator," Journal of Productivity Analysis, Springer, vol. 38(2), pages 145-154, October.
    16. Fare, Rolf & Grosskopf, Shawna & Noh, Dong-Woon & Weber, William, 2005. "Characteristics of a polluting technology: theory and practice," Journal of Econometrics, Elsevier, vol. 126(2), pages 469-492, June.
    17. Färe, Rolf & Grosskopf, Shawna & Pasurka, Carl A., 2007. "Environmental production functions and environmental directional distance functions," Energy, Elsevier, vol. 32(7), pages 1055-1066.
    18. Simar, Léopold & Vanhems, Anne & Wilson, Paul W., 2012. "Statistical inference for DEA estimators of directional distances," European Journal of Operational Research, Elsevier, vol. 220(3), pages 853-864.
    19. Ke Wang & Yujiao Xian & Yi-Ming Wei & Zhimin Huang, 2016. "Sources of carbon productivity change: A decomposition and disaggregation analysis based on global Luenberger productivity indicator and endogenous directional distance function," CEEP-BIT Working Papers 91, Center for Energy and Environmental Policy Research (CEEP), Beijing Institute of Technology.
    20. Fare, Rolf & Grosskopf, Shawna & Weber, William L., 2006. "Shadow prices and pollution costs in U.S. agriculture," Ecological Economics, Elsevier, vol. 56(1), pages 89-103, January.
    21. Matsushita, Kyohei & Yamane, Fumihiro, 2012. "Pollution from the electric power sector in Japan and efficient pollution reduction," Energy Economics, Elsevier, vol. 34(4), pages 1124-1130.
    22. Oum, Tae Hoon & Pathomsiri, Somchai & Yoshida, Yuichiro, 2013. "Limitations of DEA-based approach and alternative methods in the measurement and comparison of social efficiency across firms in different transport modes: An empirical study in Japan," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 57(C), pages 16-26.
    23. Leleu, Hervé, 2013. "Shadow pricing of undesirable outputs in nonparametric analysis," European Journal of Operational Research, Elsevier, vol. 231(2), pages 474-480.
    24. Picazo-Tadeo, Andrés J. & Beltrán-Esteve, Mercedes & Gómez-Limón, José A., 2012. "Assessing eco-efficiency with directional distance functions," European Journal of Operational Research, Elsevier, vol. 220(3), pages 798-809.
    25. Cong, Rong-Gang & Wei, Yi-Ming, 2010. "Potential impact of (CET) carbon emissions trading on China’s power sector: A perspective from different allowance allocation options," Energy, Elsevier, vol. 35(9), pages 3921-3931.
    26. Gerald Granderson & Diego Prior, 2013. "Environmental externalities and regulation constrained cost productivity growth in the US electric utility industry," Journal of Productivity Analysis, Springer, vol. 39(3), pages 243-257, June.
    27. Dong-hyun Oh, 2010. "A global Malmquist-Luenberger productivity index," Journal of Productivity Analysis, Springer, vol. 34(3), pages 183-197, December.
    28. Frances Frei & Patrick Harker, 1999. "Projections Onto Efficient Frontiers: Theoretical and Computational Extensions to DEA," Journal of Productivity Analysis, Springer, vol. 11(3), pages 275-300, June.
    29. Coggins, Jay S. & Swinton, John R., 1996. "The Price of Pollution: A Dual Approach to Valuing SO2Allowances," Journal of Environmental Economics and Management, Elsevier, vol. 30(1), pages 58-72, January.
    30. Wang, Ke & Wei, Yi-Ming & Zhang, Xian, 2013. "Energy and emissions efficiency patterns of Chinese regions: A multi-directional efficiency analysis," Applied Energy, Elsevier, vol. 104(C), pages 105-116.
    31. Chen, Yao & Du, Juan & Huo, Jiazhen, 2013. "Super-efficiency based on a modified directional distance function," Omega, Elsevier, vol. 41(3), pages 621-625.
    32. Cong, Rong-Gang & Wei, Yi-Ming, 2012. "Experimental comparison of impact of auction format on carbon allowance market," Renewable and Sustainable Energy Reviews, Elsevier, vol. 16(6), pages 4148-4156.
    33. Färe, Rolf & Grosskopf, Shawna & Pasurka, Carl, 2016. "Technical change and pollution abatement costs," European Journal of Operational Research, Elsevier, vol. 248(2), pages 715-724.
    34. Halkos, George E. & Tzeremes, Nickolaos G., 2013. "A conditional directional distance function approach for measuring regional environmental efficiency: Evidence from UK regions," European Journal of Operational Research, Elsevier, vol. 227(1), pages 182-189.
    35. Rezek, Jon P. & Campbell, Randall C., 2007. "Cost estimates for multiple pollutants: A maximum entropy approach," Energy Economics, Elsevier, vol. 29(3), pages 503-519, May.
    36. Chien-Ming Chen & Magali A. Delmas, 2012. "Measuring Eco-Inefficiency: A New Frontier Approach," Operations Research, INFORMS, vol. 60(5), pages 1064-1079, October.
    37. Dervaux, B. & Leleu, H. & Minvielle, E. & Valdmanis, V. & Aegerter, P. & Guidet, B., 2009. "Performance of French intensive care units: A directional distance function approach at the patient level," International Journal of Production Economics, Elsevier, vol. 120(2), pages 585-594, August.
    38. R. Färe & S. Grosskopf & G. Whittaker, 2013. "Directional output distance functions: endogenous directions based on exogenous normalization constraints," Journal of Productivity Analysis, Springer, vol. 40(3), pages 267-269, December.
    39. Fukuyama, Hirofumi & Weber, William L., 2009. "A directional slacks-based measure of technical inefficiency," Socio-Economic Planning Sciences, Elsevier, vol. 43(4), pages 274-287, December.
    40. Picazo-Tadeo, Andres J. & Reig-Martinez, Ernest & Hernandez-Sancho, Francesc, 2005. "Directional distance functions and environmental regulation," Resource and Energy Economics, Elsevier, vol. 27(2), pages 131-142, June.
    41. Eric Njuki & Boris E. Bravo-Ureta, 2015. "The Economic Costs of Environmental Regulation in U.S. Dairy Farming: A Directional Distance Function Approach," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 97(4), pages 1087-1106.
    42. Lee, Chia-Yen, 2016. "Nash-profit efficiency: A measure of changes in market structures," European Journal of Operational Research, Elsevier, vol. 255(2), pages 659-663.
    43. Mark Agee & Scott Atkinson & Thomas Crocker, 2012. "Child maturation, time-invariant, and time-varying inputs: their interaction in the production of child human capital," Journal of Productivity Analysis, Springer, vol. 38(1), pages 29-44, August.
    44. Wang, Ke & Wei, Yi-Ming & Zhang, Xian, 2012. "A comparative analysis of China’s regional energy and emission performance: Which is the better way to deal with undesirable outputs?," Energy Policy, Elsevier, vol. 46(C), pages 574-584.
    45. Watanabe, Michio & Tanaka, Katsuya, 2007. "Efficiency analysis of Chinese industry: A directional distance function approach," Energy Policy, Elsevier, vol. 35(12), pages 6323-6331, December.
    46. 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.
    47. Zhou, P. & Ang, B.W. & Wang, H., 2012. "Energy and CO2 emission performance in electricity generation: A non-radial directional distance function approach," European Journal of Operational Research, Elsevier, vol. 221(3), pages 625-635.
    48. Arabi, Behrouz & Munisamy, Susila & Emrouznejad, Ali & Shadman, Foroogh, 2014. "Power industry restructuring and eco-efficiency changes: A new slacks-based model in Malmquist–Luenberger Index measurement," Energy Policy, Elsevier, vol. 68(C), pages 132-145.
    49. Fare, Rolf & Logan, James, 1992. "The rate of return regulated version of Farrell efficiency," International Journal of Production Economics, Elsevier, vol. 27(2), pages 161-165, May.
    50. Fare, Rolf, et al, 1989. "Multilateral Productivity Comparisons When Some Outputs Are Undesirable: A Nonparametric Approach," The Review of Economics and Statistics, MIT Press, vol. 71(1), pages 90-98, February.
    51. Fare, R. & Grosskopf, S. & Pasurka, C., 1986. "Effects on relative efficiency in electric power generation due to environmental controls," Resources and Energy, Elsevier, vol. 8(2), pages 167-184, June.
    52. Macpherson, Alexander J. & Principe, Peter P. & Smith, Elizabeth R., 2010. "A directional distance function approach to regional environmental-economic assessments," Ecological Economics, Elsevier, vol. 69(10), pages 1918-1925, August.
    53. Chia -Yen Lee & Andrew L. Johnson, 2015. "Measuring Efficiency in Imperfectly Competitive Markets: An Example of Rational Inefficiency," Journal of Optimization Theory and Applications, Springer, vol. 164(2), pages 702-722, February.
    54. Ray, Subhash C. & Chen, Lei & Mukherjee, Kankana, 2008. "Input price variation across locations and a generalized measure of cost efficiency," International Journal of Production Economics, Elsevier, vol. 116(2), pages 208-218, December.
    55. Subhash C. Ray & Kankana Mukherjee, 2000. "Decomposition of Cost Competitiveness in U.S. Manufacturing: Some State-by-State Comparisons," Indian Economic Review, Department of Economics, Delhi School of Economics, vol. 35(2), pages 133-153, July.
    56. Chambers, Robert G. & Chung, Yangho & Fare, Rolf, 1996. "Benefit and Distance Functions," Journal of Economic Theory, Elsevier, vol. 70(2), pages 407-419, August.
    57. Juan Aparicio & José Ruiz & Inmaculada Sirvent, 2007. "Closest targets and minimum distance to the Pareto-efficient frontier in DEA," Journal of Productivity Analysis, Springer, vol. 28(3), pages 209-218, December.
    58. Bellenger, Moriah J. & Herlihy, Alan T., 2009. "An economic approach to environmental indices," Ecological Economics, Elsevier, vol. 68(8-9), pages 2216-2223, June.
    59. Lee, Chia-Yen, 2014. "Meta-data envelopment analysis: Finding a direction towards marginal profit maximization," European Journal of Operational Research, Elsevier, vol. 237(1), pages 207-216.
    60. B. Dervaux & H. Leleu & E. Minvielle & V. Valdmanis & P. Aegerter & B. Guidet, 2009. "Assessing Performance of French Intensive Care Units: A Directional Distance Function Approach at the Patient Level," Post-Print halshs-00476492, HAL.
    61. Ball, E. & Fare, R. & Grosskopf, S. & Zaim, O., 2005. "Accounting for externalities in the measurement of productivity growth: the Malmquist cost productivity measure," Structural Change and Economic Dynamics, Elsevier, vol. 16(3), pages 374-394, September.
    62. Murty, Sushama & Robert Russell, R. & Levkoff, Steven B., 2012. "On modeling pollution-generating technologies," Journal of Environmental Economics and Management, Elsevier, vol. 64(1), pages 117-135.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Fangqing Wei & Junfei Chu & Jiayun Song & Feng Yang, 2019. "A cross-bargaining game approach for direction selection in the directional distance function," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 41(3), pages 787-807, September.
    2. Ke Wang & Yujiao Xian & Yi-Ming Wei & Zhimin Huang, 2016. "Sources of carbon productivity change: A decomposition and disaggregation analysis based on global Luenberger productivity indicator and endogenous directional distance function," CEEP-BIT Working Papers 91, Center for Energy and Environmental Policy Research (CEEP), Beijing Institute of Technology.
    3. Zhou, Haibo & Yang, Yi & Chen, Yao & Zhu, Joe, 2018. "Data envelopment analysis application in sustainability: The origins, development and future directions," European Journal of Operational Research, Elsevier, vol. 264(1), pages 1-16.
    4. Wang, Ke & Wei, Yi-Ming, 2016. "Sources of energy productivity change in China during 1997–2012: A decomposition analysis based on the Luenberger productivity indicator," Energy Economics, Elsevier, vol. 54(C), pages 50-59.
    5. Ke Wang & Yi-Ming Wei & Zhimin Huang, 2017. "Environmental efficiency and abatement efficiency measurements of China¡¯s thermal power industry: A data envelopment analysis based materials balance approach," CEEP-BIT Working Papers 108, Center for Energy and Environmental Policy Research (CEEP), Beijing Institute of Technology.
    6. Sueyoshi, Toshiyuki & Yuan, Yan & Goto, Mika, 2017. "A literature study for DEA applied to energy and environment," Energy Economics, Elsevier, vol. 62(C), pages 104-124.
    7. D’Inverno, Giovanna & Carosi, Laura & Romano, Giulia & Guerrini, Andrea, 2018. "Water pollution in wastewater treatment plants: An efficiency analysis with undesirable output," European Journal of Operational Research, Elsevier, vol. 269(1), pages 24-34.
    8. Surender Kumar & Rakesh Kumar Jain, 2021. "Cost of CO2 emission mitigation and its decomposition: evidence from coal-fired thermal power sector in India," Empirical Economics, Springer, vol. 61(2), pages 693-717, August.
    9. Wang, Ke & Wei, Yi-Ming & Huang, Zhimin, 2018. "Environmental efficiency and abatement efficiency measurements of China's thermal power industry: A data envelopment analysis based materials balance approach," European Journal of Operational Research, Elsevier, vol. 269(1), pages 35-50.
    10. Deng, Zhongqi & Jiang, Nan & Pang, Ruizhi, 2021. "Factor-analysis-based directional distance function: The case of New Zealand hospitals," Omega, Elsevier, vol. 98(C).
    11. Lee, Chia-Yen, 2014. "Meta-data envelopment analysis: Finding a direction towards marginal profit maximization," European Journal of Operational Research, Elsevier, vol. 237(1), pages 207-216.
    12. Lee, Chia-Yen & Zhou, Peng, 2015. "Directional shadow price estimation of CO2, SO2 and NOx in the United States coal power industry 1990–2010," Energy Economics, Elsevier, vol. 51(C), pages 493-502.
    13. Arabi, Behrouz & Munisamy, Susila & Emrouznejad, Ali, 2015. "A new slacks-based measure of Malmquist–Luenberger index in the presence of undesirable outputs," Omega, Elsevier, vol. 51(C), pages 29-37.
    14. Manello, Alessandro, 2017. "Productivity growth, environmental regulation and win–win opportunities: The case of chemical industry in Italy and Germany," European Journal of Operational Research, Elsevier, vol. 262(2), pages 733-743.
    15. Tang, Kai & Yang, Lin & Zhang, Jianwu, 2016. "Estimating the regional total factor efficiency and pollutants’ marginal abatement costs in China: A parametric approach," Applied Energy, Elsevier, vol. 184(C), pages 230-240.
    16. Kounetas, Konstantinos & Zervopoulos, Panagiotis D., 2019. "A cross-country evaluation of environmental performance: Is there a convergence-divergence pattern in technology gaps?," European Journal of Operational Research, Elsevier, vol. 273(3), pages 1136-1148.
    17. Chen, Po-Chi & Yu, Ming-Miin & Chang, Ching-Cheng & Hsu, Shih-Hsun & Managi, Shunsuke, 2015. "The enhanced Russell-based directional distance measure with undesirable outputs: Numerical example considering CO2 emissions," Omega, Elsevier, vol. 53(C), pages 30-40.
    18. Behrouz Arabi & Susila Munisamy Doraisamy & Ali Emrouznejad & Alireza Khoshroo, 2017. "Eco-efficiency measurement and material balance principle: an application in power plants Malmquist Luenberger Index," Annals of Operations Research, Springer, vol. 255(1), pages 221-239, August.
    19. Lee, Chia-Yen & Wang, Ke, 2019. "Nash marginal abatement cost estimation of air pollutant emissions using the stochastic semi-nonparametric frontier," European Journal of Operational Research, Elsevier, vol. 273(1), pages 390-400.
    20. Lee, Chia-Yen, 2018. "Mixed-strategy Nash equilibrium in data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 266(3), pages 1013-1024.

    More about this item

    Keywords

    Data Envelopment Analysis (DEA); Least distance; Endogenous mechanism; Cost efficiency; Profit efficiency; Marginal profit maximization;
    All these keywords.

    JEL classification:

    • Q54 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics - - - Climate; Natural Disasters and their Management; Global Warming
    • Q40 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Energy - - - General

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:biw:wpaper:99. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Zhi-Fu Mi (email available below). General contact details of provider: https://edirc.repec.org/data/cebitcn.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.