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Reference Technology Sets, Free Disposal Hulls and Productivity Decompositions

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  • Diewert, Erwin
  • Fox, Kevin

Abstract

Diewert and Fox (2013) proposed decompositions of a Malmquist-type productivity index into explanatory factors, with a focus on extracting technical progress, technical efficiency change and returns to scale components. A major problem with their decompositions is that it may be difficult to determine the appropriate reference technologies. Using relatively unrestrictive regularity conditions, the paper develops a data envelopment type approach for decomposing productivity growth for a panel of production units into explanatory factors based on the Free Disposal Hull methods pioneered by Tulkens and his co-authors.

Suggested Citation

  • Diewert, Erwin & Fox, Kevin, 2013. "Reference Technology Sets, Free Disposal Hulls and Productivity Decompositions," Economics working papers erwin_diewert-2013-40, Vancouver School of Economics, revised 18 Sep 2013.
    • Handle: RePEc:ubc:bricol:erwin_diewert-2013-40
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    Cited by:

    1. Diewert, Erwin & Fox, Kevin J., 2014. "Decomposing Bjurek Productivity Indexes into Explanatory Factors," Economics working papers erwin_diewert-2014-32, Vancouver School of Economics, revised 30 Jun 2014.
    2. Tomas Balezentis & Kristiaan Kerstens & Zhiyang Shen, 2022. "Economic and Environmental Decomposition of Luenberger-Hicks-Moorsteen Total Factor Productivity Indicator: Empirical Analysis of Chinese Textile Firms With a Focus on Reporting Infeasibilities and Qu," Post-Print hal-03833245, HAL.
    3. Giovanni Cesaroni, 2025. "Centralized allocations in free disposal hull technologies," Annals of Operations Research, Springer, vol. 351(2), pages 1293-1317, August.
    4. W. Erwin Diewert & Kevin J. Fox, 2021. "The Difference Approach to Productivity Measurement and Exact Indicators," Springer Proceedings in Business and Economics, in: Christopher F. Parmeter & Robin C. Sickles (ed.), Advances in Efficiency and Productivity Analysis, pages 9-40, Springer.
    5. Tomas Balezentis & Zhiyang Shen, 2017. "An environmental Luenberger-Hicks-Moorsteen. Total Factor Productivityindicator for OECD Countries," Working Papers 2017-EQM-02, IESEG School of Management.
    6. Ang, Frederic & Kerstens, Pieter Jan, "undated". "The dynamic Luenberger-Hicks-Moorsteen productivity indicator with an application to dairy farms in South West England," 91st Annual Conference, April 24-26, 2017, Royal Dublin Society, Dublin, Ireland 258636, Agricultural Economics Society.
    7. Mocholi-Arce, Manuel & Sala-Garrido, Ramon & Molinos-Senante, Maria & Maziotis, Alexandros, 2021. "Water company productivity change: A disaggregated approach accounting for changes in inputs and outputs," Utilities Policy, Elsevier, vol. 70(C).
    8. Frederic Ang & Kristiaan Kerstens & Jafar Sadeghi, 2023. "Energy productivity and greenhouse gas emission intensity in Dutch dairy farms: A Hicks–Moorsteen by‐production approach under non‐convexity and convexity with equivalence results," Journal of Agricultural Economics, Wiley Blackwell, vol. 74(2), pages 492-509, June.
    9. W. Erwin Diewert & Kevin J. Fox, 2018. "A decomposition of US business sector TFP growth into technical progress and cost efficiency components," Journal of Productivity Analysis, Springer, vol. 50(1), pages 71-84, October.
    10. Meryem Duygun & Silvia Pazzi & Emili Tortosa-Ausina & Simona Zambelli, 2014. "Does local public ownership matter for the efficiency of water utilities? Evidence from Italy," Working Papers 2014/21, Economics Department, Universitat Jaume I, Castellón (Spain).
    11. Diewert, Erwin & Fox, Kevin J., 2019. "Productivity Indexes and National Statistics: Theory, Methods and Challenges," Microeconomics.ca working papers erwin_diewert-2019-8, Vancouver School of Economics, revised 25 Apr 2019.
    12. Hideyuki Mizobuchi & Valentin Zelenyuk, 2021. "Quadratic-mean-of-order-r indexes of output, input and productivity," Journal of Productivity Analysis, Springer, vol. 56(2), pages 133-138, December.
    13. Zhiyang Shen & Vivian Valdmanis, 2022. "Assessing total factor productivity across Africa: an empirical investigation," Journal of Productivity Analysis, Springer, vol. 58(2), pages 239-253, December.
    14. W. Erwin Diewert & Kevin J. Fox, 2017. "Decomposing Value Added Growth into Explanatory Factors," Discussion Papers 2017-02, School of Economics, The University of New South Wales.
    15. Diewert, W. Erwin & Fox, Kevin J., 2017. "Decomposing productivity indexes into explanatory factors," European Journal of Operational Research, Elsevier, vol. 256(1), pages 275-291.
    16. Hideyuki Mizobuchi & Valentin Zelenyuk, 2018. "Measuring Productivity by Quadratic-mean-of-order-of-r Indexes," CEPA Working Papers Series WP062018, School of Economics, University of Queensland, Australia.
    17. Zhiyang Shen & Kristiaan Kerstens & Tomas Baležentis, 2025. "An environmental Luenberger–Hicks–Moorsteen total factor productivity indicator: empirical analysis considering undesirable outputs either as inputs or outputs, and attention for infeasibilities," Annals of Operations Research, Springer, vol. 347(1), pages 241-263, April.
    18. Mª Pilar García-Alcober & Emili Tortosa-Ausina & Diego Prior & Manuel Illueca, 2014. "Cost and revenue efficiency in Spanish banking: What distributions show," Working Papers 2014/12, Economics Department, Universitat Jaume I, Castellón (Spain).
    19. Ang, Frederic & Kerstens, Pieter Jan, 2017. "Decomposing the Luenberger–Hicks–Moorsteen Total Factor Productivity indicator: An application to U.S. agriculture," European Journal of Operational Research, Elsevier, vol. 260(1), pages 359-375.
    20. Oh, Dong-hyun & Lee, Yong-Gil, 2016. "Productivity decomposition and economies of scale of Korean fossil-fuel power generation companies: 2001–2012," Energy, Elsevier, vol. 100(C), pages 1-9.
    21. Dariusz Kotlewski & Mirosław Błażej, 2022. "Evidence for Middle‐Income Trap Non‐occurrence in the Light of KLEMS Growth Accounting for Poland," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 68(S1), pages 22-51, April.

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    Keywords

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    JEL classification:

    • C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation
    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity
    • E23 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Production

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