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Exact Relations Between Four Definitions Of Productivity Indices And Indicators


  • Walter Briec
  • Kristiaan Kerstens
  • Nicolas Peypoch


Generalizing earlier approximation results, we establish exact relations between the Luenberger productivity indicator and the Malmquist productivity index under rather mild assumptions. Furthermore, we show that similar exact relations can be established between the Luenberger-Hicks-Moorsteen indicator and the Hicks-Moorsteen index.
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Suggested Citation

  • Walter Briec & Kristiaan Kerstens & Nicolas Peypoch, 2012. "Exact Relations Between Four Definitions Of Productivity Indices And Indicators," Bulletin of Economic Research, Wiley Blackwell, vol. 64(2), pages 265-274, April.
  • Handle: RePEc:bla:buecrs:v:64:y:2012:i:2:p:265-274
    DOI: j.1467-8586.2010.00378.x

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    References listed on IDEAS

    1. McFadden, Daniel, 1978. "Cost, Revenue, and Profit Functions," Histoy of Economic Thought Chapters,in: Fuss, Melvyn & McFadden, Daniel (ed.), Production Economics: A Dual Approach to Theory and Applications, volume 1, chapter 1 McMaster University Archive for the History of Economic Thought.
    2. Bert Balk & Rolf Färe & Shawna Grosskopf & Dimitris Margaritis, 2008. "Exact relations between Luenberger productivity indicators and Malmquist productivity indexes," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 35(1), pages 187-190, April.
    3. Robert G. Chambers & Rulon D. Pope, 1996. "Aggregate Productivity Measures," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 78(5), pages 1360-1365.
    4. Charles R. Hulten, 2001. "Total Factor Productivity: A Short Biography," NBER Chapters,in: New Developments in Productivity Analysis, pages 1-54 National Bureau of Economic Research, Inc.
    5. Bjurek, Hans, 1996. " The Malmquist Total Factor Productivity Index," Scandinavian Journal of Economics, Wiley Blackwell, vol. 98(2), pages 303-313, June.
    6. Jean-Philippe Boussemart & Walter Briec & Kristiaan Kerstens & Jean-Christophe Poutineau, 2003. "Luenberger and Malmquist Productivity Indices: Theoretical Comparisons and Empirical Illustration," Bulletin of Economic Research, Wiley Blackwell, vol. 55(4), pages 391-405, October.
    7. Edward C. Jaenicke & Laura L. Lengnick, 1999. "A Soil-Quality Index and Its Relationship to Efficiency and Productivity Growth Measures: Two Decompositions," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 81(4), pages 881-893.
    8. Fare, Rolf & Grosskopf, Shawna & Roos, Pontus, 1996. "On two definitions of productivity," Economics Letters, Elsevier, vol. 53(3), pages 269-274, December.
    9. Ball, V. Eldon & Lovell, C.A. Knox & Luu, H. & Nehring, Richard F., 2004. "Incorporating Environmental Impacts in the Measurement of Agricultural Productivity Growth," Journal of Agricultural and Resource Economics, Western Agricultural Economics Association, vol. 29(03), December.
    10. Walter Briec & Kristiaan Kerstens, 2004. "A Luenberger-Hicks-Moorsteen productivity indicator: its relation to the Hicks-Moorsteen productivity index and the Luenberger productivity indicator," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 23(4), pages 925-939, May.
    11. Robert G. Chambers, 2002. "Exact nonradial input, output, and productivity measurement," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 20(4), pages 751-765.
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    Cited by:

    1. Picazo-Tadeo, Andrés J. & Castillo-Giménez, Juana & Beltrán-Esteve, Mercedes, 2014. "An intertemporal approach to measuring environmental performance with directional distance functions: Greenhouse gas emissions in the European Union," Ecological Economics, Elsevier, vol. 100(C), pages 173-182.
    2. Pastor, Jesus T. & Zofio, Jose L., 2017. "Can Farrell's allocative efficiency be generalized by the directional distance function approach?Author-Name: Aparicio, Juan," European Journal of Operational Research, Elsevier, vol. 257(1), pages 345-351.
    3. Gustavo Ferro & María Eugenia Labaronnie & Carlos A. Romero, 2011. "Medición de cambios en productividad con indicador de Luenberger en el sector de seguros en Argentina a la salida de la crisis," Working Papers hal-00597947, HAL.
    4. Merino, Fernando, 2012. "Firms' internationalization and productivity growth," Research in Economics, Elsevier, vol. 66(4), pages 349-354.
    5. Gustavo Ferro & Carlos A. Romero, 2011. "Comparación de medidas de cambio de productividad. Las aproximaciones de Malmquist y Luenberger en una aplicación al mercado de seguros," Working Papers hal-00597946, HAL.
    6. 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.

    More about this item

    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


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