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POn Fisher Aggregation of Multi-factor Productivity Indexes

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Abstract

The goal of this paper is to investigate the question of importance of Fisher aggregation of the Paasche and Laspeyres versions of Malmquist quantity and productivity indexes from both theoretical and empirical perspectives. We discuss existing justification and provide an alternative theoretical justification based on results from functional equations literature. We also use real data (from Kumar and Russell (2002, American Economic Review)) to illustrate how dramatic the differences in conclusions can be in practice depending on whether one employs Laspeyres or Paasche productivity indexes.

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  • Rolf Färe & Valentin Zelenyuk, 2020. "POn Fisher Aggregation of Multi-factor Productivity Indexes," CEPA Working Papers Series WP082020, School of Economics, University of Queensland, Australia.
    • Handle: RePEc:qld:uqcepa:151
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    File URL: https://economics.uq.edu.au/files/19689/WP082020.pdf
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    1. Bert Balk & Rolf Färe & Shawna Grosskopf, 2003. "The theory of economic price and quantity indicators," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 23(1), pages 149-164, December.
    2. Färe, Rolf & Mizobuchi, Hideyuki & Zelenyuk, Valentin, 2021. "Hicks neutrality and homotheticity in technologies with multiple inputs and multiple outputs," Omega, Elsevier, vol. 101(C).
    3. Léopold Simar & Paul W. Wilson, 2015. "Statistical Approaches for Non-parametric Frontier Models: A Guided Tour," International Statistical Review, International Statistical Institute, vol. 83(1), pages 77-110, April.
    4. Rolf Fare & Valentin Zelenyuk, 2005. "On Farrell's Decomposition and Aggregation," International Journal of Business and Economics, School of Management Development, Feng Chia University, Taichung, Taiwan, vol. 4(2), pages 167-171, August.
    5. Antonio Peyrache, 2013. "Multilateral productivity comparisons and homotheticity," Journal of Productivity Analysis, Springer, vol. 40(1), pages 57-65, August.
    6. Balk,Bert M., 2012. "Price and Quantity Index Numbers," Cambridge Books, Cambridge University Press, number 9781107404960.
    7. Bjurek, Hans, 1996. " The Malmquist Total Factor Productivity Index," Scandinavian Journal of Economics, Wiley Blackwell, vol. 98(2), pages 303-313, June.
    8. Park, Byeong U. & Simar, Léopold & Zelenyuk, Valentin, 2008. "Local likelihood estimation of truncated regression and its partial derivatives: Theory and application," Journal of Econometrics, Elsevier, vol. 146(1), pages 185-198, September.
    9. Chambers,Robert G., 1988. "Applied Production Analysis," Cambridge Books, Cambridge University Press, number 9780521314275.
    10. Oleg Badunenko & Diego Romero‐Ávila, 2013. "Financial Development And The Sources Of Growth And Convergence," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 54(2), pages 629-663, May.
    11. Samuelson, Paul A & Swamy, S, 1974. "Invariant Economic Index Numbers and Canonical Duality: Survey and Synthesis," American Economic Review, American Economic Association, vol. 64(4), pages 566-593, September.
    12. Färe, Rolf & Zelenyuk, Valentin, 2019. "On Luenberger input, output and productivity indicators," Economics Letters, Elsevier, vol. 179(C), pages 72-74.
    13. John R. Hicks, 1961. "The Measurement of Capital in Relation to the Measurement of Other Economic Aggregates," International Economic Association Series, in: D. C. Hague (ed.), The Theory of Capital, chapter 0, pages 18-31, Palgrave Macmillan.
    14. H. Funke & G. Hacker & J. Voeller, 1979. "Fisher's Circular Test Reconsidered," Swiss Journal of Economics and Statistics (SJES), Swiss Society of Economics and Statistics (SSES), vol. 115(IV), pages 677-688, December.
    15. Caves, Douglas W & Christensen, Laurits R & Diewert, W Erwin, 1982. "Multilateral Comparisons of Output, Input, and Productivity Using Superlative Index Numbers," Economic Journal, Royal Economic Society, vol. 92(365), pages 73-86, March.
    16. 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.
    17. 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.
    18. Subodh Kumar & R. Robert Russell, 2002. "Technological Change, Technological Catch-up, and Capital Deepening: Relative Contributions to Growth and Convergence," American Economic Review, American Economic Association, vol. 92(3), pages 527-548, June.
    19. Sickles,Robin C. & Zelenyuk,Valentin, 2019. "Measurement of Productivity and Efficiency," Cambridge Books, Cambridge University Press, number 9781107036161.
    20. Richard H. Moorsteen, 1961. "On Measuring Productive Potential and Relative Efficiency," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 75(3), pages 451-467.
    21. Daniel J. Henderson & R. Robert Russell, 2005. "Human Capital And Convergence: A Production-Frontier Approach ," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 46(4), pages 1167-1205, November.
    22. Eichhorn, W, 1976. "Fisher's Tests Revisited," Econometrica, Econometric Society, vol. 44(2), pages 247-256, March.
    23. Chambers Robert G. & Fare Rolf, 1994. "Hicks' Neutrality and Trade Biased Growth: A Taxonomy," Journal of Economic Theory, Elsevier, vol. 64(2), pages 554-567, December.
    24. Balk, B.M. & Zofío, J.L., 2018. "The Many Decompositions of Total Factor Productivity Change," ERIM Report Series Research in Management ERS-2018-003-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    25. Diewert, W E, 1980. "Capital and the Theory of Productivity Measurement," American Economic Review, American Economic Association, vol. 70(2), pages 260-267, May.
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    More about this item

    Keywords

    Fisher; Laspeyres; Paasche; Malmquist; Productivity Indexes;
    All these keywords.

    JEL classification:

    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity
    • E22 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Investment; Capital; Intangible Capital; Capacity
    • E23 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Production
    • E24 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Employment; Unemployment; Wages; Intergenerational Income Distribution; Aggregate Human Capital; Aggregate Labor Productivity
    • O47 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - Empirical Studies of Economic Growth; Aggregate Productivity; Cross-Country Output Convergence

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