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Multilateral productivity comparisons and homotheticity

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  • Antonio Peyrache

Abstract

In this paper it is shown that a well known procedure (GEKS) of transitivizing a bilateral system of productivity comparisons is implicitly a way of imposing a homothetic structure onto the data. The main implication of this result is that deviations between the bilateral and the multilateral (GEKS) indexes can be interpreted as a measure of local deviation from the homothetic assumption. This establishes an additional link between homotheticity and transitivity. Copyright Springer Science+Business Media, LLC 2013

Suggested Citation

  • Antonio Peyrache, 2013. "Multilateral productivity comparisons and homotheticity," Journal of Productivity Analysis, Springer, vol. 40(1), pages 57-65, August.
    • Handle: RePEc:kap:jproda:v:40:y:2013:i:1:p:57-65
    DOI: 10.1007/s11123-012-0298-7
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    References listed on IDEAS

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    1. Alexandra Daskovska & Léopold Simar & Sébastien Bellegem, 2010. "Forecasting the Malmquist productivity index," Journal of Productivity Analysis, Springer, vol. 33(2), pages 97-107, April.
    2. Balk,Bert M., 2012. "Price and Quantity Index Numbers," Cambridge Books, Cambridge University Press, number 9781107404960, September.
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    4. Primont, Daniel & Primont, Diane, 1994. "Homothetic non-parametric production models," Economics Letters, Elsevier, vol. 45(2), pages 191-195, June.
    5. van Veelen, Matthijs, 2009. "The apples and oranges theorem for price indices," Economics Letters, Elsevier, vol. 103(1), pages 12-14, April.
    6. 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.
    7. D. S.P. Rao (ed.), 2009. "Purchasing Power Parities of Currencies," Books, Edward Elgar Publishing, number 3725.
    8. Matthijs van Veelen, 2002. "An Impossibility Theorem Concerning Multilateral International Comparison of Volumes," Econometrica, Econometric Society, vol. 70(1), pages 369-375, January.
    9. Kevin J. Fox, 2003. "An Economic Justification for the EKS Multilateral Index," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 49(3), pages 407-413, September.
    10. Fare, Rolf & Grosskopf, Shawna & Roos, Pontus, 1996. "On two definitions of productivity," Economics Letters, Elsevier, vol. 53(3), pages 269-274, December.
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    Cited by:

    1. Rolf Färe & Valentin Zelenyuk, 2021. "On aggregation of multi-factor productivity indexes," Journal of Productivity Analysis, Springer, vol. 55(2), pages 107-133, April.
    2. Peyrache, Antonio, 2024. "A homothetic data generated technology," European Journal of Operational Research, Elsevier, vol. 316(1), pages 255-267.
    3. Valentin Zelenyuk, 2014. "Scale efficiency and homotheticity: equivalence of primal and dual measures," Journal of Productivity Analysis, Springer, vol. 42(1), pages 15-24, August.
    4. Hideyuki Mizobuchi, 2017. "Productivity indexes under Hicks neutral technical change," Journal of Productivity Analysis, Springer, vol. 48(1), pages 63-68, August.
    5. 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.
    6. Antonio Peyrache, 2024. "Homothetic Data Generated Production Metatechnologies," CEPA Working Papers Series WP022024, School of Economics, University of Queensland, Australia.
    7. Rolf Färe & Valentin Zelenyuk, 2019. "On the Aggregation of the Paasche and Laspeyres Malmquist Indexes," CEPA Working Papers Series WP122019, School of Economics, University of Queensland, Australia.

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    More about this item

    Keywords

    Multilateral comparisons; Productivity; EKS; Homotheticity; Transitivity; Hicks neutrality; D24;
    All these keywords.

    JEL classification:

    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity

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