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Malmquist and Törnqvist Productivity Indexes: Returns to Scale and Technical Progress with Imperfect Competition

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  • Diewert, Erwin
  • Fox, Kevin J.

Abstract

Caves, Christensen and Diewert proposed a method for estimating a theoretical productivity index for a firm using Törnqvist input and output indexes, augmented by exogenous estimates of local returns to scale. However, in order to implement their method, they assumed that the firm maximized revenue in each period, conditional on the observed input vector in each period, taking output prices as fixed. This assumption is not warranted when there are increasing returns to scale. Thus in the present paper, it is assumed that the firm solves a monopolistic profit maximization problem when there are increasing returns to scale and the results of Caves, Christensen and Diewert are modified in accordance with this assumption.

Suggested Citation

  • Diewert, Erwin & Fox, Kevin J., 2010. "Malmquist and Törnqvist Productivity Indexes: Returns to Scale and Technical Progress with Imperfect Competition," Economics working papers erwin_diewert-2010-5, Vancouver School of Economics, revised 13 Jul 2010.
    • Handle: RePEc:ubc:bricol:erwin_diewert-2010-5
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    File URL: http://faculty.arts.ubc.ca/ediewert/dp1003.pdf
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    Citations

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    Cited by:

    1. W. Erwin Diewert, 2022. "Duality in Production," Springer Books, in: Subhash C. Ray & Robert G. Chambers & Subal C. Kumbhakar (ed.), Handbook of Production Economics, chapter 3, pages 57-168, Springer.
    2. Feng, Guohua & Serletis, Apostolos, 2010. "A primal Divisia technical change index based on the output distance function," Journal of Econometrics, Elsevier, vol. 159(2), pages 320-330, December.
    3. 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.
    4. Malin Song & Jun Tao & Shuhong Wang, 2015. "FDI, technology spillovers and green innovation in China: analysis based on Data Envelopment Analysis," Annals of Operations Research, Springer, vol. 228(1), pages 47-64, May.
    5. Burda, Michael C. & Severgnini, Battista, 2014. "Solow residuals without capital stocks," Journal of Development Economics, Elsevier, vol. 109(C), pages 154-171.
    6. Hideyuki Mizobuchi, 2014. "Returns to scale effect in labour productivity growth," Journal of Productivity Analysis, Springer, vol. 42(3), pages 293-304, December.
    7. Carlo Milana & Leopoldo Nascia & Alessandro Zeli, 2013. "Decomposing multifactor productivity in Italy from 1998 to 2004: evidence from large firms and SMEs using DEA," Journal of Productivity Analysis, Springer, vol. 40(1), pages 99-109, August.
    8. 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.
    9. Merino, Fernando, 2012. "Firms' internationalization and productivity growth," Research in Economics, Elsevier, vol. 66(4), pages 349-354.
    10. Sheng, Yu & Zhao, Shiji & Nossal, Katarina & Zhang, Dandan, 2015. "Productivity and farm size in Australian agriculture: reinvestigating the returns to scale," Australian Journal of Agricultural and Resource Economics, Australian Agricultural and Resource Economics Society, vol. 59(1), January.
    11. Sheng, Yu & Chancellor, Will, 2019. "Exploring the relationship between farm size and productivity: Evidence from the Australian grains industry," Food Policy, Elsevier, vol. 84(C), pages 196-204.
    12. W. Erwin Diewert & Takanobu Nakajima & Alice Nakamura & Emi Nakamura & Masao Nakamura, 2011. "Returns to scale: concept, estimation and analysis of Japan's turbulent 1964–88 economy," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 44(2), pages 451-485, May.
    13. Ang, Frederic & Kerstens, Pieter Jan, 2020. "A superlative indicator for the Luenberger-Hicks-Moorsteen productivity indicator: Theory and application," European Journal of Operational Research, Elsevier, vol. 285(3), pages 1161-1173.

    More about this item

    Keywords

    Productivity; index numbers; Malmquist indexes; Törnqvist indexes; returns to scale; non-competitive behavior; flexible functional forms.;
    All these keywords.

    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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