IDEAS home Printed from https://ideas.repec.org/p/msh/ebswps/2010-7.html
   My bibliography  Save this paper

A Primal Divisia Technical Change Index Based on the Output Distance Function

Author

Listed:
  • Guohua Feng
  • Apostolos Serletis

Abstract

We derive a primal Divisia technical change index based on the output distance function and further show the validity of this index from both economic and axiomatic points of view. In particular, we derive the primal Divisia technical change index by total differentiation of the output distance function with respect to a time trend. We then show that this index is dual to the Jorgenson and Griliches (1967) dual Divisia total factor productivity growth (TFPG) index when both the output and input markets are competitive; dual to the Diewert and Fox (2008) markup-adjusted revenue-share based dual Divisia technical change index when market power is limited to output markets; dual to the Denny et al. (1981) and Fuss (1994) cost-elasticity-share based dual Divisia TFPG index when market power is limited to output markets and constant returns to scale is present; and also dual to a markup-and-markdown adjusted Divisia technical change index when market power is present in both output and input markets. Finally, we show that the primal Divisia technical change index satisfies the properties of identity, commensurability, monotonicity, and time reversal. It also satisfies the property of proportionality in the presence of path independence, which in turn requires separability between inputs and outputs and homogeneity of subaggregator functions.

Suggested Citation

  • Guohua Feng & Apostolos Serletis, 2010. "A Primal Divisia Technical Change Index Based on the Output Distance Function," Monash Econometrics and Business Statistics Working Papers 7/10, Monash University, Department of Econometrics and Business Statistics.
    • Handle: RePEc:msh:ebswps:2010-7
    as

    Download full text from publisher

    File URL: http://www.buseco.monash.edu.au/ebs/pubs/wpapers/2010/wp7-10.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Melvyn A. Fuss, 1994. "Productivity Growth in Canadian Telecommunications," Canadian Journal of Economics, Canadian Economics Association, vol. 27(2), pages 371-392, May.
    2. Small, Kenneth A., 1999. "Economies of scale and self-financing rules with non-competitive factor markets," Journal of Public Economics, Elsevier, vol. 74(3), pages 431-450, December.
    3. Diewert, W. Erwin & Fox, Kevin J., 2008. "On the estimation of returns to scale, technical progress and monopolistic markups," Journal of Econometrics, Elsevier, vol. 145(1-2), pages 174-193, July.
    4. D. W. Jorgenson & Z. Griliches, 1967. "The Explanation of Productivity Change," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 34(3), pages 249-283.
    5. Balk,Bert M., 2012. "Price and Quantity Index Numbers," Cambridge Books, Cambridge University Press, number 9781107404960, January.
    6. William A. Barnett, 2000. "Economic Monetary Aggregates: An Application of Index Number and Aggregation Theory," Contributions to Economic Analysis, in: The Theory of Monetary Aggregation, pages 11-48, Emerald Group Publishing Limited.
    7. C. Lovell, 2003. "The Decomposition of Malmquist Productivity Indexes," Journal of Productivity Analysis, Springer, vol. 20(3), pages 437-458, November.
    8. 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.
    9. Feng, Guohua & Serletis, Apostolos, 2008. "Productivity trends in U.S. manufacturing: Evidence from the NQ and AIM cost functions," Journal of Econometrics, Elsevier, vol. 142(1), pages 281-311, January.
    10. Chambers,Robert G., 1988. "Applied Production Analysis," Cambridge Books, Cambridge University Press, number 9780521314275.
    11. Caves, Douglas W & Christensen, Laurits R, 1980. "The Relative Efficiency of Public and Private Firms in a Competitive Environment: The Case of Canadian Railroads," Journal of Political Economy, University of Chicago Press, vol. 88(5), pages 958-976, October.
    12. J. Peter Neary, 2004. "Rationalizing the Penn World Table: True Multilateral Indices for International Comparisons of Real Income," American Economic Review, American Economic Association, vol. 94(5), pages 1411-1428, December.
    13. Luis Orea, 2002. "Parametric Decomposition of a Generalized Malmquist Productivity Index," Journal of Productivity Analysis, Springer, vol. 18(1), pages 5-22, July.
    14. W. Diewert & Alice Nakamura, 2003. "Index Number Concepts, Measures and Decompositions of Productivity Growth," Journal of Productivity Analysis, Springer, vol. 19(2), pages 127-159, April.
    15. Charles R. Hulten, 2009. "Growth Accounting," NBER Working Papers 15341, National Bureau of Economic Research, Inc.
    16. Hulten, Charles R, 1973. "Divisia Index Numbers," Econometrica, Econometric Society, vol. 41(6), pages 1017-1025, November.
    17. Bert M. Balk, 2005. "Divisia price and quantity indices: 80 years after," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 59(2), pages 119-158, May.
    18. Basu, Susanto & Fernald, John G, 1997. "Returns to Scale in U.S. Production: Estimates and Implications," Journal of Political Economy, University of Chicago Press, vol. 105(2), pages 249-283, April.
    19. Robert Chambers & Rolf Färe, 1993. "Input-output separability in production models and its structural consequences," Journal of Economics, Springer, vol. 57(2), pages 197-202, June.
    20. Star, Spencer & Hall, Robert E, 1976. "An Approximate Divisia Index of Total Factor Productivity," Econometrica, Econometric Society, vol. 44(2), pages 257-263, March.
    21. W. Diewert & Kevin Fox, 2010. "Malmquist and Törnqvist productivity indexes: returns to scale and technical progress with imperfect competition," Journal of Economics, Springer, vol. 101(1), pages 73-95, September.
    22. 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.
    23. Balk, Bert M., 2009. "On The Relation Between Gross Output– And Value Added–Based Productivity Measures: The Importance Of The Domar Factor," Macroeconomic Dynamics, Cambridge University Press, vol. 13(S2), pages 241-267, September.
    24. Diewert, W. E., 1976. "Exact and superlative index numbers," Journal of Econometrics, Elsevier, vol. 4(2), pages 115-145, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Holtkamp, A.M. & Brummer, B., 2018. "Environmental efficiency of smallholder rubber production," 2018 Conference, July 28-August 2, 2018, Vancouver, British Columbia 277518, International Association of Agricultural Economists.
    2. Mamatzakis, Emmanuel & matousek, roman & vu, anh, 2019. "The interplay between problem loans and Japanese bank productivity," MPRA Paper 92960, University Library of Munich, Germany.
    3. Feng, Guohua & Zhang, Xiaohui, 2012. "Productivity and efficiency at large and community banks in the US: A Bayesian true random effects stochastic distance frontier analysis," Journal of Banking & Finance, Elsevier, vol. 36(7), pages 1883-1895.
    4. Guohua Feng & Bin Peng & Xiaohui Zhang, 2017. "Productivity and efficiency at bank holding companies in the U.S.: a time-varying heterogeneity approach," Journal of Productivity Analysis, Springer, vol. 48(2), pages 179-192, December.
    5. Feng, Guohua & Serletis, Apostolos, 2014. "Undesirable outputs and a primal Divisia productivity index based on the directional output distance function," Journal of Econometrics, Elsevier, vol. 183(1), pages 135-146.
    6. James J. Heckman & Apostolos Serletis, "undated". "Introduction to Internally Consistent Modeling, Aggregation, Inference, and Policy," Working Papers 2014-73, Department of Economics, University of Calgary, revised 29 Sep 2014.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Burda, Michael C. & Severgnini, Battista, 2014. "Solow residuals without capital stocks," Journal of Development Economics, Elsevier, vol. 109(C), pages 154-171.
    3. Feng, Guohua & Serletis, Apostolos, 2014. "Undesirable outputs and a primal Divisia productivity index based on the directional output distance function," Journal of Econometrics, Elsevier, vol. 183(1), pages 135-146.
    4. Barnett, William A. & Erwin Diewert, W. & Zellner, Arnold, 2011. "Introduction to measurement with theory," Journal of Econometrics, Elsevier, vol. 161(1), pages 1-5, March.
    5. Athanasoglou, Panayiotis P. & Georgiou, Evangelia A. & Staikouras, Christos C., 2009. "Assessing output and productivity growth in the banking industry," The Quarterly Review of Economics and Finance, Elsevier, vol. 49(4), pages 1317-1340, November.
    6. 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.
    7. 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.
    8. Joseph Plasmans, 2011. "Productivity and Competition from a Global Point of View," Chapters, in: Jonathan Michie (ed.), The Handbook of Globalisation, Second Edition, chapter 14, Edward Elgar Publishing.
    9. 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.
    10. Feng, Guohua & Serletis, Apostolos, 2008. "Productivity trends in U.S. manufacturing: Evidence from the NQ and AIM cost functions," Journal of Econometrics, Elsevier, vol. 142(1), pages 281-311, January.
    11. 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.
    12. W. Diewert & Kevin Fox, 2010. "Malmquist and Törnqvist productivity indexes: returns to scale and technical progress with imperfect competition," Journal of Economics, Springer, vol. 101(1), pages 73-95, September.
    13. 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.
    14. Diewert, W. Erwin, 2017. "Productivity Measurement in the Public Sector: Theory and Practice," Microeconomics.ca working papers erwin_diewert-2017-1, Vancouver School of Economics, revised 02 Feb 2017.
    15. Hideyuki Mizobuchi, 2014. "Returns to scale effect in labour productivity growth," Journal of Productivity Analysis, Springer, vol. 42(3), pages 293-304, December.
    16. Hideyuki Mizobuchi, 2022. "Measuring the shift in the short-run production frontier," Evolutionary and Institutional Economics Review, Springer, vol. 19(1), pages 271-300, April.
    17. Diewert, W. Erwin & Fox, Kevin J., 2016. "Kevin J. Fox Interview of W. Erwin Diewert," Microeconomics.ca working papers erwin_diewert-2016-6, Vancouver School of Economics, revised 02 Jun 2016.
    18. Bos, J.W.B. & van Santen, P.C. & Schilp, P., 2013. "The importance of reallocation for productivity growth: Evidence from European and US banking," Research Memorandum 056, Maastricht University, Graduate School of Business and Economics (GSBE).
    19. Hideyuki Mizobuchi, 2017. "A superlative index number formula for the Hicks-Moorsteen productivity index," Journal of Productivity Analysis, Springer, vol. 48(2), pages 167-178, December.
    20. W. Erwin Diewert & Kevin J. Fox, 2014. "Decomposing Bjurek Productivity Indexes into Explanatory Factors," Discussion Papers 2014-33, School of Economics, The University of New South Wales.

    More about this item

    Keywords

    Output distance function; Divisia technical change index; Imperfect competition; Axiomatic properties; Path independence.;
    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
    • O47 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - Empirical Studies of Economic Growth; Aggregate Productivity; Cross-Country Output Convergence

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:msh:ebswps:2010-7. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Professor Xibin Zhang (email available below). General contact details of provider: https://edirc.repec.org/data/dxmonau.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.