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

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  • 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
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    References listed on IDEAS

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    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.

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    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

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