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Decomposing Bjurek Productivity Indexes into Explanatory Factors

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  • W. Erwin Diewert

    (University of British Columbia and School of Economics, Australian School of Business, the University of New South Wales)

  • Kevin J. Fox

    (School of Economics, Australian School of Business, the University of New South Wales)

Abstract

Caves, Christensen, Diewert introduced Malmquist output, input and productivity indexes into production theory in a systematic way. This paper revisits the debate on how to decompose Bjurek’s concept of a Malmquist productivity index into explanatory factors, with a focus on extracting technical progress, technical efficiency change, and returns to scale components. In order to define these components, a reference technology is required. The paper does not make any convexity assumptions on the reference technology but instead follows the example of Tulkens and his coauthors in assuming that the reference technology satisfies free disposability assumptions. The existence and properties of the underlying distance functions of the productivity decomposition are proven under relatively unrestrictive assumptions. The paper provides for the first time a theoretical justification for the geometric average form of the Bjurek productivity index.

Suggested Citation

  • 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.
    • Handle: RePEc:swe:wpaper:2014-33
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    File URL: http://research.economics.unsw.edu.au/RePEc/papers/2014-33.pdf
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    References listed on IDEAS

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    1. Hideyuki Mizobuchi, 2015. "Multiple Directions for Measuring Biased Technical Change," CEPA Working Papers Series WP092015, School of Economics, University of Queensland, Australia.

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    More about this item

    Keywords

    Productivity indexes; Malmquist indexes; technical efficiency; technical progress; returns to scale; Data Envelopment Analysis; Free Disposal Hulls; nonparametric approaches to production theory; distance functions;
    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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