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A Paradigm Shift from Production Function to Production Copula: Statistical Description of Production Activity of Firms

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  • H. Iyetomi
  • H. Aoyama
  • Y. Fujiwara
  • Y. Ikeda
  • W. Souma

Abstract

Heterogeneity of economic agents is emphasized in a new trend of macroeconomics. Accordingly the new emerging discipline requires one to replace the production function, one of key ideas in the conventional economics, by an alternative which can take an explicit account of distribution of firms' production activities. In this paper we propose a new idea referred to as production copula; a copula is an analytic means for modeling dependence among variables. Such a production copula predicts value added yielded by firms with given capital and labor in a probabilistic way. It is thereby in sharp contrast to the production function where the output of firms is completely deterministic. We demonstrate empirical construction of a production copula using financial data of listed firms in Japan. Analysis of the data shows that there are significant correlations among their capital, labor and value added and confirms that the values added are too widely scattered to be represented by a production function. We employ four models for the production copula, that is, trivariate versions of Frank, Gumbel and survival Clayton and non-exchangeable trivariate Gumbel; the last one works best.

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  • H. Iyetomi & H. Aoyama & Y. Fujiwara & Y. Ikeda & W. Souma, 2009. "A Paradigm Shift from Production Function to Production Copula: Statistical Description of Production Activity of Firms," Papers 0902.1576, arXiv.org, revised Nov 2010.
    • Handle: RePEc:arx:papers:0902.1576
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    References listed on IDEAS

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    1. Masanao Aoki, "undated". "Reconstructing Macroeconomics: A Perspective from Statistical Physics and Combinatorial Stochastic Processes," UCLA Economics Online Papers 390, UCLA Department of Economics.
    2. Aoki,Masanao & Yoshikawa,Hiroshi, 2011. "Reconstructing Macroeconomics," Cambridge Books, Cambridge University Press, number 9781107634206, October.
    3. Souma, Wataru & Ikeda, Yuichi & Iyetomi, Hiroshi & Fujiwara, Yoshi, 2009. "Distribution of Labour Productivity in Japan over the Period 1996--2006," Economics Discussion Papers 2009-2, Kiel Institute for the World Economy (IfW Kiel).
    4. Fujiwara, Yoshi & Iyetomi, Hiroshi & Ikeda, Yuichi & Souma, Wataru, 2009. "Distribution of Labour Productivity in Japan over the Period 1996-2006," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 3, pages 1-14.
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