IDEAS home Printed from
   My bibliography  Save this paper

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


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


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.

Suggested Citation

  • 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,, revised Nov 2010.
  • Handle: RePEc:arx:papers:0902.1576

    Download full text from publisher

    File URL:
    File Function: Latest version
    Download Restriction: no

    References listed on IDEAS

    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. repec:sae:ecolab:v:16:y:2006:i:2:p:1-2 is not listed on IDEAS
    3. Aoki,Masanao & Yoshikawa,Hiroshi, 2007. "Reconstructing Macroeconomics," Cambridge Books, Cambridge University Press, number 9780521831062.
    4. Nikolay Nenovsky & S. Statev, 2006. "Introduction," Post-Print halshs-00260898, HAL.
    Full references (including those not matched with items on IDEAS)

    More about this item


    Access and download statistics


    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:arx:papers:0902.1576. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (arXiv administrators). General contact details of provider: .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.