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A paradigm shift from production function to production copula: statistical description of production activity of firms

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  • Hiroshi Iyetomi
  • Hideaki Aoyama
  • Yoshi Fujiwara
  • Yuichi Ikeda
  • Wataru Souma

Abstract

The heterogeneity of economic agents is emphasized in a new trend in macroeconomics. Accordingly, the new emerging discipline requires one to replace the production function, one of the key ideas in conventional economics, by an alternative that can take explicit account of the distribution of firms' production activities. In this paper we propose a new idea referred to as a production copula; a copula is an analytic means for modeling the dependence among variables. Such a production copula predicts the value added 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 the empirical construction of a production copula using financial data of listed Japanese firms. Analysis of the data shows that there are significant correlations among 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 latter was found to be the best.

Suggested Citation

  • Hiroshi Iyetomi & Hideaki Aoyama & Yoshi Fujiwara & Yuichi Ikeda & Wataru Souma, 2012. "A paradigm shift from production function to production copula: statistical description of production activity of firms," Quantitative Finance, Taylor & Francis Journals, vol. 12(9), pages 1453-1466, December.
    • Handle: RePEc:taf:quantf:v:12:y:2012:i:9:p:1453-1466
    DOI: 10.1080/14697688.2010.548823
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    Cited by:

    1. Constantino, Michel & Candido, Osvaldo & Tabak, Benjamin M. & da Costa, Reginaldo Brito, 2017. "Modeling stochastic frontier based on vine copulas," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 595-609.
    2. Hardik Rajpal & Omar A Guerrero, 2023. "Synergistic Small Worlds that Drive Technological Sophistication," Papers 2301.04579, arXiv.org, revised Jul 2023.
    3. Atushi Ishikawa & Shouji Fujimoto & Takayuki Mizuno & Tsutomu Watanabe, 2016. "Long-term firm growth properties derived from short-term laws of sales and number of employees in Japan and France," Evolutionary and Institutional Economics Review, Springer, vol. 13(2), pages 409-422, December.

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