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A statistical equilibrium model of competitive firms

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  • Alfarano, Simone
  • Milaković, Mishael
  • Irle, Albrecht
  • Kauschke, Jonas

Abstract

We find that the empirical density of firm profit rates, measured as returns on assets, is markedly non-Gaussian and reasonably well described by an exponential power (or Subbotin) distribution. We start from a statistical equilibrium model that leads to a stationary Subbotin density in the presence of complex interactions among competitive heterogeneous firms. To investigate the dynamics of firm profitability, we construct a diffusion process that has the Subbotin distribution as its stationary probability density. This leads to a phenomenologically inspired interpretation of variations in the shape parameter of the Subbotin distribution, which essentially measures the competitive pressure in and across industries. Our findings have profound implications both for the previous literature on the ‘persistence of profits’ as well as for understanding competition as a dynamic process. Our main formal finding is that firms' idiosyncratic efforts and the tendency for competition to equalize profit rates are two sides of the same coin, and that a ratio of these two effects ultimately determines the dispersion of the equilibrium distribution.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Dynamics and Control.

Volume (Year): 36 (2012)
Issue (Month): 1 ()
Pages: 136-149

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Handle: RePEc:eee:dyncon:v:36:y:2012:i:1:p:136-149

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Web page: http://www.elsevier.com/locate/jedc

Related research

Keywords: Statistical equilibrium; Diffusion process; Stochastic differential equation; Maximum entropy principle; Profit rate; Return on assets; Subbotin distribution; Exponential power distribution; Laplace distribution;

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References

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Citations

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Cited by:
  1. Erlingsson, Einar Jón & Alfarano, Simone & Raberto, Marco & Stefánsson, Hlynur, 2012. "On the distributional properties of size, pro fit and growth of Icelandic firms," MPRA Paper 35857, University Library of Munich, Germany.
  2. Cohen, Morrel H. & Eliazar, Iddo I., 2013. "Econophysical visualization of Adam Smith’s invisible hand," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(4), pages 813-823.
  3. Philipp Mundt & Mishael Milakovic & Simone Alfarano, 2014. "Gibrat's law redux: Think profitability instead of growth," Working Papers 2014/02, Economics Department, Universitat Jaume I, Castellón (Spain).
  4. Y. Malevergne & A. Saichev & D. Sornette, 2010. "Zipf's law and maximum sustainable growth," Papers 1012.0199, arXiv.org.
  5. Alfarano, Simone & Förster, Niels & Milaković, Mishael & Mundt, Philipp, 2013. "The real versus the financial economy: A global tale of stability versus volatility," Economics Discussion Papers 2013-8, Kiel Institute for the World Economy.
  6. F. Wagner & M. Milaković & S. Alfarano, 2010. "What distinguishes individual stocks from the index?," The European Physical Journal B - Condensed Matter and Complex Systems, Springer, vol. 73(1), pages 23-28, January.
  7. Eliazar, Iddo I. & Cohen, Morrel H., 2013. "On the physical interpretation of statistical data from black-box systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(13), pages 2924-2939.
  8. Lunardi, José T. & Miccichè, Salvatore & Lillo, Fabrizio & Mantegna, Rosario N. & Gallegati, Mauro, 2014. "Do firms share the same functional form of their growth rate distribution? A statistical test," Journal of Economic Dynamics and Control, Elsevier, vol. 39(C), pages 140-164.
  9. Toda, Alexis Akira, 2012. "The double power law in income distribution: Explanations and evidence," Journal of Economic Behavior & Organization, Elsevier, vol. 84(1), pages 364-381.
  10. Metzig, Cornelia & Gordon, Mirta B., 2014. "A model for scaling in firms’ size and growth rate distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 398(C), pages 264-279.

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