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A Statistical Equilibrium Model of Competitive Firms

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

Abstract

We argue that the complex interactions of competitive heterogeneous firms lead to a statistical equilibrium distribution of firms? profit rates, which turns out to be an exponential power (or Subbotin) distribution. Moreover, we construct a diffusion process that has the Subbotin distribution as its stationary probability density, leading to a phenomenologically inspired interpretation of variations in the shape parameter of the statistical equilibrium distribution. Our main finding is that firms? idiosyncratic efforts and the tendency for competition to equalize profit rates are two sides of the same coin.

Suggested Citation

  • Irle, Albrecht & Milaković, Mishael & Alfarano, Simone & Kauschke, Jonas, 2008. "A Statistical Equilibrium Model of Competitive Firms," Economics Working Papers 2008-10, Christian-Albrechts-University of Kiel, Department of Economics.
  • Handle: RePEc:zbw:cauewp:7362
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    Cited by:

    1. Scharfenaker, Ellis & dos Santos, Paulo L., 2015. "The distribution and regulation of Tobin’s q," Economics Letters, Elsevier, vol. 137(C), pages 191-194.
    2. Marko Petrovic & Andrea Teglio & Simone Alfarano, 2016. "The role of bank credit allocation: Evidence from the Spanish economy," Working Papers 2016/17, Economics Department, Universitat Jaume I, Castellón (Spain).
    3. Ellis Scharfenaker, 2015. "A Quantal Response Model of Firm Competition," Working Papers 1507, New School for Social Research, Department of Economics.
    4. Giacomo Livan & Simone Alfarano & Mishael Milaković & Enrico Scalas, 2015. "A spectral perspective on excess volatility," Applied Economics Letters, Taylor & Francis Journals, vol. 22(9), pages 745-750, June.
    5. Einar Erlingsson & Simone Alfarano & Marco Raberto & Hlynur Stefánsson, 2013. "On the distributional properties of size, profit and growth of Icelandic firms," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 8(1), pages 57-74, April.
    6. Philipp Mundt & Simone Alfarano & Mishael Milakovic, 2016. "Gibrat’s Law Redux: think profitability instead of growth," Industrial and Corporate Change, Oxford University Press, vol. 25(4), pages 549-571.
    7. repec:bla:metroe:v:68:y:2017:i:3:p:465-499 is not listed on IDEAS
    8. Halvarsson, Daniel, 2013. "Identifying High-Growth Firms," Ratio Working Papers 215, The Ratio Institute.
    9. Gregor Semieniuk & Ellis Scharfenaker, 2014. "A Bayesian Latent Variable Mixture Model for Filtering Firm Profit Rate," SCEPA working paper series. SCEPA's main areas of research are macroeconomic policy, inequality and poverty, and globalization. 2014-1, Schwartz Center for Economic Policy Analysis (SCEPA), The New School.
    10. 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.
    11. Eliazar, Iddo & Cohen, Morrel H., 2014. "On social inequality: Analyzing the rich–poor disparity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 401(C), pages 148-158.
    12. Reiner Franke, 2015. "How Fat-Tailed is US Output Growth?," Metroeconomica, Wiley Blackwell, vol. 66(2), pages 213-242, May.
    13. Eliazar, Iddo, 2014. "From entropy-maximization to equality-maximization: Gauss, Laplace, Pareto, and Subbotin," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 415(C), pages 479-492.
    14. 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.
    15. Williams, Michael A. & Baek, Grace & Park, Leslie Y. & Zhao, Wei, 2016. "Global evidence on the distribution of economic profit rates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 458(C), pages 356-363.
    16. 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.
    17. Mundt, Philipp & Förster, Niels & Alfarano, Simone & Milakovi?, Mishael, 2014. "The real versus the financial economy: A global tale of stability versus volatility," Economics - The Open-Access, Open-Assessment E-Journal, Kiel Institute for the World Economy (IfW), vol. 8, pages 1-26.
    18. Malevergne, Y. & Saichev, A. & Sornette, D., 2013. "Zipf's law and maximum sustainable growth," Journal of Economic Dynamics and Control, Elsevier, vol. 37(6), pages 1195-1212.
    19. 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.
    20. Kleiber, Christian, 2012. "The Generalized Lognormal Distribution and the Stieltjes Moment Problem," Working papers 2012/15, Faculty of Business and Economics - University of Basel.
    21. 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.
    22. Ellis Scharfenaker & Duncan Foley, 2017. "Maximum Entropy Estimation of Statistical Equilibrium in Economic Quantal Response Models," Working Papers 1710, New School for Social Research, Department of Economics, revised May 2017.
    23. Ellis Scharfenaker & Gregor Semieniuk, 2015. "A Statistical Equilibrium Approach to the Distribution of Profit Rates," SCEPA working paper series. SCEPA's main areas of research are macroeconomic policy, inequality and poverty, and globalization. 2015-05, Schwartz Center for Economic Policy Analysis (SCEPA), The New School.
    24. 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;EDP Sciences, vol. 73(1), pages 23-28, January.

    More about this item

    Keywords

    Statistical equilibrium; maximum entropy principle; diffusion process; stochastic differential equation; competition; profit rate;

    JEL classification:

    • D21 - Microeconomics - - Production and Organizations - - - Firm Behavior: Theory
    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
    • E10 - Macroeconomics and Monetary Economics - - General Aggregative Models - - - General
    • L10 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - General

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