IDEAS home Printed from https://ideas.repec.org/a/eee/dyncon/v36y2012i1p136-149.html
   My bibliography  Save this article

A statistical equilibrium model of competitive firms

Author

Listed:
  • 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.

Suggested Citation

  • Alfarano, Simone & Milaković, Mishael & Irle, Albrecht & Kauschke, Jonas, 2012. "A statistical equilibrium model of competitive firms," Journal of Economic Dynamics and Control, Elsevier, vol. 36(1), pages 136-149.
  • Handle: RePEc:eee:dyncon:v:36:y:2012:i:1:p:136-149
    DOI: 10.1016/j.jedc.2011.07.002
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0165188911001424
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Giorgio Fagiolo & Mauro Napoletano & Andrea Roventini, 2008. "Are output growth-rate distributions fat-tailed? some evidence from OECD countries," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 23(5), pages 639-669.
    2. John Cable & Dennis Mueller, 2008. "Testing for Persistence of Profits' Differences Across Firms," International Journal of the Economics of Business, Taylor & Francis Journals, vol. 15(2), pages 201-228.
    3. Giorgio Fagiolo & Lucia Alessi & Matteo Barigozzi & Marco Capasso, 2010. "On the distributional properties of household consumption expenditures: the case of Italy," Empirical Economics, Springer, vol. 38(3), pages 717-741, June.
    4. Glen, Jack & Lee, Kevin & Singh, Ajit, 2001. "Persistence of profitability and competition in emerging markets," Economics Letters, Elsevier, vol. 72(2), pages 247-253, August.
    5. Adelina Gschwandtner, 2005. "Profit persistence in the 'very' long run: evidence from survivors and exiters," Applied Economics, Taylor & Francis Journals, vol. 37(7), pages 793-806.
    6. Maruyama, Nobuhiro & Odagiri, Hiroyuki, 2002. "Does the 'persistence of profits' persist?: a study of company profits in Japan, 1964-97," International Journal of Industrial Organization, Elsevier, vol. 20(10), pages 1513-1533, December.
    7. Geroski, Paul A & Jacquemin, Alexis, 1988. "The Persistence of Profits: A European Comparison," Economic Journal, Royal Economic Society, vol. 98(391), pages 375-389, June.
    8. Foley Duncan K., 1994. "A Statistical Equilibrium Theory of Markets," Journal of Economic Theory, Elsevier, vol. 62(2), pages 321-345, April.
    9. Giulio Bottazzi & Elena Cefis & Giovanni Dosi, 2002. "Corporate growth and industrial structures: some evidence from the Italian manufacturing industry," Industrial and Corporate Change, Oxford University Press, vol. 11(4), pages 705-723, August.
    10. Giulio Bottazzi & Angelo Secchi & Federico Tamagni, 2008. "Productivity, profitability and financial performance," Industrial and Corporate Change, Oxford University Press, vol. 17(4), pages 711-751, August.
    11. Castaldi, Carolina & Milakovic, Mishael, 2007. "Turnover activity in wealth portfolios," Journal of Economic Behavior & Organization, Elsevier, vol. 63(3), pages 537-552, July.
    12. Young, Allyn A., 1928. "Increasing Returns and Economic Progress," History of Economic Thought Articles, McMaster University Archive for the History of Economic Thought, vol. 38, pages 527-542.
    13. S. V. Buldyrev & F. Pammolli & M. Riccaboni & K. Yamasaki & D.-F. Fu & K. Matia & H. E. Stanley, 2007. "A generalized preferential attachment model for business firms growth rates," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 57(2), pages 131-138, May.
    14. Xavier Gabaix, 2011. "The Granular Origins of Aggregate Fluctuations," Econometrica, Econometric Society, vol. 79(3), pages 733-772, May.
    15. Alfarano, Simone & Milakovic, Mishael, 2008. "Does classical competition explain the statistical features of firm growth?," Economics Letters, Elsevier, vol. 101(3), pages 272-274, December.
    16. Mueller, Dennis C, 1977. "The Persistence of Profits above the Norm," Economica, London School of Economics and Political Science, vol. 44(176), pages 369-380, November.
    17. Giulio Bottazzi & Angelo Secchi, 2003. "Common Properties and Sectoral Specificities in the Dynamics of U.S. Manufacturing Companies," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 23(3_4), pages 217-232, December.
    18. Stutzer, Michael, 1996. " A Simple Nonparametric Approach to Derivative Security Valuation," Journal of Finance, American Finance Association, vol. 51(5), pages 1633-1652, December.
    19. Giulio Bottazzi & Angelo Secchi, 2006. "Explaining the distribution of firm growth rates," RAND Journal of Economics, RAND Corporation, vol. 37(2), pages 235-256, June.
    20. George J. Stigler, 1957. "Perfect Competition, Historically Contemplated," Journal of Political Economy, University of Chicago Press, vol. 65, pages 1-1.
    21. Wagner, Friedrich & Milaković, Mishael & Alfarano, Simone, 2010. "Firm profitability and the network of organizational capabilities," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(21), pages 4769-4775.
    22. Vickers, John, 1995. "Concepts of Competition," Oxford Economic Papers, Oxford University Press, vol. 47(1), pages 1-23, January.
    23. Jack Glen & Kevin Lee & Ajit Singh, 2003. "Corporate profitability and the dynamics of competition in emerging markets: a time series analysis," Economic Journal, Royal Economic Society, vol. 113(491), pages 465-484, November.
    24. G. Bottazzi & E. Cefis & G. Dosi & A. Secchi, 2007. "Invariances and Diversities in the Patterns of Industrial Evolution: Some Evidence from Italian Manufacturing Industries," Small Business Economics, Springer, vol. 29(1), pages 137-159, June.
    25. Goddard, J. A. & Wilson, J. O. S., 1999. "The persistence of profit: a new empirical interpretation," International Journal of Industrial Organization, Elsevier, vol. 17(5), pages 663-687, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


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

    JEL classification:

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

    Statistics

    Access and download statistics

    Corrections

    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:eee:dyncon:v:36:y:2012:i:1:p:136-149. 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: (Dana Niculescu). General contact details of provider: http://www.elsevier.com/locate/jedc .

    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.