IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this paper or follow this series

Colloquium: Statistical mechanics of money, wealth, and income

  • Victor M. Yakovenko
  • J. Barkley Rosser

This Colloquium reviews statistical models for money, wealth, and income distributions developed in the econophysics literature since the late 1990s. By analogy with the Boltzmann-Gibbs distribution of energy in physics, it is shown that the probability distribution of money is exponential for certain classes of models with interacting economic agents. Alternative scenarios are also reviewed. Data analysis of the empirical distributions of wealth and income reveals a two-class distribution. The majority of the population belongs to the lower class, characterized by the exponential ("thermal") distribution, whereas a small fraction of the population in the upper class is characterized by the power-law ("superthermal") distribution. The lower part is very stable, stationary in time, whereas the upper part is highly dynamical and out of equilibrium.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL: http://arxiv.org/pdf/0905.1518
File Function: Latest version
Download Restriction: no

Paper provided by arXiv.org in its series Papers with number 0905.1518.

as
in new window

Length:
Date of creation: May 2009
Date of revision: Dec 2009
Publication status: Published in Reviews of Modern Physics 81, 1703 (2009)
Handle: RePEc:arx:papers:0905.1518
Contact details of provider: Web page: http://arxiv.org/

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

as in new window
  1. Arnab Chatterjee & Bikas K. Chakrabarti, 2007. "Kinetic Exchange Models for Income and Wealth Distributions," Papers 0709.1543, arXiv.org, revised Nov 2007.
  2. Silva, A. Christian & Prange, Richard E. & Yakovenko, Victor M., 2004. "Exponential distribution of financial returns at mesoscopic time lags: a new stylized fact," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 344(1), pages 227-235.
  3. Marco Raberto & Silvano Cincott & Sergio M. Focardi & Michele Marchesi, 2002. "Traders’ long-run wealth in an artificial financial market," Computing in Economics and Finance 2002 301, Society for Computational Economics.
  4. Dieter Braun, 2006. "Nonequilibrium Thermodynamics of Wealth Condensation," Papers physics/0601191, arXiv.org.
  5. Wright, Ian, 2008. "Implicit Microfoundations for Macroeconomics," Economics Discussion Papers 2008-41, Kiel Institute for the World Economy.
  6. Thomas Piketty & Emmanuel Saez, 2003. "Income Inequality In The United States, 1913-1998," The Quarterly Journal of Economics, MIT Press, vol. 118(1), pages 1-39, February.
  7. E. Scalas & U. Garibaldi & S. Donadio, 2007. "Statistical equilibrium in simple exchange games I," The European Physical Journal B - Condensed Matter and Complex Systems, Springer, vol. 60(2), pages 271-272, November.
  8. Thomas Lux & Didier Sornette, 1999. "On Rational Bubbles and Fat Tails," Discussion Paper Serie B 458, University of Bonn, Germany.
  9. Arnab Chatterjee & Bikas K. Chakrabarti, 2006. "Kinetic market models with single commodity having price fluctuations," Papers physics/0609069, arXiv.org, revised Dec 2006.
  10. Silver, Jonathan & Slud, Eric & Takamoto, Keiji, 2002. "Statistical Equilibrium Wealth Distributions in an Exchange Economy with Stochastic Preferences," Journal of Economic Theory, Elsevier, vol. 106(2), pages 417-435, October.
  11. Banerjee, Anand & Yakovenko, Victor M. & Di Matteo, T., 2006. "A study of the personal income distribution in Australia," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 370(1), pages 54-59.
  12. Fujiwara, Yoshi & Souma, Wataru & Aoyama, Hideaki & Kaizoji, Taisei & Aoki, Masanao, 2003. "Growth and fluctuations of personal income," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 321(3), pages 598-604.
  13. Bouchaud, Jean-Philippe & Mézard, Marc, 2000. "Wealth condensation in a simple model of economy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 282(3), pages 536-545.
  14. Arnab Chatterjee & Bikas K. Chakrabarti & S. S. Manna, 2003. "Pareto Law in a Kinetic Model of Market with Random Saving Propensity," Papers cond-mat/0301289, arXiv.org, revised Jan 2004.
  15. F. Clementi & M. Gallegati, 2004. "Power Law Tails in the Italian Personal Income Distribution," Papers cond-mat/0408067, arXiv.org.
  16. Xavier Gabaix & Parameswaran Gopikrishnan & Vasiliki Plerou & H. Eugene Stanley, 2006. "Institutional Investors and Stock Market Volatility," The Quarterly Journal of Economics, MIT Press, vol. 121(2), pages 461-504, May.
  17. Anand Banerjee & Victor M. Yakovenko & T. Di Matteo, 2006. "A study of the personal income distribution in Australia," Papers physics/0601176, arXiv.org.
  18. Urna Basu & P. K. Mohanty, 2008. "Modeling wealth distribution in growing markets," The European Physical Journal B - Condensed Matter and Complex Systems, Springer, vol. 65(4), pages 585-589, October.
  19. Wright, Ian, 2005. "The social architecture of capitalism," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 346(3), pages 589-620.
  20. Wataru Souma & Makoto Nirei, 2005. "Empirical study and model of personal income," Papers physics/0505173, arXiv.org.
  21. F. Clementi & M. Gallegati, 2005. "Pareto's Law of Income Distribution: Evidence for Germany, the United Kingdom, and the United States," Papers physics/0504217, arXiv.org, revised Mar 2006.
  22. Clementi, F. & Di Matteo, T. & Gallegati, M., 2006. "The power-law tail exponent of income distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 370(1), pages 49-53.
  23. Rawlings, Philip K. & Reguera, David & Reiss, Howard, 2004. "Entropic basis of the Pareto law," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 343(C), pages 643-652.
  24. Chatterjee, Arnab & K. Chakrabarti, Bikas & Manna, S.S, 2004. "Pareto law in a kinetic model of market with random saving propensity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 335(1), pages 155-163.
  25. Solomon, Sorin & Richmond, Peter, 2001. "Power laws of wealth, market order volumes and market returns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 299(1), pages 188-197.
  26. Xi, Ning & Ding, Ning & Wang, Yougui, 2005. "How required reserve ratio affects distribution and velocity of money," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 357(3), pages 543-555.
  27. Richmond, Peter & Repetowicz, Przemek & Hutzler, Stefan & Coelho, Ricardo, 2006. "Comments on recent studies of the dynamics and distribution of money," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 370(1), pages 43-48.
  28. A. Chatterjee & B. K. Chakrabarti, 2006. "Kinetic market models with single commodity having price fluctuations," The European Physical Journal B - Condensed Matter and Complex Systems, Springer, vol. 54(3), pages 399-404, December.
  29. Braun, Dieter, 2001. "Assets and liabilities are the momentum of particles and antiparticles displayed in Feynman-graphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 290(3), pages 491-500.
  30. Smith, Eric & Foley, Duncan K., 2008. "Classical thermodynamics and economic general equilibrium theory," Journal of Economic Dynamics and Control, Elsevier, vol. 32(1), pages 7-65, January.
  31. Angle, John, 2006. "The Inequality Process as a wealth maximizing process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 367(C), pages 388-414.
  32. Ning Xi & Ning Ding & Yougui Wang, 2005. "How Required Reserve Ratio Affects Distribution and Velocity of Money," Papers physics/0507160, arXiv.org.
  33. Arnab Chatterjee, 2009. "Kinetic models for wealth exchange on directed networks," Papers 0901.2857, arXiv.org.
  34. Stauffer, Dietrich, 2004. "Introduction to statistical physics outside physics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 336(1), pages 1-5.
  35. Blume Lawrence E., 1993. "The Statistical Mechanics of Strategic Interaction," Games and Economic Behavior, Elsevier, vol. 5(3), pages 387-424, July.
  36. Braun, Dieter, 2006. "Nonequilibrium thermodynamics of wealth condensation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 369(2), pages 714-722.
  37. Ausloos, Marcel & Pe¸kalski, Andrzej, 2007. "Model of wealth and goods dynamics in a closed market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 373(C), pages 560-568.
  38. Gallegati, Mauro & Keen, Steve & Lux, Thomas & Ormerod, Paul, 2006. "Worrying trends in econophysics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 370(1), pages 1-6.
  39. Stanley, H.E. & Afanasyev, V. & Amaral, L.A.N. & Buldyrev, S.V. & Goldberger, A.L. & Havlin, S. & Leschhorn, H. & Maass, P. & Mantegna, R.N. & Peng, C.-K. & Prince, P.A. & Salinger, M.A. & Stanley, M., 1996. "Anomalous fluctuations in the dynamics of complex systems: from DNA and physiology to econophysics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 224(1), pages 302-321.
  40. A. Christian Silva & Richard E. Prange & Victor M. Yakovenko, 2004. "Exponential distribution of financial returns at mesoscopic time lags: a new stylized fact," Papers cond-mat/0401225, arXiv.org, revised Jul 2004.
  41. Arnab Das & Sudhakar Yarlagadda, 2004. "An analytic treatment of the Gibbs-Pareto behavior in wealth distribution," Papers cond-mat/0409329, arXiv.org, revised Mar 2005.
  42. Repetowicz, Przemysław & Hutzler, Stefan & Richmond, Peter, 2005. "Dynamics of money and income distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 356(2), pages 641-654.
  43. Anirban Chakraborti & Bikas K. Chakrabarti, 2000. "Statistical mechanics of money: How saving propensity affects its distribution," Papers cond-mat/0004256, arXiv.org, revised Jun 2000.
  44. A. Chatterjee & B. K. Chakrabarti, 2007. "Kinetic exchange models for income and wealth distributions," The European Physical Journal B - Condensed Matter and Complex Systems, Springer, vol. 60(2), pages 135-149, November.
  45. E. Samanidou & E. Zschischang & D. Stauffer & T. Lux, 2007. "Agent-based Models of Financial Markets," Papers physics/0701140, arXiv.org.
  46. F. Clementi & M. Gallegati & G. Kaniadakis, 2007. "κ-generalized statistics in personal income distribution," The European Physical Journal B - Condensed Matter and Complex Systems, Springer, vol. 57(2), pages 187-193, 05.
  47. A. Chatterjee, 2009. "Kinetic models for wealth exchange on directed networks," The European Physical Journal B - Condensed Matter and Complex Systems, Springer, vol. 67(4), pages 593-598, February.
  48. Arnab Chatterjee & Bikas K. Chakrabarti & Robin B. Stinchcombe, 2005. "Master equation for a kinetic model of trading market and its analytic solution," Papers cond-mat/0501413, arXiv.org, revised Aug 2005.
  49. Ball, Philip, 2002. "The physical modelling of society: a historical perspective," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 314(1), pages 1-14.
  50. Martin Shubik, 2000. "The Theory of Money," Cowles Foundation Discussion Papers 1253, Cowles Foundation for Research in Economics, Yale University.
  51. Ali Saif, M. & Gade, Prashant M., 2007. "Emergence of power-law in a market with mixed models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 384(2), pages 448-456.
  52. Jean-Philippe Bouchaud & Marc Mezard, 2000. "Wealth condensation in a simple model of economy," Science & Finance (CFM) working paper archive 500026, Science & Finance, Capital Fund Management.
  53. A. Chakraborti & B.K. Chakrabarti, 2000. "Statistical mechanics of money: how saving propensity affects its distribution," The European Physical Journal B - Condensed Matter and Complex Systems, Springer, vol. 17(1), pages 167-170, September.
  54. Bhattacharyya, Pratip & Chatterjee, Arnab & Chakrabarti, Bikas K., 2007. "A common mode of origin of power laws in models of market and earthquake," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 381(C), pages 377-382.
  55. Sorin Solomon & Peter Richmond, 2001. "Power Laws of Wealth, Market Order Volumes and Market Returns," Papers cond-mat/0102423, arXiv.org, revised Apr 2001.
  56. Chakraborti, Anirban & Pradhan, Srutarshi & Chakrabarti, Bikas K., 2001. "A self-organising model of market with single commodity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 297(1), pages 253-259.
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:arx:papers:0905.1518. 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)

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 references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link 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 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.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.