The New Palgrave Dictionary of Economics

2018 Edition
| Editors: Macmillan Publishers Ltd

Power Laws

  • Xavier Gabaix
Reference work entry


A power law is the form taken by a remarkable number of regularities in economics, and is a relation of the type Y = kXα, where Y and X are variables of interest, α is called the power law exponent, and k is a constant. Many economic laws take the form of power laws, in particular macroeconomic scaling laws, the distribution of income, wealth, size of cities and firms, and the distribution of financial variables such as returns and trading volume. This article surveys the empirical evidence and the theoretical explanations for the occurrence of power laws.


Cities GARCH effects Gibrat’s law Matching Networks Pareto laws Power laws Proportional random growth Quantity theory of money Scaling laws Stock market volatility Stylized facts Superstars, economics of Trading volume Universality Urban economics Zipf’s law 

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  1. Axtell, R. 2001. Zipf distribution of U.S. firm sizes. Science 293: 1818–1820.CrossRefGoogle Scholar
  2. Brown, J.H., and G.B. West. 2000. Scaling in biology. Oxford: Oxford University Press.Google Scholar
  3. Champernowne, D. 1953. A model of income distribution. Economic Journal 83: 318–351.CrossRefGoogle Scholar
  4. Embrechts, P., C. Kluppelberg, and T. Mikosch. 1997. Modelling extremal events for insurance and finance. New York: Springer.CrossRefGoogle Scholar
  5. Fujiwara, Y., C. Di Guilmi, H. Aoyama, M. Gallegati, and W. Souma. 2004. Do Pareto–Zipf and Gibrat laws hold true? An analysis with European firms. Physica A 335: 197–216.CrossRefGoogle Scholar
  6. Gabaix, X. 1999. Zipf’s law for cities: An explanation. Quarterly Journal of Economics 114: 739–767.CrossRefGoogle Scholar
  7. Gabaix, X. 2006. The granular origins of aggregate fluctuations. Working paper, MIT.Google Scholar
  8. Gabaix, X., P. Gopikrishnan, V. Plerou, and H.E. Stanley. 2003. A theory of power law distributions in financial market fluctuations. Nature 423: 267–230.CrossRefGoogle Scholar
  9. Gabaix, X., P. Gopikrishnan, V. Plerou, and H.E. Stanley. 2006. Institutional investors and stock market volatility. Quarterly Journal of Economics 121: 461–504.CrossRefGoogle Scholar
  10. Gabaix, X., and R. Ibragimov. 2006. Log (Rank-1/2): A simple way to improve the OLS estimation of tail exponents. Working paper: Harvard University.Google Scholar
  11. Gabaix, X., and Y. Ioannides. 2004. The evolution of the city size distributions. In Handbook of regional and urban economics, ed. V. Henderson and J.-F. Thisse, Vol. 4. Amsterdam: North-Holland.Google Scholar
  12. Gabaix, X., and A. Landier. 2008. Why has CEO pay increased so much? Quarterly Journal of Economics 123: 49–100.CrossRefGoogle Scholar
  13. Gopikrishnan, P., V. Plerou, L. Amaral, M. Meyer, and H.E. Stanley. 1999. Scaling of the distribution of fluctuations of financial market indices. Physical Review E 60: 5305–5316.CrossRefGoogle Scholar
  14. Gopikrishnan, P., V. Plerou, X. Gabaix, and H.E. Stanley. 2000. Statistical properties of share volume traded in financial markets. Physical Review E 62: R4493–R4496.CrossRefGoogle Scholar
  15. Ioannides, Y.M., and H.G. Overman. 2003. Zipf’s law for cities: An empirical examination. Regional Science and Urban Economics 33(2): 127–137.CrossRefGoogle Scholar
  16. Jessen, A.H., and T. Mikosch. 2006. Regularly varying functions. Publications de l’Institut Mathématique, Nouvelle Série 80: 171–192.Google Scholar
  17. Luttmer, E.G.J. 2007. Selection, growth, and the size distribution of firms. Quarterly Journal of Economics 122(3).Google Scholar
  18. Mulligan, C., and A. Shleifer. 2005. The extent of the market and the supply of regulation. Quarterly Journal of Economics 120: 1445–1473.CrossRefGoogle Scholar
  19. Plerou, V., P. Gopikrishnan, L. Amaral, X. Gabaix, and H.E. Stanley. 2000. Economic fluctuations and anomalous diffusion. Physical Review E 62(3): R3023–R3026.CrossRefGoogle Scholar
  20. Rossi-Hansberg, E., and M. Wright. 2007. Urban structure and growth. Review of Economic Studies 74: 597–624.CrossRefGoogle Scholar
  21. Schumpeter, J. 1949. Vilfredo Pareto (1848–1923). Quarterly Journal of Economics 63: 147–172.CrossRefGoogle Scholar
  22. Simon, H. 1955. On a class of skew distribution functions. Biometrika 44: 425–440.CrossRefGoogle Scholar
  23. Sornette, D. 2001. Critical phenomena in natural sciences. New York: Springer.Google Scholar

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© Macmillan Publishers Ltd. 2018

Authors and Affiliations

  • Xavier Gabaix
    • 1
  1. 1.