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Power Laws in Economics and Finance

  • Xavier Gabaix

A power law is the form taken by a large number of surprising empirical regularities in economics and finance. This article surveys well-documented empirical power laws concerning income and wealth, the size of cities and firms, stock market returns, trading volume, international trade, and executive pay. It reviews detail-independent theoretical motivations that make sharp predictions concerning the existence and coefficients of power laws, without requiring delicate tuning of model parameters. These theoretical mechanisms include random growth, optimization, and the economics of superstars coupled with extreme value theory. Some of the empirical regularities currently lack an appropriate explanation. This article highlights these open areas for future research.

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Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 14299.

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Date of creation: Sep 2008
Date of revision:
Publication status: published as Xavier Gabaix, 2009. "Power Laws in Economics and Finance," Annual Review of Economics, Annual Reviews, vol. 1(1), pages 255-294, 05.
Handle: RePEc:nbr:nberwo:14299
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  1. Charles I. Jones, 2005. "The Shape of Production Functions and the Direction of Technical Change," The Quarterly Journal of Economics, Oxford University Press, vol. 120(2), pages 517-549.
  2. Kwok Tong Soo, 2004. "Zipf's law for cities: a cross country investigation," LSE Research Online Documents on Economics 19947, London School of Economics and Political Science, LSE Library.
  3. Durlauf,S.N., 2003. "Complexity and emperical economics," Working papers 2, Wisconsin Madison - Social Systems.
  4. Mark Wright & Esteban Rossi-Hansberg, 2004. "Urban Structure and Growth," 2004 Meeting Papers 33, Society for Economic Dynamics.
  5. Xavier Gabaix, 1999. "Zipf's Law for Cities: An Explanation," The Quarterly Journal of Economics, Oxford University Press, vol. 114(3), pages 739-767.
  6. Fujiwara, Yoshi & Di Guilmi, Corrado & Aoyama, Hideaki & Gallegati, Mauro & Souma, Wataru, 2004. "Do Pareto–Zipf and Gibrat laws hold true? An analysis with European firms," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 335(1), pages 197-216.
  7. Parameswaran Gopikrishnan & Vasiliki Plerou & Xavier Gabaix & H. Eugene Stanley, 2000. "Statistical Properties of Share Volume Traded in Financial Markets," Papers cond-mat/0008113,
  8. Eugene F. Fama, 1963. "Mandelbrot and the Stable Paretian Hypothesis," The Journal of Business, University of Chicago Press, vol. 36, pages 420.
  9. Challet, Damien & Marsili, Matteo & Zhang, Yi-Cheng, 2004. "Minority Games: Interacting agents in financial markets," OUP Catalogue, Oxford University Press, number 9780198566403, December.
  10. Makoto Nirei & Wataru Souma, 2007. "A Two Factor Model Of Income Distribution Dynamics," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 53(3), pages 440-459, 09.
  11. Klass, Oren S. & Biham, Ofer & Levy, Moshe & Malcai, Ofer & Solomon, Sorin, 2006. "The Forbes 400 and the Pareto wealth distribution," Economics Letters, Elsevier, vol. 90(2), pages 290-295, February.
  12. Dennis W. Jansen & Casper de Vries, 1988. "On the frequency of large stock returns: putting booms and busts into perspective," Working Papers 1989-006, Federal Reserve Bank of St. Louis.
  13. Ioannides, Yannis M. & Overman, Henry G., 2003. "Zipf's law for cities: an empirical examination," Regional Science and Urban Economics, Elsevier, vol. 33(2), pages 127-137, March.
  14. Xavier Gabaix & Rustam Ibragimov, 2007. "Rank-1/2: A Simple Way to Improve the OLS Estimation of Tail Exponents," NBER Technical Working Papers 0342, National Bureau of Economic Research, Inc.
  15. Fabrizio Lillo & Rosario N. Mantegna, 2001. "Power law relaxation in a complex system: Omori law after a financial market crash," Papers cond-mat/0111257,, revised Jun 2003.
  16. Xavier Gabaix, 2008. "Variable Rare Disasters: A Tractable Theory of Ten Puzzles in Macro-finance," American Economic Review, American Economic Association, vol. 98(2), pages 64-67, May.
  17. Brock,W.A. & Durlauf,S.N., 2000. "Discrete choice with social interactions," Working papers 7, Wisconsin Madison - Social Systems.
  18. Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," The Journal of Business, University of Chicago Press, vol. 36, pages 394.
  19. Cordoba, Juan Carlos, 2010. "On the Distribution of City Sizes," Staff General Research Papers Archive 32121, Iowa State University, Department of Economics.
  20. Lux, Thomas & Sornette, Didier, 2002. "On Rational Bubbles and Fat Tails," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 34(3), pages 589-610, August.
  21. Gilles Duranton, 2007. "Urban Evolutions: The Fast, the Slow, and the Still," American Economic Review, American Economic Association, vol. 97(1), pages 197-221, March.
  22. J-P. Bouchaud, 2001. "Power laws in economics and finance: some ideas from physics," Quantitative Finance, Taylor & Francis Journals, vol. 1(1), pages 105-112.
  23. Jensen, Michael C & Murphy, Kevin J, 1990. "Performance Pay and Top-Management Incentives," Journal of Political Economy, University of Chicago Press, vol. 98(2), pages 225-64, April.
  24. Tomoya Mori & Koji Nishikimi & Tony E. Smith, 2008. "The Number-Average Size Rule: A New Empirical Relationship Between Industrial Location And City Size," Journal of Regional Science, Wiley Blackwell, vol. 48(1), pages 165-211.
  25. Barro, Robert, 2006. "Rare Disasters and Asset Markets in the Twentieth Century," Scholarly Articles 3208215, Harvard University Department of Economics.
  26. Alex Edmans & Xavier Gabaix & Augustin Landier, 2009. "A Multiplicative Model of Optimal CEO Incentives in Market Equilibrium," Review of Financial Studies, Society for Financial Studies, vol. 22(12), pages 4881-4917, December.
  27. Baker, G.P. & Jensen, M.C. & Murphy, K.J., 1988. "Compensation And Incentives: Practice Vs. Theory," Papers 88-05, Rochester, Business - Managerial Economics Research Center.
  28. Xavier Gabaix, 2005. "The Granular Origins of Aggregate Fluctuations," 2005 Meeting Papers 470, Society for Economic Dynamics.
  29. Steven N. Durlauf, 1993. "Nonergodic Economic Growth," Review of Economic Studies, Oxford University Press, vol. 60(2), pages 349-366.
  30. Xavier Gabaix & Parameswaran Gopikrishnan & Vasiliki Plerou & H. Eugene Stanley, 2005. "Institutional Investors and Stock Market Volatility," NBER Working Papers 11722, National Bureau of Economic Research, Inc.
  31. Peter F. Kostiuk, 1990. "Firm Size and Executive Compensation," Journal of Human Resources, University of Wisconsin Press, vol. 25(1), pages 90-105.
  32. Vasco M Carvalho, 2008. "Aggregate Fluctuations and the Network Structure of Intersectoral Trade," 2008 Meeting Papers 1062, Society for Economic Dynamics.
  33. Gabaix, Xavier & Ioannides, Yannis M., 2004. "The evolution of city size distributions," Handbook of Regional and Urban Economics, in: J. V. Henderson & J. F. Thisse (ed.), Handbook of Regional and Urban Economics, edition 1, volume 4, chapter 53, pages 2341-2378 Elsevier.
  34. Atkinson, A. B. & Piketty, Thomas (ed.), 2007. "Top Incomes Over the Twentieth Century: A Contrast Between Continental European and English-Speaking Countries," OUP Catalogue, Oxford University Press, number 9780199286881, December.
  35. Esteban Rossi-Hansberg & Mark L. J. Wright, 2006. "Establishment size dynamics in the aggregate economy," Staff Report 382, Federal Reserve Bank of Minneapolis.
  36. Elhanan Helpman & Marc J. Melitz & Stephen R. Yeaple, 2004. "Export Versus FDI with Heterogeneous Firms," American Economic Review, American Economic Association, vol. 94(1), pages 300-316, March.
  37. Fu, Dongfeng & Pammolli, Fabio & Buldyrev, Sergey V. & Riccaboni, Massimo & Matia, Kaushik & Yamasaki, Kazuko & Stanley, H. Eugene, 2005. "The Growth of Business Firms: Theoretical Framework and Empirical Evidence," MPRA Paper 15905, University Library of Munich, Germany.
  38. Xavier Gabaix & Augustin Landier, 2008. "Why has CEO Pay Increased So Much?," The Quarterly Journal of Economics, Oxford University Press, vol. 123(1), pages 49-100.
  39. Peter Bak & Kan Chen & Jose Scheinkman & Michael Woodford, 1992. "Aggregate Fluctuations from Independent Sectoral Shocks: Self-Organized Criticality in a Model of Production and Inventory Dynamics," NBER Working Papers 4241, National Bureau of Economic Research, Inc.
  40. J. Barkley Rosser, 2009. "Introduction," Chapters, in: Handbook of Research on Complexity, chapter 1 Edward Elgar Publishing.
  41. Vasiliki Plerou & Parameswaran Gopikrishnan & Luis. A. Nunes Amaral & Xavier Gabaix & H. Eugene Stanley, 1999. "Economic Fluctuations and Diffusion," Papers cond-mat/9912051,
  42. V. Plerou & P. Gopikrishnan & L. A. N. Amaral & M. Meyer & H. E. Stanley, 1999. "Scaling of the distribution of price fluctuations of individual companies," Papers cond-mat/9907161,
  43. Nirei, Makoto, 2006. "Threshold behavior and aggregate fluctuation," Journal of Economic Theory, Elsevier, vol. 127(1), pages 309-322, March.
  44. Xavier Gabaix, 1999. "Zipf's Law and the Growth of Cities," American Economic Review, American Economic Association, vol. 89(2), pages 129-132, May.
  45. Edward E. Leamer & James Levinsohn, 1994. "International Trade Theory: The Evidence," NBER Working Papers 4940, National Bureau of Economic Research, Inc.
  46. Martin L. Weitzman, 2007. "Subjective Expectations and Asset-Return Puzzles," American Economic Review, American Economic Association, vol. 97(4), pages 1102-1130, September.
  47. Marko Tervio, 2008. "The Difference That CEOs Make: An Assignment Model Approach," American Economic Review, American Economic Association, vol. 98(3), pages 642-68, June.
  48. Matthieu Wyart & Jean-Philippe Bouchaud & Julien Kockelkoren & Marc Potters & Michele Vettorazzo, 2008. "Relation between bid-ask spread, impact and volatility in order-driven markets," Quantitative Finance, Taylor & Francis Journals, vol. 8(1), pages 41-57.
  49. Taisei Kaizoji, 2005. "A Precursor of Market Crashes," Papers physics/0510055,, revised Mar 2006.
  50. Fujiwara, Yoshi, 2004. "Zipf law in firms bankruptcy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 337(1), pages 219-230.
  51. Rosen, Sherwin, 1981. "The Economics of Superstars," American Economic Review, American Economic Association, vol. 71(5), pages 845-58, December.
  52. Geoffrey B. West & James H. Brown & Brian J. Enquist, 1997. "A General Model for the Origin of Allometric Scaling Laws in Biology," Working Papers 97-03-019, Santa Fe Institute.
  53. Stanley, Michael H. R. & Buldyrev, Sergey V. & Havlin, Shlomo & Mantegna, Rosario N. & Salinger, Michael A. & Eugene Stanley, H., 1995. "Zipf plots and the size distribution of firms," Economics Letters, Elsevier, vol. 49(4), pages 453-457, October.
  54. Ofer Malcai & Ofer Biham & Peter Richmond & Sorin Solomon, 2002. "Theoretical Analysis and Simulations of the Generalized Lotka-Volterra Model," Papers cond-mat/0208514,
  55. Austan Goolsbee & Judith Chevalier, 2002. "Measuring Prices and Price Competition Online: Amazon and Barnes and Noble," Yale School of Management Working Papers ysm290, Yale School of Management, revised 12 Sep 2008.
  56. Levy, Moshe, 2003. "Are rich people smarter?," Journal of Economic Theory, Elsevier, vol. 110(1), pages 42-64, May.
  57. Thomas Chaney, 2008. "Distorted Gravity: The Intensive and Extensive Margins of International Trade," American Economic Review, American Economic Association, vol. 98(4), pages 1707-21, September.
  58. Krugman, Paul, 1996. "Confronting the Mystery of Urban Hierarchy," Journal of the Japanese and International Economies, Elsevier, vol. 10(4), pages 399-418, December.
  59. Joseph Persky, 1992. "Retrospectives: Pareto's Law," Journal of Economic Perspectives, American Economic Association, vol. 6(2), pages 181-192, Spring.
  60. Mulligan, Casey B, 1997. "Scale Economies, the Value of Time, and the Demand for Money: Longitudinal Evidence from Firms," Journal of Political Economy, University of Chicago Press, vol. 105(5), pages 1061-79, October.
  61. Duranton, Gilles, 2006. "Some foundations for Zipf's law: Product proliferation and local spillovers," Regional Science and Urban Economics, Elsevier, vol. 36(4), pages 542-563, July.
  62. Sattinger, Michael, 1993. "Assignment Models of the Distribution of Earnings," Journal of Economic Literature, American Economic Association, vol. 31(2), pages 831-80, June.
  63. Sorin Solomon & Peter Richmond, 2001. "Power Laws of Wealth, Market Order Volumes and Market Returns," Papers cond-mat/0102423,, revised Apr 2001.
  64. Parameswaran Gopikrishnan & Vasiliki Plerou & Luis A. Nunes Amaral & Martin Meyer & H. Eugene Stanley, 1999. "Scaling of the distribution of fluctuations of financial market indices," Papers cond-mat/9905305,
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