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Power Laws in Economics and Finance

Gabaix, Xavier·2009·Annual Review of Economics

Abstract

A power law (PL) is the form taken by a large number of surprising empirical regularities in economics and finance. This review surveys well-documented empirical PLs regarding 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 PLs, 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 empirical regularities currently lack an appropriate explanation. This article highlights these open areas for future research.

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Crossref · 10.1146/annurev.economics.050708.142940

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  • The exponent α ≈ 2.0 is closer to concentrated capital income (α ≈ 1.5) than to labor income.

    “This places creator earnings closer to concentrated capital income ( α ≈ 1 . 5) (Gabaix 2009; Rishabh Kumar 2024) than to labor income, suggesting multiplicative and compounding effects drive online creator earnings (Strauss et al. 2024).”

    From "Rich-Get-Richer"? Platform Attention and Earnings Inequality using Patreon Earnings Data (2025) · cites this paper as Gabaix 2009

  • In the digital realm, each new click or view is more likely to go to creators who already have substantial visibility, resulting in a 'rich-get-richer' dynamic commonly observed on platforms governed by algorithmic curation.

    “In the digital realm, each new click or view is more likely to go to creators who already have substantial visibility, resulting in a 'rich-get-richer' dynamic commonly observed on platforms governed by algorithmic curation (Barabasi 2005; Jackson et al. 2008; Gabaix 2009; Vidal et al. 2011; Easley, J. Kleinberg, et al. 2010; Barabási et al. 2011; Barbosa et al. 2018).”

    From "Rich-Get-Richer"? Platform Attention and Earnings Inequality using Patreon Earnings Data (2025) · cites this paper as Gabaix 2009

  • Participants who accumulate more engagement become even more likely to attract future interactions.

    “This compounding of initial advantage, also called a 'superstar effect' in economics (Gabaix 2009; Autor et al. 2020), means that participants who accumulate more engagement become even more likely to attract future interactions.”

    From "Rich-Get-Richer"? Platform Attention and Earnings Inequality using Patreon Earnings Data (2025) · cites this paper as Gabaix 2009

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Research works printed but not linked: 156

  1. Acemoglu D, 2009, Innovation by entrants and incumbents
  2. 10.1051/jp1:1997180 · DOI
  3. 10.3386/w14214 · DOI
  4. Atkinson AB, 2007, Top Incomes over the Twentieth Century, 10.1093/oso/9780199286881.001.0001 · DOI
  5. 10.1023/B:REIO.0000038273.50622.ec · DOI
  6. Auerbach F, 1913, Petermanns Geogr. Mitt., 59, 74
  7. 10.1126/science.1062081 · DOI · Paper page
  8. 10.1016/0035-5054(93)90023-V · DOI
  9. 10.2307/2328185 · DOI
  10. 10.1086/298230 · DOI
  11. 10.1162/qjec.121.3.823 · DOI
  12. 10.1002/0470012382 · DOI
  13. 10.1016/j.physa.2007.05.059 · DOI
  14. Benhabib J, 2007, The distribution of wealth: intergenerational transmission and redistributive policies
  15. 10.1086/427675 · DOI
  16. 10.1080/713665538 · DOI
  17. 10.1016/B978-012374258-2.50006-3 · DOI
  18. Bouchaud JP, 2004, Theory of Financial Risk and Derivative Pricing: From Statistical Physics to Risk Management
  19. 10.1017/CBO9780511818745 · DOI
  20. 10.1111/1467-937X.00168 · DOI
  21. 10.1103/PhysRevE.60.1412 · DOI
  22. 10.1177/030913338200600101 · DOI
  23. Carvalho V, 2008, Aggregate fluctuations and the network structure of intersectoral trade
  24. Challet D, 2005, Minority Games: Interacting Agents in Financial Markets
  25. 10.2307/2227127 · DOI
  26. 10.1257/aer.98.4.1707 · DOI
  27. 10.1023/A:1024634613982 · DOI
  28. Clauset A, 2008, Power-law distributions in empirical data
  29. 10.1016/j.jue.2007.01.005 · DOI
  30. 10.2307/2230529 · DOI
  31. 10.1103/PhysRevE.72.016112 · DOI
  32. De Vany A, 2003, Hollywood Economics, 10.4324/9780203489970 · DOI
  33. di Giovanni J, 2009, International trade and aggregate fluctuations in granular economies
  34. 10.1016/j.physa.2003.12.015 · DOI
  35. 10.1007/PL00011112 · DOI
  36. 10.1016/j.regsciurbeco.2006.03.008 · DOI
  37. 10.1257/aer.97.1.197 · DOI
  38. 10.2307/2298061 · DOI
  39. 10.1111/j.1468-0297.2005.01003.x · DOI
  40. 10.1257/0002828041301560 · DOI
  41. 10.1093/rfs/hhn117 · DOI
  42. 10.1257/0002828043052303 · DOI
  43. Estoup JB, 1916, Les gammes sténographiques
  44. 10.1086/294633 · DOI
  45. Frydman C, 2007, Historical trends in executive compensation, 1936-2003
  46. 10.1073/pnas.0509543102 · DOI
  47. 10.1016/j.physa.2004.01.037 · DOI
  48. 10.1162/003355399556133 · DOI
  49. 10.1257/aer.89.2.129 · DOI
  50. Gabaix X, 2007, The granular origins of aggregate fluctuations
  51. 10.3386/w13724 · DOI
  52. 10.1038/nature01624 · DOI
  53. Gabaix X, 2005, Are stock market crashes outliers?
  54. 10.1162/qjec.2006.121.2.461 · DOI
  55. Gabaix X, 2008, Rank-1/2: a simple way to improve the OLS estimation of tail exponents
  56. Gabaix X, 2008, A simple OLS test of power law behavior
  57. Gabaix X, Ioannides Y. 2004.The evolution of the city size distributions. InHandbook of Regional and Urban Economics, ed. Henderson V, Thisse JF, 4:2341–78.Oxford:Elsevier · DOI
  58. 10.1162/qjec.2008.123.1.49 · DOI
  59. Gibrat R, 1931, Les Inégalités Économiques
  60. 10.1103/PhysRevE.62.R4493 · DOI
  61. 10.1103/PhysRevE.60.5305 · DOI
  62. 10.1214/aoap/1177005985 · DOI
  63. 10.1214/aos/1176343247 · DOI
  64. Hinloopen J, 2008, Comparative advantage, the rank-size rule, and Zipf's law
  65. Hsu W, 2008, Central place theory and Zipf's law
  66. 10.1093/rfs/hhn021 · DOI
  67. Ijiri Y, 1964, Am. Econ. Rev., 54, 77
  68. Ijiri Y, 1979, Skew Distributions and the Sizes of Business Firms
  69. 10.1016/S0166-0462(02)00006-6 · DOI
  70. 10.1146/annurev.economics.050708.143238 · DOI
  71. 10.2307/2109682 · DOI
  72. 10.1086/261677 · DOI · Paper page
  73. Johnson NF, 2006, Universal patterns underlying ongoing wars and terrorism
  74. Jones C, 2005, Q. J. Econ., 120, 517
  75. 10.1140/epjb/e2006-00142-9 · DOI
  76. 10.1007/BF02392040 · DOI
  77. 10.2139/ssrn.1015987 · DOI
  78. 10.1016/j.econlet.2005.08.020 · DOI · Paper page
  79. 10.1002/0471457175 · DOI
  80. 10.2307/2171741 · DOI
  81. 10.2307/145728 · DOI
  82. 10.1287/moor.1030.0071 · DOI
  83. 10.1006/jjie.1996.0023 · DOI
  84. Leamer E, Levinsohn J. 1995.International trade theory: the evidence. InHandbook of International Economics, ed. G Grossman, K Rogoff, 3:1339–94.Amsterdam:North-Holland · DOI
  85. 10.1016/S0022-0531(03)00024-3 · DOI
  86. 10.1093/acprof:oso/9780195162592.003.0006 · DOI
  87. 10.1257/aer.99.4.1672 · DOI
  88. 10.1142/S0129183196000491 · DOI
  89. 10.1103/PhysRevE.68.016119 · DOI
  90. 10.1103/PhysRevE.60.1390 · DOI
  91. 10.2307/3003596 · DOI · Paper page
  92. 10.1162/qjec.122.3.1103 · DOI
  93. 10.1080/096031096333917 · DOI
  94. 10.1353/mcb.2002.0004 · DOI
  95. 10.1126/science.281.5384.1840 · DOI
  96. 10.1103/PhysRevE.66.031102 · DOI
  97. 10.1103/PhysRevE.60.1299 · DOI
  98. Malevergne Y, 2008, Zipf's law for firms: relevance of birth and death processes
  99. Mandelbrot B. 1953.An informational theory of the statistical structure of languages. InCommunication Theory, ed. Jackson W, pp. 486–502.Woburn, MA:Butterworth
  100. 10.2307/1911802 · DOI
  101. 10.1086/294632 · DOI
  102. 10.1007/978-1-4757-2763-0 · DOI
  103. 10.1103/PhysRevE.58.295 · DOI
  104. 10.1038/376046a0 · DOI
  105. 10.1103/PhysRevLett.80.4831 · DOI
  106. 10.1016/S0378-4371(98)00075-2 · DOI
  107. 10.1103/PhysRevLett.80.2741 · DOI
  108. 10.1016/S0378-4371(01)00301-6 · DOI
  109. 10.1006/anbe.1998.1000 · DOI
  110. 10.1111/1468-0262.00467 · DOI · Paper page
  111. 10.1080/15427951.2004.10129088 · DOI · Paper page
  112. 10.1111/j.1467-9787.2008.00550.x · DOI
  113. 10.1086/262105 · DOI
  114. Mulligan C, 2002, Square root rules without inventory management
  115. 10.3386/w10234 · DOI
  116. 10.1080/00107510500052444 · DOI
  117. Newman M, 2006, The Structure and Dynamics of Networks
  118. 10.1016/j.jet.2004.08.006 · DOI
  119. 10.1111/j.1475-4991.2007.00242.x · DOI
  120. 10.1016/S0378-4371(99)00086-2 · DOI
  121. Pareto V, 1896, Cours d'Economie Politique
  122. 10.1257/jep.6.2.181 · DOI
  123. 10.1103/PhysRevE.60.6519 · DOI
  124. 10.1103/PhysRevE.62.R3023 · DOI
  125. 10.1103/PhysRevE.71.046131 · DOI
  126. 10.1103/PhysRevE.76.046109 · DOI
  127. 10.1016/S0165-1765(01)00524-9 · DOI · Paper page
  128. 10.1073/pnas.0810478105 · DOI
  129. 10.2307/1884268 · DOI
  130. Rosen S, 1981, Am. Econ. Rev., 71, 845
  131. Rosen S. 1992.Contracts and the market for executives. InContract Economics, ed. L Werin, H Wijkander, pp. 181–211.Cambridge, MA:Oxford, Blackwell
  132. 10.1257/aer.97.5.1639 · DOI
  133. 10.1111/j.1467-937X.2007.00432.x · DOI
  134. 10.3386/w15409 · DOI
  135. Sattinger M, 1993, J. Econ. Lit., 31, 831
  136. 10.2307/1883096 · DOI
  137. 10.1093/biomet/42.3-4.425 · DOI
  138. 10.1016/S0378-4371(01)00295-3 · DOI
  139. 10.1016/j.regsciurbeco.2004.04.004 · DOI
  140. Sornette D, 2004, Critical Phenomena in Natural Sciences
  141. 10.1103/RevModPhys.71.S358 · DOI
  142. 10.1038/379804a0 · DOI
  143. 10.1016/0165-1765(95)00696-D · DOI
  144. Steindl J, 1965, Random Processes and the Growth of Firms
  145. 10.1257/aer.97.1.222 · DOI
  146. Taleb M, 2007, The Black Swan
  147. 10.1257/aer.98.3.642 · DOI
  148. 10.2307/1426858 · DOI
  149. 10.1103/PhysRevE.76.016109 · DOI
  150. 10.1257/aer.97.4.1102 · DOI
  151. West GB, Brown JH, Enquist BJ. 2000.The origin of universal scaling laws in biology. InScaling in Biology, ed. Brown JH, West GB, pp. 87–112.Oxford, UK:Oxford Univ. Press · DOI
  152. 10.2307/1905385 · DOI
  153. 10.1080/14697680701344515 · DOI
  154. 10.1098/rstb.1925.0002 · DOI
  155. 10.1103/PhysRevLett.79.523 · DOI
  156. Zipf GK, 1949, Human Behavior and the Principle of Least Effort

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Metadata

Authors
Gabaix, X.
Affiliations
Stern School, New York University, New York, NY 10012;
Venue
Annual Review of Economics
Published
2009-09
Volume
1
Issue
1
Pages
255-294
ISSN
  • 1941-1383
  • 1941-1391
Cited by
907
References
5
Language
en

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