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Power Laws in Economics and Finance
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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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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Cites
Emergence of Scaling in Random Networks
Barabási, A.-L., & Albert, R. (1999) · Science · doi:10.1126/science.286.5439.509 · Cited by 36,135
A General Model for the Origin of Allometric Scaling Laws in Biology
West, G. B., Brown, J. H., & Enquist, B. J. (1997) · Science · doi:10.1126/science.276.5309.122 · Cited by 5,016
Embrechts, P., Klüppelberg, C., & Mikosch, T. (1997) · doi:10.1007/978-3-642-33483-2 · Cited by 4,402
Export Versus FDI with Heterogeneous Firms
Helpman, E., Melitz, M. J., & Yeaple, S. R. (2004) · American Economic Review · doi:10.1257/000282804322970814 · Cited by 4,030
Jessen, H., & Mikosch, T. (2006) · Publications de l'Institut Mathematique · doi:10.2298/pim0694171j · Cited by 236
Flagged first, then by citations
Research works printed but not linked: 156
- Acemoglu D, 2009, Innovation by entrants and incumbents
- 10.1051/jp1:1997180 · DOI
- 10.3386/w14214 · DOI
- Atkinson AB, 2007, Top Incomes over the Twentieth Century, 10.1093/oso/9780199286881.001.0001 · DOI
- 10.1023/B:REIO.0000038273.50622.ec · DOI
- Auerbach F, 1913, Petermanns Geogr. Mitt., 59, 74
- 10.1126/science.1062081 · DOI · Paper page
- 10.1016/0035-5054(93)90023-V · DOI
- 10.2307/2328185 · DOI
- 10.1086/298230 · DOI
- 10.1162/qjec.121.3.823 · DOI
- 10.1002/0470012382 · DOI
- 10.1016/j.physa.2007.05.059 · DOI
- Benhabib J, 2007, The distribution of wealth: intergenerational transmission and redistributive policies
- 10.1086/427675 · DOI
- 10.1080/713665538 · DOI
- 10.1016/B978-012374258-2.50006-3 · DOI
- Bouchaud JP, 2004, Theory of Financial Risk and Derivative Pricing: From Statistical Physics to Risk Management
- 10.1017/CBO9780511818745 · DOI
- 10.1111/1467-937X.00168 · DOI
- 10.1103/PhysRevE.60.1412 · DOI
- 10.1177/030913338200600101 · DOI
- Carvalho V, 2008, Aggregate fluctuations and the network structure of intersectoral trade
- Challet D, 2005, Minority Games: Interacting Agents in Financial Markets
- 10.2307/2227127 · DOI
- 10.1257/aer.98.4.1707 · DOI
- 10.1023/A:1024634613982 · DOI
- Clauset A, 2008, Power-law distributions in empirical data
- 10.1016/j.jue.2007.01.005 · DOI
- 10.2307/2230529 · DOI
- 10.1103/PhysRevE.72.016112 · DOI
- De Vany A, 2003, Hollywood Economics, 10.4324/9780203489970 · DOI
- di Giovanni J, 2009, International trade and aggregate fluctuations in granular economies
- 10.1016/j.physa.2003.12.015 · DOI
- 10.1007/PL00011112 · DOI
- 10.1016/j.regsciurbeco.2006.03.008 · DOI
- 10.1257/aer.97.1.197 · DOI
- 10.2307/2298061 · DOI
- 10.1111/j.1468-0297.2005.01003.x · DOI
- 10.1257/0002828041301560 · DOI
- 10.1093/rfs/hhn117 · DOI
- 10.1257/0002828043052303 · DOI
- Estoup JB, 1916, Les gammes sténographiques
- 10.1086/294633 · DOI
- Frydman C, 2007, Historical trends in executive compensation, 1936-2003
- 10.1073/pnas.0509543102 · DOI
- 10.1016/j.physa.2004.01.037 · DOI
- 10.1162/003355399556133 · DOI
- 10.1257/aer.89.2.129 · DOI
- Gabaix X, 2007, The granular origins of aggregate fluctuations
- 10.3386/w13724 · DOI
- 10.1038/nature01624 · DOI
- Gabaix X, 2005, Are stock market crashes outliers?
- 10.1162/qjec.2006.121.2.461 · DOI
- Gabaix X, 2008, Rank-1/2: a simple way to improve the OLS estimation of tail exponents
- Gabaix X, 2008, A simple OLS test of power law behavior
- 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
- 10.1162/qjec.2008.123.1.49 · DOI
- Gibrat R, 1931, Les Inégalités Économiques
- 10.1103/PhysRevE.62.R4493 · DOI
- 10.1103/PhysRevE.60.5305 · DOI
- 10.1214/aoap/1177005985 · DOI
- 10.1214/aos/1176343247 · DOI
- Hinloopen J, 2008, Comparative advantage, the rank-size rule, and Zipf's law
- Hsu W, 2008, Central place theory and Zipf's law
- 10.1093/rfs/hhn021 · DOI
- Ijiri Y, 1964, Am. Econ. Rev., 54, 77
- Ijiri Y, 1979, Skew Distributions and the Sizes of Business Firms
- 10.1016/S0166-0462(02)00006-6 · DOI
- 10.1146/annurev.economics.050708.143238 · DOI
- 10.2307/2109682 · DOI
- 10.1086/261677 · DOI · Paper page
- Johnson NF, 2006, Universal patterns underlying ongoing wars and terrorism
- Jones C, 2005, Q. J. Econ., 120, 517
- 10.1140/epjb/e2006-00142-9 · DOI
- 10.1007/BF02392040 · DOI
- 10.2139/ssrn.1015987 · DOI
- 10.1016/j.econlet.2005.08.020 · DOI · Paper page
- 10.1002/0471457175 · DOI
- 10.2307/2171741 · DOI
- 10.2307/145728 · DOI
- 10.1287/moor.1030.0071 · DOI
- 10.1006/jjie.1996.0023 · DOI
- 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
- 10.1016/S0022-0531(03)00024-3 · DOI
- 10.1093/acprof:oso/9780195162592.003.0006 · DOI
- 10.1257/aer.99.4.1672 · DOI
- 10.1142/S0129183196000491 · DOI
- 10.1103/PhysRevE.68.016119 · DOI
- 10.1103/PhysRevE.60.1390 · DOI
- 10.2307/3003596 · DOI · Paper page
- 10.1162/qjec.122.3.1103 · DOI
- 10.1080/096031096333917 · DOI
- 10.1353/mcb.2002.0004 · DOI
- 10.1126/science.281.5384.1840 · DOI
- 10.1103/PhysRevE.66.031102 · DOI
- 10.1103/PhysRevE.60.1299 · DOI
- Malevergne Y, 2008, Zipf's law for firms: relevance of birth and death processes
- Mandelbrot B. 1953.An informational theory of the statistical structure of languages. InCommunication Theory, ed. Jackson W, pp. 486–502.Woburn, MA:Butterworth
- 10.2307/1911802 · DOI
- 10.1086/294632 · DOI
- 10.1007/978-1-4757-2763-0 · DOI
- 10.1103/PhysRevE.58.295 · DOI
- 10.1038/376046a0 · DOI
- 10.1103/PhysRevLett.80.4831 · DOI
- 10.1016/S0378-4371(98)00075-2 · DOI
- 10.1103/PhysRevLett.80.2741 · DOI
- 10.1016/S0378-4371(01)00301-6 · DOI
- 10.1006/anbe.1998.1000 · DOI
- 10.1111/1468-0262.00467 · DOI · Paper page
- 10.1080/15427951.2004.10129088 · DOI · Paper page
- 10.1111/j.1467-9787.2008.00550.x · DOI
- 10.1086/262105 · DOI
- Mulligan C, 2002, Square root rules without inventory management
- 10.3386/w10234 · DOI
- 10.1080/00107510500052444 · DOI
- Newman M, 2006, The Structure and Dynamics of Networks
- 10.1016/j.jet.2004.08.006 · DOI
- 10.1111/j.1475-4991.2007.00242.x · DOI
- 10.1016/S0378-4371(99)00086-2 · DOI
- Pareto V, 1896, Cours d'Economie Politique
- 10.1257/jep.6.2.181 · DOI
- 10.1103/PhysRevE.60.6519 · DOI
- 10.1103/PhysRevE.62.R3023 · DOI
- 10.1103/PhysRevE.71.046131 · DOI
- 10.1103/PhysRevE.76.046109 · DOI
- 10.1016/S0165-1765(01)00524-9 · DOI · Paper page
- 10.1073/pnas.0810478105 · DOI
- 10.2307/1884268 · DOI
- Rosen S, 1981, Am. Econ. Rev., 71, 845
- Rosen S. 1992.Contracts and the market for executives. InContract Economics, ed. L Werin, H Wijkander, pp. 181–211.Cambridge, MA:Oxford, Blackwell
- 10.1257/aer.97.5.1639 · DOI
- 10.1111/j.1467-937X.2007.00432.x · DOI
- 10.3386/w15409 · DOI
- Sattinger M, 1993, J. Econ. Lit., 31, 831
- 10.2307/1883096 · DOI
- 10.1093/biomet/42.3-4.425 · DOI
- 10.1016/S0378-4371(01)00295-3 · DOI
- 10.1016/j.regsciurbeco.2004.04.004 · DOI
- Sornette D, 2004, Critical Phenomena in Natural Sciences
- 10.1103/RevModPhys.71.S358 · DOI
- 10.1038/379804a0 · DOI
- 10.1016/0165-1765(95)00696-D · DOI
- Steindl J, 1965, Random Processes and the Growth of Firms
- 10.1257/aer.97.1.222 · DOI
- Taleb M, 2007, The Black Swan
- 10.1257/aer.98.3.642 · DOI
- 10.2307/1426858 · DOI
- 10.1103/PhysRevE.76.016109 · DOI
- 10.1257/aer.97.4.1102 · DOI
- 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
- 10.2307/1905385 · DOI
- 10.1080/14697680701344515 · DOI
- 10.1098/rstb.1925.0002 · DOI
- 10.1103/PhysRevLett.79.523 · DOI
- Zipf GK, 1949, Human Behavior and the Principle of Least Effort
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Moll, B., Rachel, L., & Restrepo, P. (2022) · Econometrica · doi:10.3982/ecta19417 · Cited by 148
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Metadata
- Authors
- Gabaix, X.
- Affiliations
- Stern School, New York University, New York, NY 10012;
- Venue
- Annual Review of Economics
- Publisher
- Annual Reviews
- 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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