Empirical Economics

, Volume 41, Issue 2, pp 473–486 | Cite as

Power laws in top wealth distributions: evidence from Canada

  • Tomson OgwangEmail author
Original Paper


This article investigates Pareto power law (PPL) behavior at the top of the Canadian wealth distribution. To this end, Canadian Business data on the wealthiest 100 Canadians for the years 1999–2008 are used. The resulting estimates of the PPL exponent ranged from approximately 1.0 to 1.3 depending on the year of analysis and the estimation method used. These estimates are roughly comparable to those based on Forbes’ list of the wealthiest 400 Americans. Furthermore, whereas modified OLS and maximum likelihood estimates of the power law exponents conform to Zipf’s law, the OLS estimates do not. These results raise some concerns about deducing the magnitudes of and trends in the power law exponents based on a single estimation method and highlight the importance of extensive hypothesis testing for model adequacy. The battery of diagnostic tests pertaining to PPL behavior at the top of the Canadian wealth distribution yields some conflicting results.


Pareto power law Zipf’s law Wealth Inequality 

JEL Classification

C46 D31 


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  1. Adamic LA, Huberman BA (2002) Zipf’s law and the internet. Glottometrics 3: 143–150Google Scholar
  2. Alegria C, Schaeck K (2008) On measuring concentration in banking systems. Financ Res Lett 5: 59–67CrossRefGoogle Scholar
  3. Ausloos M, Miáiewicz J, Sanglier M (2004) The durations of recession and prosperity: does their distribution follow a power or exponential law?. Physica A 339: 548–558CrossRefGoogle Scholar
  4. Axtell RL (2001) Zipf distribution of U.S. firm sizes. Science 293: 1818–1820CrossRefGoogle Scholar
  5. Bai MY, Zhu HB (2010) Power law and multiscaling properties of the Chinese stock market. Physica A 389: 1883–1890CrossRefGoogle Scholar
  6. Balakrishnan PV, Miller JM, Shankar SG (2008) Power laws and evolutionary trends in stock markets. Econ Lett 98: 194–200CrossRefGoogle Scholar
  7. Bauke H (2007) Parameter estimation for power law distributions by maximum likelihood. Eur Phys J B 58: 167–173CrossRefGoogle Scholar
  8. Bouchard JP (2001) Power laws in economics and finance: some ideas from physics. Quant Financ 1: 105–112CrossRefGoogle Scholar
  9. Cajueiro DO, Tabak BM, Werneck FK (2009) Can we predict crashes? The case of the Brazilian stock market. Physica A 388: 1603–1609CrossRefGoogle Scholar
  10. Chatterjee, A, Yarlagadda, S, Chakrabarti, BK (eds) (2005) Econophysics of wealth distributions. Springer, MilanGoogle Scholar
  11. Cirillo P, Hüsler J (2009) On the upper tail of Italian firms’ size distribution. Physica A 388: 1546–1554CrossRefGoogle Scholar
  12. Clauset A, Shalizi CR, Newman MEJ (2009) Power-law distributions in empirical data. SIAM Rev 51: 661–703CrossRefGoogle Scholar
  13. Clementi F, Gallegati M (2005) Power law tails in the Italian personal income distribution. Physica A 350: 427–438CrossRefGoogle Scholar
  14. Coelho R, Néda Z, Ramasco JJ, Santos MA (2005) A family network model of wealth distribution in societies. Physica A 353: 515–528CrossRefGoogle Scholar
  15. Coelho R, Richmond P, Barry J, Hutzler S (2008) Double power laws in income and wealth distributions. Physica A 387: 3847–3851CrossRefGoogle Scholar
  16. Cordoba JC (2008) On the distribution of city sizes. J Urban Econ 63: 177–197CrossRefGoogle Scholar
  17. D’Agostino RB, Stephens MA (1986) Goodness-of-fit techniques. Marcel Dekker, New YorkGoogle Scholar
  18. Di Guilmi C, Gaffeo E, Gallegati M (2003) Power law scaling in the world income distribution. Econ Bull 15: 1–7Google Scholar
  19. Ding N, Wang YG (2007) Power-law tail in the Chinese wealth distribution. Chin Phys Lett 24: 2434–2436CrossRefGoogle Scholar
  20. Drăguleascu A, Yakovenko VM (2001) Exponential and power-law probability distributions of wealth and income in the United Kingdom and the United States. Physica A 299: 213–221CrossRefGoogle Scholar
  21. Eryiğit M, Çukur S, Eryigit R (2009) Tail distributions of index fluctuations in world markets. Physica A 388: 1879–1886CrossRefGoogle Scholar
  22. Fujiwara Y, Souma W, Kaizoji T, Aoki M (2003) Growth and fluctuations of personal income. Physica A 321: 598–604CrossRefGoogle Scholar
  23. Furceri D (2008) Zipf’s law and world income distribution. Appl Econ Lett 15: 921–923CrossRefGoogle Scholar
  24. Gabaix X (2009) Power laws in economics and finance. Annu Rev Econ 1: 255–293CrossRefGoogle Scholar
  25. Gabaix X, Ibragimov R (2009) Rank-1/2: a simple way to improve the OLS estimation of tail exponents. J Bus Econ Stat. doi: 10.1198/jbes.2009.06157
  26. Gaffeo E, Gallegati M, Palestrini A (2003a) On the size distribution of firms: additional evidence from the G7 Countries. Physica A 324: 117–123CrossRefGoogle Scholar
  27. Gaffeo E, Gallegati M, Giulioni G, Palestrini A (2003b) Power laws and macroeconomic fluctuations. Physica A 324: 408–416CrossRefGoogle Scholar
  28. Gallegati M, Keen S, Lux T, Ormerod P (2006) Worrying trends in econophysics. Physica A 370: 1–6CrossRefGoogle Scholar
  29. Goldstein A, Morris SA, Yen GG (2004) Problems with fitting to the power-law distribution. Physica A 41: 255–258Google Scholar
  30. Hu MB, Jiang R, Wu QS, Wu YH (2007) Simulating the wealth distribution with a richest-following strategy on scale-free network. Physica A 381: 467–472CrossRefGoogle Scholar
  31. Jayadev A (2008) A power law tail in India’s wealth distribution: evidence from survey data. Physica A 387: 270–276CrossRefGoogle Scholar
  32. Klass OS, Biham O, Levy M, Malcai O, Solomon S (2006) The Forbes 400 and the Pareto wealth distribution. Econ Lett 90: 290–295CrossRefGoogle Scholar
  33. Klass OS, Biham O, Levy M, Malcai O, Solomon S (2007) The Forbes 400, the Pareto power-law and efficient markets. Eur Phys J B 55: 143–147CrossRefGoogle Scholar
  34. Kleiber C, Kotz S (2003) Statistical size distributions in economics and actuarial sciences. Wiley series in probability and statistics. Wiley-InterScience, New JerseyCrossRefGoogle Scholar
  35. Kvam PH, Vidakovic B (2007) Nonparametric statistics with applications to science and engineering. Wiley series in probability and statistics. Wiley-InterScience, New JerseyCrossRefGoogle Scholar
  36. Levy M, Levy H (2003) Investment talent and the Pareto wealth distribution: theoretical and experimental analysis. Rev Econ Stat 85: 709–725CrossRefGoogle Scholar
  37. Levy M, Solomon S (1997) New evidence for the power-law distribution of wealth. Physica A 242: 90–94CrossRefGoogle Scholar
  38. Morissette R, Zhang X (2007) Revisiting wealth inequality. Persp Labour Income 19: 6–17Google Scholar
  39. Morissette R, Zhang X, Drolet M (2006) The evolution of wealth inequality in Canada, 1984–99. In: Wolff EN (ed) International perspectives on household wealth. Levy Economics Institute, USA, pp 151–192Google Scholar
  40. Newman MEJ (2005) Power laws, pareto distributions and Zipf’s law. Contemp Phys 46: 323–351CrossRefGoogle Scholar
  41. Sinha S (2006) Evidence for power-law tail of the wealth distribution in India. Physica A 359: 555–562CrossRefGoogle Scholar
  42. Soo KT (2005) Zipf’s law for cities: a cross-country investigation. Reg Sci Urban Econ 35: 239–253CrossRefGoogle Scholar
  43. Ulubaşoğlu MA, Hazari BR (2004) Zipf’s law strikes again: the case of tourism. J Econ Geogr 4: 459–472Google Scholar
  44. Urzúa CM (2000) A simple and efficient test for Zipf’s law. Econ Lett 66: 257–260CrossRefGoogle Scholar
  45. Zhang J, Chen Q, Wang Y (2009) Zipf distribution in top Chinese firms and an economic explanation. Physica A 388: 2020–2024CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Department of EconomicsBrock UniversitySt. CatharinesCanada

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