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Power laws in top wealth distributions: evidence from Canada

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Abstract

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.

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References

  • Adamic LA, Huberman BA (2002) Zipf’s law and the internet. Glottometrics 3: 143–150

    Google Scholar 

  • Alegria C, Schaeck K (2008) On measuring concentration in banking systems. Financ Res Lett 5: 59–67

    Article  Google Scholar 

  • 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: 548–558

    Article  Google Scholar 

  • Axtell RL (2001) Zipf distribution of U.S. firm sizes. Science 293: 1818–1820

    Article  Google Scholar 

  • Bai MY, Zhu HB (2010) Power law and multiscaling properties of the Chinese stock market. Physica A 389: 1883–1890

    Article  Google Scholar 

  • Balakrishnan PV, Miller JM, Shankar SG (2008) Power laws and evolutionary trends in stock markets. Econ Lett 98: 194–200

    Article  Google Scholar 

  • Bauke H (2007) Parameter estimation for power law distributions by maximum likelihood. Eur Phys J B 58: 167–173

    Article  Google Scholar 

  • Bouchard JP (2001) Power laws in economics and finance: some ideas from physics. Quant Financ 1: 105–112

    Article  Google Scholar 

  • Cajueiro DO, Tabak BM, Werneck FK (2009) Can we predict crashes? The case of the Brazilian stock market. Physica A 388: 1603–1609

    Article  Google Scholar 

  • Chatterjee, A, Yarlagadda, S, Chakrabarti, BK (eds) (2005) Econophysics of wealth distributions. Springer, Milan

    Google Scholar 

  • Cirillo P, Hüsler J (2009) On the upper tail of Italian firms’ size distribution. Physica A 388: 1546–1554

    Article  Google Scholar 

  • Clauset A, Shalizi CR, Newman MEJ (2009) Power-law distributions in empirical data. SIAM Rev 51: 661–703

    Article  Google Scholar 

  • Clementi F, Gallegati M (2005) Power law tails in the Italian personal income distribution. Physica A 350: 427–438

    Article  Google Scholar 

  • Coelho R, Néda Z, Ramasco JJ, Santos MA (2005) A family network model of wealth distribution in societies. Physica A 353: 515–528

    Article  Google Scholar 

  • Coelho R, Richmond P, Barry J, Hutzler S (2008) Double power laws in income and wealth distributions. Physica A 387: 3847–3851

    Article  Google Scholar 

  • Cordoba JC (2008) On the distribution of city sizes. J Urban Econ 63: 177–197

    Article  Google Scholar 

  • D’Agostino RB, Stephens MA (1986) Goodness-of-fit techniques. Marcel Dekker, New York

    Google Scholar 

  • Di Guilmi C, Gaffeo E, Gallegati M (2003) Power law scaling in the world income distribution. Econ Bull 15: 1–7

    Google Scholar 

  • Ding N, Wang YG (2007) Power-law tail in the Chinese wealth distribution. Chin Phys Lett 24: 2434–2436

    Article  Google Scholar 

  • 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: 213–221

    Article  Google Scholar 

  • Eryiğit M, Çukur S, Eryigit R (2009) Tail distributions of index fluctuations in world markets. Physica A 388: 1879–1886

    Article  Google Scholar 

  • Fujiwara Y, Souma W, Kaizoji T, Aoki M (2003) Growth and fluctuations of personal income. Physica A 321: 598–604

    Article  Google Scholar 

  • Furceri D (2008) Zipf’s law and world income distribution. Appl Econ Lett 15: 921–923

    Article  Google Scholar 

  • Gabaix X (2009) Power laws in economics and finance. Annu Rev Econ 1: 255–293

    Article  Google Scholar 

  • 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

  • Gaffeo E, Gallegati M, Palestrini A (2003a) On the size distribution of firms: additional evidence from the G7 Countries. Physica A 324: 117–123

    Article  Google Scholar 

  • Gaffeo E, Gallegati M, Giulioni G, Palestrini A (2003b) Power laws and macroeconomic fluctuations. Physica A 324: 408–416

    Article  Google Scholar 

  • Gallegati M, Keen S, Lux T, Ormerod P (2006) Worrying trends in econophysics. Physica A 370: 1–6

    Article  Google Scholar 

  • Goldstein A, Morris SA, Yen GG (2004) Problems with fitting to the power-law distribution. Physica A 41: 255–258

    Google Scholar 

  • 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: 467–472

    Article  Google Scholar 

  • Jayadev A (2008) A power law tail in India’s wealth distribution: evidence from survey data. Physica A 387: 270–276

    Article  Google Scholar 

  • Klass OS, Biham O, Levy M, Malcai O, Solomon S (2006) The Forbes 400 and the Pareto wealth distribution. Econ Lett 90: 290–295

    Article  Google Scholar 

  • 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: 143–147

    Article  Google Scholar 

  • Kleiber C, Kotz S (2003) Statistical size distributions in economics and actuarial sciences. Wiley series in probability and statistics. Wiley-InterScience, New Jersey

    Book  Google Scholar 

  • Kvam PH, Vidakovic B (2007) Nonparametric statistics with applications to science and engineering. Wiley series in probability and statistics. Wiley-InterScience, New Jersey

    Book  Google Scholar 

  • Levy M, Levy H (2003) Investment talent and the Pareto wealth distribution: theoretical and experimental analysis. Rev Econ Stat 85: 709–725

    Article  Google Scholar 

  • Levy M, Solomon S (1997) New evidence for the power-law distribution of wealth. Physica A 242: 90–94

    Article  Google Scholar 

  • Morissette R, Zhang X (2007) Revisiting wealth inequality. Persp Labour Income 19: 6–17

    Google Scholar 

  • 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 151–192

  • Newman MEJ (2005) Power laws, pareto distributions and Zipf’s law. Contemp Phys 46: 323–351

    Article  Google Scholar 

  • Sinha S (2006) Evidence for power-law tail of the wealth distribution in India. Physica A 359: 555–562

    Article  Google Scholar 

  • Soo KT (2005) Zipf’s law for cities: a cross-country investigation. Reg Sci Urban Econ 35: 239–253

    Article  Google Scholar 

  • Ulubaşoğlu MA, Hazari BR (2004) Zipf’s law strikes again: the case of tourism. J Econ Geogr 4: 459–472

    Google Scholar 

  • Urzúa CM (2000) A simple and efficient test for Zipf’s law. Econ Lett 66: 257–260

    Article  Google Scholar 

  • Zhang J, Chen Q, Wang Y (2009) Zipf distribution in top Chinese firms and an economic explanation. Physica A 388: 2020–2024

    Article  Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Economics, Brock University, 500 Glenridge Avenue, St. Catharines, ON, L2S 3A1, Canada

    Tomson Ogwang

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  1. Tomson Ogwang
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Correspondence to Tomson Ogwang.

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Ogwang, T. Power laws in top wealth distributions: evidence from Canada. Empir Econ 41, 473–486 (2011). https://doi.org/10.1007/s00181-010-0384-5

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