Do wealth distributions follow power laws? Evidence from ‘rich lists’

Brzeziński, Michał

doi:10.1016/j.physa.2014.03.052

Cited by 79 publications

(36 citation statements)

References 29 publications

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“…The actual spreads of incomes and wealth in nations around the world are described by a range of distributions—exponential, log-normal, gamma, and power-law [17] [18] [19] [20]. The wealth of agents is sampled from a standard normal distribution for the purpose of this paper, but our findings are also robust for exponential and log-normal distributions.…”

Section: Model Definition and Specificationsmentioning

confidence: 94%

Dynamics of Transformation from Segregation to Mixed Wealth Cities

Sahasranaman

2016

PLoS ONE

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We model the dynamics of a variation of the Schelling model for agents described simply by a continuously distributed variable—wealth. Agent movement is not dictated by agent choice as in the classic Schelling model, but by their wealth status. Agents move to neighborhoods where their wealth is not lesser than that of some proportion of their neighbors, the threshold level. As in the case of the classic Schelling model, we find here that wealth-based segregation occurs and persists. However, introducing uncertainty into the decision to move—that is, with some probability, if agents are allowed to move even though the threshold condition is contravened—we find that even for small proportions of such disallowed moves, the dynamics no longer yield segregation but instead sharply transition into a persistent mixed wealth distribution, consistent with empirical findings of Benenson, Hatna, and Or. We investigate the nature of this sharp transformation, and find that it is because of a non-linear relationship between allowed moves (moves where threshold condition is satisfied) and disallowed moves (moves where it is not). For small increases in disallowed moves, there is a rapid corresponding increase in allowed moves (before the rate of increase tapers off and tends to zero), and it is the effect of this non-linearity on the dynamics of the system that causes the rapid transition from a segregated to a mixed wealth state. The contravention of the tolerance condition, sanctioning disallowed moves, could be interpreted as public policy interventions to drive de-segregation. Our finding therefore suggests that it might require limited, but continually implemented, public intervention—just sufficient to enable a small, persistently sustained fraction of disallowed moves so as to trigger the dynamics that drive the transformation from a segregated to mixed equilibrium.

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Section: Model Definition and Specificationsmentioning

confidence: 94%

Dynamics of Transformation from Segregation to Mixed Wealth Cities

Sahasranaman

2016

PLoS ONE

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“…Whether the Pareto Type 1 distribution provides satisfactory fit to wealth recorded in the Forbes rich lists is somewhat controversial; see Ogwang (), Brzezinski () and Capehart (). The debate revolves around the reliability of Kolmogorov–Smirnov type of goodness‐of‐fit tests when data are measured with error.…”

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confidence: 99%

Wealth Inequality: A Survey

Cowell

Kerm

2015

Journal of Economic Surveys

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“…In fact, in the CSN paper where empirical data is tested against a power law (PL), log-normal, exponential (EXP), stretched exponential, and a power law with cut-off, the exponential distribution consistently performs poorer than the other distributions. This was also the case when Brzezinski tested the upper-tail wealth data for China, Russia, US, and the World using the CSN method [25]. In these papers, the data might truly be non-exponentially distributed, so it is not surprising the exponential fits fail.…”

Section: Introductionmentioning

confidence: 95%

Finite Sample Corrections for Parameters Estimation and Significance Testing

Teh

Tay

et al. 2018

Front. Appl. Math. Stat.

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An increasingly important problem in the era of Big Data is fitting data to distributions. However, many stop at visually inspecting the fits or use the coefficient of determination as a measure of the goodness of fit. In general, goodness-of-fit measures do not allow us to tell which of several distributions fit the data best. Also, the likelihood of drawing the data from a distribution can be low even when the fit is good. To overcome these limitations, Clauset et al. advocated a three-step procedure for fitting any distribution: (i) estimate parameter(s) accurately, (ii) choosing and calculating an appropriate goodness of fit, (iii) test its significance to determine how likely this goodness of fit will appear in samples of the distribution. When we perform this significance testing on exponential distributions, we often obtain low significance values despite the fits being visually good. This led to our realization that most fitting methods do not account for effects due to the finite number of elements and the finite largest element. The former produces sample size dependence in the goodness of fits and the latter introduces a bias in the estimated parameter and the goodness of fit. We propose modifications to account for both and show that these corrections improve the significance of the fits of both real and simulated data. In addition, we used simulations and analytical approximations to verify that convergence rate of the estimated parameters toward its true value depends on how fast the largest element converge to infinity, and provide fast inversion formulas to obtain p-values directly from the adjusted test statistics, in place of doing more Monte Carlo simulations.

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Do wealth distributions follow power laws? Evidence from ‘rich lists’

Cited by 79 publications

References 29 publications

Dynamics of Transformation from Segregation to Mixed Wealth Cities

Dynamics of Transformation from Segregation to Mixed Wealth Cities

Wealth Inequality: A Survey

Finite Sample Corrections for Parameters Estimation and Significance Testing

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