Generalized Pareto Curves: Theory and Applications

Abstract

We define generalized Pareto curves as the curve of inverted Pareto coe cients b(p), where b(p) is the ratio between average income or wealth above rank p and the p-th quantile Q(p) (i.e. b(p) = E[X|X > Q(p)]/Q(p)). We use them to characterize entire distributions, including places like the top where power laws are a good description, and places further down where they are not. We develop a method to nonparametrically recover the entire distribution based on tabulated income or wealth data as is generally available from tax authorities, which produces smooth and realistic shapes of generalized Pareto curves. Using detailed tabulations from quasi-exhaustive tax data, we demonstrate the precision of our method both empirically and analytically. It gives better results than the most commonly used interpolation techniques. Finally, we use Pareto curves to identify recurring distributional patterns, and connect those findings to the existing literature that explains observed distributions by random growth models.

Dynamics of contentment

“…For the developed countries, the ratio between the average income and the nominal gross domestic product per capita is approximately 0.7-0.8 suggesting that L 2 ≈ 0.2 ÷ 0.3 For L 2 = 0.2 the value M s = 2.5 yields pre-tax rate of the wealth increase of the wealthiest individuals considered here, M = M max = 7.0, of approximately 20% in line with the average values reported for the developed countries, e.g. Blanchet et al [2017]; these values are used in what follows.…”

“…Equation 11 means that this growth is faster than linear reflecting the correlation between higher levels of investment, risk and return open to the wealthiest Blanchet et al [2017]. For the developed countries, the ratio between the average income and the nominal gross domestic product per capita is approximately 0.7-0.8 suggesting that L 2 ≈ 0.2 ÷ 0.3 For L 2 = 0.2 the value M s = 2.5 yields pre-tax rate of the wealth increase of the wealthiest individuals considered here, M = M max = 7.0, of approximately 20% in line with the average values reported for the developed countries, e.g.…”

Capital Accumulation, Private Property, and Rising Inequality in China, 1978–2015

“…Individual owners have land use rights that can be transmitted to their children as long as they stay in the countryside (more precisely, as long they keep their rural Hukou), but lose all rights to the land if they move permanently to the cities (their land is then returned to the local government and allocated to other individuals). 6 The rights of private owners have gradually increased over time, as both land use and transmission rights were gradually extended in the 1980s and 1990s. To reflect this development, we assume that the public property share in agricultural land gradually declined from 70 percent in 1978 to 40 percent in 2015.…”

“…We also show how our results would be 5 At this stage, Chinese data sources do not allow to decompose private wealth into personal wealth (households) and non-profit wealth (non-profit institutions, usually a relatively small part of private wealth), so we only provide series for aggregate private wealth (personal plus non-profit). 6 There are two type of Hukou (residence registrations): agriculture Hukou (in rural China) and non-agriculture Hukou (in urban China). People with agriculture Hukou from rural China can keep their agriculture Hukou even when they are working in the cities, and in this way they are still entitled to their lands.…”

Keeping Up With the Novaks? Income Distribution as a Determinant of Household Debt in CESEE

“…Second, we applied Pareto correction to handle possible misreporting of the upper tail of the income distribution in our data set (Atkinson, 2017). Thus, we estimate a Pareto-shaped distribution for the top quintile of the distribution which should yield more realistic values of income and its distribution (in line with, for instance, Piketty and Saez, 2003;Blanchet et al, 2017or Eckerstorfer et al, 2016. To perform a Pareto distribution for top incomes, we need two parameters: (i) the size parameter m and (ii) the shape parameter (or Pareto's alpha).…”