Fig 1.
The distribution of wealth in the United States 1930–2010.
A: The probability density reconstructed from the compiled historical data for 2007 (blue) and the probability density function of the approximated log-normal distribution (μ = 11.4 and σ = 1.75) (dashed red); B: The Lorenz curve of the wealth distribution for compiled historical data (blue) and for an approximated log-normal distribution (dashed red). The log-normal distribution parameters used were μ = 11.4 and σ = 1.75; C-E: The share of wealth owned by the top 10% of the population (C), the top 1% (D) and the top 0.1% (E). The presented data are by the courtesy of Gabriel Zucman [22, 23].
Fig 2.
The characteristic behavior of the stochastic model.
A: An illustration of the division to deciles—every time step i, each individual, with labor income L and wealth W is attached to a certain decile in labor income (χL) and wealth (χW) according to the distribution of the entire population; B: The decile mobility for 10 years is calculated following equation Eq (2) with P ranging from 0 to 0.4 per year. The decile mobility in the US was 75%–80% for 10-year periods during the past 50 years [44], leading to P values of 0.15–0.2 per year. The dashed red curve demonstrates that the decile mobility exponentially increases with P; C: The dependence of ΘΓ on the labor income decile [41–43]; D: The dependence of ΘR on the wealth decile; E: The model results for the distribution of wealth in the United States. The results were calculated for the historical values of the model parameters in the period 1930–2010, after 10 years (purple), 50 years (pink) and 80 years (light blue).
Fig 3.
The dependence of the model results on max (ΘR).
A: The dependence of the correlation between the model results and the historical data on max (ΘR) (black). Also presented is the dependence of 1/L2 metric between the model results and historical data on max (ΘR) (dark grey); B: The model results for the top 10% share of wealth in the United States during 1930–2010 for different values of max (ΘR). The results produced by implementing the described model were calculated using the historical data for the various parameters [22, 23]. The historical data (blue) were taken from Saez and Zucman [22].
Fig 4.
The model results for the top 10% share of wealth in the United States during 1930–2010.
A: The results produced by implementing the described model were calculated using the historical data for the various parameters [22, 23]. These results are presented with economic mobility (P = 0.18 per year) (red). The historical data (blue) were taken from Saez and Zucman [22]; B-C: The top 10% share of wealth in the United States with averaged parameters during 1980–2010. The calculations were done for nominal parameters (red) and for each parameter, with its values during 1980–2010 taken as their average during 1930–1980, while the other parameters were taken with their nominal historical values. In B—average growth rate (orange), average α (light green) and average rent income fraction (gray). In C—average savings fraction (magenta). The dotted gray line separates the calculation using the nominal parameter values and the averaged parameter value; D: The model results for the top 10% share of wealth for nominal parameters (P = 0.18 per year) (red) and without economic mobility (P = 0 per year) (dark green). Also presented are the model results without economic mobility and optimized value of max (ΘR) (dashed dark green). In the presented calculation max (ΘR) = 1.3.
Fig 5.
The historical values of the model parameters 1930–2010.
The data are presented for the GDP growth rate (orange), private savings fraction (magenta) and rent income fraction (gray) for the periods 1930–1970 (A) and 1970–2010 (B). In addition, the historical values of the α fraction (light green) are presented (C). The data were taken from Saez and Zucman [22].
Fig 6.
Retrospective predictions of the wealth inequality in the US.
The blue and red curves present the historical market behavior and the model behavior for the historical values of the parameters, respectively (see Fig 4). The results for the various scenarios during 1980–2010 (A) and during 2000–2010 (B) are also presented: Unchanged parameter scenario (solid black curve), decreasing savings scenario (red diamonds), decreasing savings and increasing α scenario (red stars) and increasing savings and decreasing α scenario (green crosses). The significant difference between the results for the increasing savings and decreasing α scenario in (A) and (B) is due to the fast savings fraction increase in (B) (from 4% to 15% within 10 years), compared to a mild increase in (A) (from 7% to 15% within 30 years). The dotted gray line separates the calculation using historical parameter values and the retrospective prediction.
Fig 7.
Predictions of future wealth inequality.
The blue and red curves present the historical and model results, respectively (see Fig 4). The dashed curves display the predictions of the future inequality. The results for the various parameter scenarios during 2010–2030 are also presented: extrapolated parameter scenario (triangles), increasing savings scenario (squares) and increasing α scenario (circles). In addition, a linear extrapolation of the wealth inequality during 2000–2010 to 2010–2030 is presented as well (dashed blue curve). The dotted gray line separates the calculation using historical parameter values and the prediction for future inequality.
Fig 8.
Prediction of the top and mid deciles shares of wealth.
The solid red and cyan curves present the model results for the share of wealth owned by the top and mid deciles, respectively. These results were calculated using the historical parameter values. The dashed curves display the projections of the future share of wealth for the nominal constant parameter scenario. The projections of the future share of wealth for the increasing savings scenario are presented for the top 10% share (black squares) and for the mid 10% share (black diamonds). The dotted gray line separates the calculation using historical parameter values and the projection for future inequality.