## 9/28/15

### gender-dependent distribution of population with income above the Pareto threshold

As we discussed in Section 1, another aggregate variable derived from PID and sensitive to work experience is the portion of people with the highest incomes, there the highest incomes are defined as those distributed according the Pareto law. The long-term observations in the USA reveal significant increase in the age when this portion achieves its maximum value with growing GDP per capita. Figure 17 displays five curves for selected years between 1967 and 2014. Each curve represents the age-dependent ratio of the population above predefined thresholds and total population. We have selected the thresholds (\$11,000 for 1967, \$20,000 for 1977, \$43,000 for 1990, \$65,000 for 2001, and \$87,000 for 2014) which provide approximately the same peak value of the respective ratio – 18%, which is accompanied by the same total portion of population above these thresholds - from 7.5% in 1977 to 9% in 2014. So, the integral share of population with income (male and female) above the Pareto threshold is retained at the level of 9%. One should also to take into account the deficit of female population with income before 1977. The age of peak value increases with time, as discussed in Section 1. All curves are bell shaped – for the youngest and eldest population participation in the highest incomes is negligible. The rate of growth at the initial stage is the highest in 1967 and the slowest in the 2000s. Beyond the critical age, two curves for 1967 and 1977 fall faster and reach 2% at the age of 70. The rate of fall in 2014 is the lowermost and the curve drops to 5% level at the age of 80. This observation should be reproduced by our model.

There are two genders in the total population which have different contributions to the total population with the highest incomes. Figure 9 suggests that the women’s participation above the Pareto threshold in the 1960s and 1970s was extremely low.  Figure 18 displays curves similar to those in Figure 17 with the same thresholds, but for two genders separately.  In 1967, the share of rich females was less than 3% of the number of women with income, which was approximately 60% of the total number of females. Since the contribution of women was so low, the male population occupied almost all positions in the high income range. Therefore, the curves in Figure 17 and the males’ curves in Figure 18 do not differ for 1967 and 1977; expect the males’ peak portion is 28%. The women’s share has been increasing since the earlier 1980s and approximately 10% of women between 35 and 65 years of age had incomes above \$87,000 in 2014. These women displaced men from the top income zone and only 22% to 24% of males had incomes above the same threshold.

Figure 17.  The portion of people above the Pareto threshold for various years between 1967 and 2014. Relevant thresholds are shown in the Figure.

Figure 18. The portion of males (left panel) and females (right panel) above the Pareto threshold for various years between 1967 and 2014. Thresholds are the same as in Figure 17.

Figure 19. The ratio of male and female portions in Figure 18.

The females’ contribution is still lower and one can estimate the time when the current convergence tendency will end in equal representation. Figure 19 shows the age-dependent ratio of the curves in the left and right panels of Figure 18. In 1967, the ratio peaks at 30 years of age and achieves the level of 30 and above. In 1980, the ratio hovers near 10 and then drops to 6 to 8 in 1990.  In the 21st century, the ratio falls to 3.5 in 2001 and currently is between 2 and 3.  The trend is quasi-exponential (R2=0.98) and the extrapolated curve will reach 1.0 in 2025-2030. This is the expected time of gender equality as related to participation in the Pareto distribution. The trend may change in the future, however. To model the past numbers of females above the Pareto threshold we may adjust the relevant defining parameters to fit the exponential fall in the male/female ratio.

Figure 20. Pair-wise comparison of male and female curves for selected years between 1967 and 2014.

Figure 20 illustrates the evolution of age dependence with time and compares male and female curves. We have estimated the age-dependent curves for the portion of population above given thresholds similar to those in Figure 18 and normalized them to their peak values. Male and female curves are compared on the year-by-year basis. The thresholds in Figure 20 are lowered in order to obtain more reliable estimates with smaller fluctuations. The negative effect of the deceased thresholds is that they are now below the Pareto one for males but still above that for females. The total portion of people above these thresholds varies from 13% in 1977 to 17% in 2014. In 1967, the males curve grows at a high rate from 23 years of age, peaks at 35 years of age, and then falls to 0 at 75 years of age. The female curve grows slowly with large fluctuations and has a sharp peak at 55 years of age. In 1977, the female curve peaks at 47 years of age and has a plateau till 65 years. After a period of expedite growth in the females’ share between 1977 and 1980, we observe that the male and female curves become closer and closer from 1990 to 2014. This is only relative convergence, however. The absolute levels differ by a factor of 2.5 in 2014. Women are as efficient as men when they get in the top income percentiles. They are underrepresented however.

Figure 21. The age-dependent potion of females in 1967 and 1977 when the Pareto thresholds are decreased to the level corresponding to women, as illustrated in Figure 9. Left panel: absolute portion. Right panel: normalized to peak value and smoother with MA(7).

The discrepancy between the male and female curves in Figure 20 observed in 1967 and 1977 may be induced by the difference in the Pareto thresholds. For females, it is much lower, as Figure 9 shows. In Figure 21 we display the age-dependent portions of females with income above \$6,000 in 1967 and \$14,000 in 1977, instead of \$9,000 and \$17,000, respectively, in Figure 20. The peak values are now around 20% of females with income; it has to be reduced according to the total share with income below 70% (see Figure 11). In terms of shape, both curves are now similar to those in Figure 15, which presents the mean income curves.