Income Inequality: Race And Gender Issues

For the level of measurement accuracy of the overall personal income distribution, the model predicts the increase in the peak age quite well. Our model is extensively used in fine data analysis and accurate predictions.  The US society is not a homogeneous one and genders and races demonstrate different features and long-term behaviour.  In the next paragraph, we consider some differences between races and genders.

Figure 2. The evolution of age-dependent nominal mean income between 1967 and 2013. 

Figure 3. The evolution of age-dependent mean income between 1967 and 2013.  Both curves in Figure 2 were smoothed with an eight-year-moving-average and then normalized to their respective peak values.

Figure 4. Comparison of the observed mean (averaged in five-year bins except the bin between 15 and 24 years of age) income dependence on work experience (open circles) and that predicted by our model (dotted line) for 1998. The model provides annual estimates. The age of peak mean income is accurately predicted as well as the shape of the observed curve. Our model describes the whole period between 1929 (start of the GDP time series in the U.S.) and 2013.

Figure 5. The evolution of mean income in the youngest age group. The actual mean income estimates for 1962 (red circles) and 2012 (black circles) are estimated from microeconomic data obtained from the IPUMS. The model predictions are shown by red and black lines, respectively. The best fit model year for actual 1962 data is obtained for the year of 1958. Considering the decreasing level of accuracy of GDP and mean income estimates in the past, this difference is just a marginal one.  

Race and gender: unfairness of income distribution

Figure 6 repeats Figures 2 and 3 for the mean income of white male population. Here we use the income values averaged in ten-year-wide bins (e.g., from 15 to 24 years of age) as reported by the CB. The curves for white males have the same striking feature as observed in the overall income distribution – the increase in the age of mean income peak. Figure 7 supports this observation by showing two similar curves for people with Hispanic origin. As for white males, the age of peak mean income increases with time.

The observed increase in the peak age in the mean income curve is a reliable feature which is accurately (in quantitative terms) explained by our model. However, there also exists the difference between mean income curves for different genders and races. For example, the mean income curve for white males peaks at higher age than the overall curve, as Figure 8 demonstrates. Figures 9 and 10 reveal the same feature in the mean income curves for male and female population, respectively, and compare three races. Figure 11 illustrates the fact that the most recent mean income trajectories of the “lagging” gender and races actually almost repeat the earlier trajectories for the “leading” gender-race configuration. All these observations are a challenge to our model predicting that the age distribution of mean income depends only on the real GDP per capita. Everything else being equal, the shape of mean income curve for white males must be similar to the shape of mean income distribution for all other gender-race configurations. Assuming the model is correct our current task is to find the model feature which does not fit reality for some reason. It is worth to identify this (-ese) reason(s) in order to understand its (their) impact on the distribution of personal income in the USA. If the impact is negative and can be controlled by socio-economic measures, one has to develop an adequate policy to improve the performance of the U.S. economy and likely society.  


Figure 6. The evolution of age-dependent mean income for white male between 1974 and 2013.  Upper panel – real mean income. Lower panel: both curves in the upper panel were normalized to their respective peak values.

Figure 7. The evolution of the age-dependent mean income for Hispanic population. 

Figure 8. The age-dependent mean income distribution for all population, male, and white male in 2011. 

Figure 9.  Comparison of the age-dependent mean income distribution in 2013 (2012 for Hispanic) for three races of male population. The white male distribution peaks at a larger age with the black and Hispanic population having similar peaks.

Figure 10.  Comparison of the age-dependent mean income distribution for three races of female population. The white male distribution peaks at a slightly larger age, but the difference with the black and Hispanic population is much smaller than for white male.

Figure 11. Comparison of mean income evolution with age for white and black male and female. Both curves for the whites lead by approximately 25 years corresponding curves for the blacks. The similarity of shapes is extraordinary, considering the lag of 25 years.

Our model is based on an assumption that any income is earned by a person with a given work capability (which is slightly different from the term “human capital”, but the latter term is adopted in the conventional economics as the productive force related to people) which is applied to some working instrument (aka work capital - the real value of all machinery, equipment, buildings, hardware, software, brands, etc.) Formally, the relationship between income, personal capability, and the size working instrument is similar to the Cobb-Douglas production function linking total production to labour and capital for the whole economy, but at the personal level. The key difference between mathematical representation of our model and the Cobb-Douglas function consists in the additional term describing all external and internal forces counteracting otherwise unlimited income growth (similar to term discounting adopted in economics). We call this process “dissipation” as adopted in physics since the rate of “discounting” is proportional to the attained level of income and inversely proportional to the size of work instrument. A good example from physics would be the evolution of average temperature in a sphere heated by homogeneously distributed internal source and cooled only through its surface. When the energy flux through the surface is proportional to its temperature, the final (stationary) temperature depends only on the sphere radius, ceteris paribus. Numerous observations confirm that the growth of personal income with age together with the income averaged over the whole population follows the same trajectory as the temperature of a sphere heated from zero.

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