This study is devoted to cross country comparison of specific characteristics related to personal income distribution (PID). Not all countries provide open access to their estimates of income obtained from surveys, tax and administrative records. The U.S. has likely the best system of income measurements and the longest historic time series, with almost all data (except may be data in the highest income range) available in digital format from various governmental agencies, private companies, and universities. For the U.S., we have already presented select results of the comprehensive study conducted since 2003 [1,2]. There are two characteristics which best express the evolution of personal income distribution (PID) with age and time. First characteristic is related to the mean income dependence on age which evolves in time following up the increasing real GDP per capita. The age of peak mean income grows as the root square of the real GDP per capita and this phenomenon in clearly observed in the personal income data published by the U.S. Census Bureau since 1947. A similar feature is observed in the dependence on age of the proportion of people with the highest incomes, which in the second characteristic of the PID in the U.S.
Both studied dependencies on age provide the level of income aggregation which best balances the clarity of observed changes and suppression of larger fluctuations related to numerous revisions to survey questionnaires (i.e. revisions to personal income definition) and the accuracy of measurements themselves. For example, while two studied characteristics demonstrate well measurable changes, the estimated values of Gini ratio for the CPS personal incomes has just marginal fluctuation between 0.50 and 0.52 since 1962 . We use the CPS data for people with reported income to calculate a consistent time series for this ratio for the whole period between 1947 and 2014. At the same time, the level of fluctuations observed in the original microdata is so high that there is no explanation of the observed changes in narrow age and income bins for sequential years.
Therefore, the dependence of mean income and proportion of people with the highest incomes on age provides reliable measures of the evolutionary behavior and robust statistical inferences related to the driving force behind this evolution. The U.S. data gives the best and longest historical prospective of time and age dependent processes in the personal income distribution. However, there is always a question about the universal character of the observed evolution with real GDP per capita. This study answers this question to the extent limited by the availability and accuracy of personal income data. (We are going to proceed with new dataset when available.) On the whole, we give a positive answer – the dependence of mean income and the proportion of people with the highest incomes on age as observed in the USA is reproduced one-to-one (considering data accuracy) in Canada, New Zealand, and the UK. The curves observed in these three countries repeat those observed in the U.S. for the years when the level real GDP per capita was the same. This observation seems to prove that the evolution of personal income (at least in these four countries) follows the same path, i.e. this is a universal characteristic related the only driving force - real GDP per capita.
1. Personal income definition
We start with a slightly provocative statement that there exists no comprehensive and accurate definition of personal income, which can be used for a true estimate of age/gender/race-dependent properties. There are several operational definitions of personal income measuring different portions of the true personal income, the definition of which does not exist so far. Having no genuine income values one is forced to use only available data. In such a situation, the accuracy and coherency of sequential estimates are two most important issues. To conduct a reliable quantitative analysis, one can use any constant portion of the true value and get almost the same predictive power of the obtained relationships as that obtained from the true value itself. For example, a voltmeter accurately measures a voltage using just a small portion of total electric current.
When several sources of data are available it is worth to compare how similar are the features we study as estimated from different datasets. For example, do they reveal the same dependence of mean income on age? This is important aspect of the study by itself since it provides a reasonable constraint on data accuracy. In a cross country comparison, it is especially important because the datasets reported by countries may have different sources. For example, the UK provides an extensive set of income time series based on tax data, while New Zealand publishes the results of annual income surveys conducted in the second quarter of each year. For the U.S. both sets are available and thus it is a straightforward task to compare them before we study other countries.
Figure 1 schematically compares the personal income estimates as reported by three agencies, which provide related statistics: the Bureau of Economic Analysis (BEA), the Census Bureau (CB), and the Internal Revenue Service (IRS). The BEA has been reporting accurate aggregate estimates of the total personal income (PI) and its distribution over major sources (e.g., wage and salary, contributions for employee pension and insurance funds, personal income receipts on assets, etc.) since 1929. With all important procedures, tools and estimates allowing tight control over other sources of income data, the BEA does not provide fine structure of the personal income distribution in the USA. For the purposes of our study, it does not report age, gender and race distribution of personal incomes. This set of personal data cannot be used. In Figure 1, only the ratio of total personal income (PI) and Gross Domestic Income (GDI=GDP) since 1947 is presented. In the year of 1947, the annual income surveys in the U.S. were started.
The Internal Revenue Service provides the longest time series of income data – some variables begin in 1913. Figure 1 depicts two time series related to the IRS. The number of individual tax returns (a proxy to the number of people) is divided by the total working age population (age 15 and above) for the same year and represents the portion of people with income. In the 1950s and 1960s, the proportion of people with (IRS) income was between 50% and 52%. In the 2000s and 2010s, this proportion was between 57% and 60%. The total income reported to the IRS, which is called Adjusted Gross Income (AGI) is divided by the GDI and represents the portion of personal income (according to the IRS definition) in the GDI. The BEA carries out annual inspections of all incomes included in the AGI and reports very specific errors in the IRS statistics. For example, the gap between the AGI estimate reported by the NIPA (National Income and Product Accounts) and that of the IRS reached 15% in 2005. This gap puts some constraint on the accuracy of the IRS personal income estimates. Unfortunately, these errors are aggregated. They are not distributed over age and so on.
There are several income time series reported by the IRS, which can be used in our study. They include the number of people in finite bins extended to $10,000,000. This is a very high income in comparison with the current level of $250,000 in the CPS, which is, however, reported only from the mid-2000s. The IRS datasets are of crucial importance for estimating the properties of the highest incomes distribution, i.e. the portion of people above some high threshold. The Pareto law implies that the PID above such a threshold should follow up the power law. In addition, the income distribution in five-year age bins (and for two genders) is published for the year of 1998. Similar distributions for ten-year bins are available for the years between 2008 and 2012.
Figure 1. The proportion of people with income reported by the Census Bureau from the Current Population Surveys (CPS) and the number of returns reported by the Internal revenue Service (IRS) in the total working age population. The proportion of total personal income reported by the CB and IRS in the Gross Domestic Income (GDI=GDP). For comparison of various definition, the estimate of personal income estimate (PI) reported by the Bureau of Economic Analysis is shown.
The Census Bureau provides the finest distributions of personal income over numerous parameters. The Census Bureau uses the mechanism of annual Current Population Surveys to measure personal incomes in approximately 80,000 households. In order to map this smaller population subset to the entire U.S. population the CB uses the age-gender-race dependent scaling coefficients for each person in the CPS. By construction, this approach has much lower measurement accuracy for underrepresented categories. For example, young black females with higher incomes have very low probability to be present in the CPS. Sometimes, one or two persons represent the whole population in the same age-gender-race category. As a consequence, larger fluctuations are observed in the related distributions. In Figure 1, the portion of population with income (as reported in the CPS) in the total working age population is presented together with the portion of the CPS total income in the GDI. The total CPS income is also the estimate obtained from the 80,000 households and then scaled to the whole population. In 2012, the CPS population universe presumably included approximately 87% people with income; the IRS gave only 57%. At the same time, the figure of total personal income reported by the CB was about 57% of the GDI, i.e. the same as reported by the IRS. The CB has a quite specific definition of personal income: “CPS money income is defined as total pre-tax cash income earned by persons, excluding certain lump sum payments and excluding capital gains”, while “BEA personal income is the income received by persons from participation in production, from government and business transfer payments, and from government interest.TP 1 PT BEA estimates personal income largely from administrative data sources” (Ruser et al., 2004). Therefore, the CB’s personal income estimates are also known as “CPS money income”. It is important that larger part of the difference between the CB’s and BEA’s estimates (around 25% of the CB’s income) can be explained by the differences in income sources. The error in wage and salary estimates (underreporting) in the CPS can reach 5% to 10% of the total CPS income.
This is the level of accuracy of personal income data we have to work with. In addition, the IRS dataset has a significant problem with the population coverage. The proportion of people with income not only relatively small but also varies with time. Together with the observed high-amplitude oscillations in the AGI the variations in the number of returns induces measureable fluctuations in the high-level estimates of inequality (e.g. the Gini ratio) e, with the less aggregated measures of personal income experiencing even larger disturbances. In this sense, the CPS data set has clear advantages since all income estimates are scaled to the whole population. As a consequence, the measures of income inequality are not changing much due to data inconsistency over time.
Detailed comparison of the PIDs reported by the IRS and CB is beyond the scope of this study. Merging of the IRS high-income data and CPS low-income estimates is a delicate issue and deserves a special study, which may result is a more reliable time series based on a more precise definition of personal income. Here, we compare only one of the characteristics under investigation – the evolution of mean income with age. Figure 2 displays the distribution of people and income over age as reported by the CPS and IRS for the year of 1998. This is the only year when the age dependent mean income is reported by the IRS in narrower age bins. For the years between 2008 and 2012, the IRS reported mean incomes in age bins incompatible with those used by the CB. The CPS counts more people in all age bins and larger total incomes everywhere.
Dividing the total income by the number of people in a given age bin we obtain an estimate of mean income. Figure 3 depicts various mean income curves as reported by the IRS and Census Bureau. To present the CPS data, we use three different data sets. The IPUMS provides the original income measurements (microdata), which allow calculation of mean incomes in one-year bins. The resulting curve in Figure 3 is characterized by visible fluctuations, which are especially large near the peak mean income. Therefore, these estimates are not helpful for accurate comparison with the IRS data. The mean income reported by the CB in five-year bins (see Table PINC-01. Selected Characteristics of People 15 Years and Over, by Total Money Income in 1998, Work Experience in 1998) provides the best case comparison with the IRS data, while the mean income distribution in ten-year bins may cause some problem in the estimation of the age corresponding to the peak mean income.
Figure 3 reveals the difference in income sources used by the CPS and IRS. The Census Bureau reports higher mean incomes for the youngest and eldest population. At the same time, the IRS mean income is higher for ages between 40 and 65 years. The largest difference is observed near the peak mean income. Despite the discrepancy in the IRS and CPS curves, the most important observation is that the age when these curves reach their peak values are very close. To better illustrate the coincidence of peaks in the mean income distribution we normalized all curves to their peak values. Figure 4 displays two curves for five-year bins and also presents the curve obtained from the IPUMS microdata but now smoothed with a centred nine-year moving average – MA(9). All three curves are characterized by peak at 52.5 years. This is the age of the largest mean income in 1998. As we know, the peak age in the U.S. has been increasing with real GDP per capita and was above 55 years in 2012.
In this Section, we demonstarte that income estimates provided by the Census Bureau and IRS are close in dimensionless representation. This result is valuable for further comparison of income data obtained by various agencies in different countries. For example, we assume that the similarity of CPS and IRS data in the U.S. allows us to compare tax-related data reported by the UK for a given year and some CPS data twenty to thirty years earlier.
Figure 2. The number of people (upper panel) and total income (lower panel) in five-year bins (except the bin between 15 and 24 years of age) as reported by the IRS and CPS for the year of 1998.
Figure 3. The mean income as a function of age as reported by the Census Bureau (CPS) and the Internal Revenue Service (IRS) for 1998. This is the only year with a fine (five-year age bins) age-dependent personal income distribution reported by the IRS. For comparison, we use the set of microdata published by the IPUMS for 1998. To illustrate the difference in the presentation of income in various bins, the mean income curve based on ten-year bins borrowed from the CB historical dataset is also shown. The mean income for the youngest and eldest age groups is higher than that reported by the IRS. Between 40 and 65 years of age, the IRS mean income is higher.
Figure 4. The IRS and CPS microdata curves in Figure 3 are normalized to their peak values. The age of peak mean income is the same for the CPS and IRS.
2. Cross country comparison
2.1. GDP per capita
The main assumption of our study is the dependence of some aggregated properties of personal income distribution only on real GDP per capita. This implies that countries with lower GDP per capita have to repeat PID features observed in the countries with higher GDP per capita. To compare different countries we borrowed real GDP per capita estimates from the Total Economy Database (TED) operated by the Conference Board. Figure 5 displays the evolution of real GDP per capita in the USA, UK, Canada, and New Zealand as expressed in 1990 US$ converted at Geary Khamis PPPs. As we assume that the accuracy of income measurement has been increasing with time the most recent estimates for the latter three countries likely have some advantages to be used for a reliable cross country comparison.
In Figure 5, three horizontal dotted lines show the level of GDP per capita in some country specific year between 2011 and 2014. Their intersections with the USA curve provide the years when the US personal income presumably had the same aggregated characteristics. For example, real GDP per capita in the UK was $23,272 in 2012. In the USA, approximately the same level was observed in 1992 ($23,363). For New Zealand, the estimate of $20,526 in 2014 gives 1985 as the matching year. In Canada, the level of $25,400 in 2011 corresponds to that measured in the USA in 1996. One has to take into account that the PPP values are subject to revision and may not be accurate for some countries and years. Moreover, the PPP curves may differ dramatically from those expressed in domestic currency. Then a problem arises which of two estimates is better to use for our cross country comparison.
Figure 5. The evolution of real GDP per capita in 1990 US$ (converted at Geary Khamis PPPs) as borrowed from the Total Economy Database reported by the Conference Board. Cross comparison of the dynamics of personal income evolution in four (English speaking) developed countries for which we have retrieved data from open sources – Canada, New Zealand, the UK, and the USA. Three horizontal dotted lines show the level of GDP per capita in three countries in some country-specific years between 2011and 2014 and their intersections with the USA curve provide the years when the US personal income presumably had the same characteristics.
2.2. The United Kingdom
The United Kingdom is the first country to compare with the U.S. All income-related tables were borrowed from “Distribution of median and mean income and tax by age range and gender”, which is a part of the UK Government portal. The age-dependent income data are obtained from the Survey of Personal Incomes (SPI), an annual sample survey carried out by HM Revenue & Customs. The income tables include only information on individuals liable to UK income tax, i.e. sources of income are restricted to tax purposes only. Therefore, the UK income tables are better to be compared to those reported by the U.S. IRS. In paragraph 2.1, we found that the level real GDP per capita in the UK lags by about 20 years behind that measured in the USA. Under our framework, the shape of the age-dependent mean income curves depends only on real GDP per capita. Then the U.S. curve to compare to the 2012 UK mean income is that for 1992. Since the data on the years before 1993 are not available from the IRS we have to use the CPS income tables. Such a replacement may introduce some distortions in matching process. However, as shown in Section 1, the IRS and CPS estimates of peak mean income age are very close.
We start with the time history of age-dependent mean income in the UK, which is confined to the years between 1999 and 2012, since the original tables (1999-2000 through 2012-2013) are available only for this period. There are no estimates for 2008 as the relevant table is not published. Figure 6 presents the evolution of age-dependent (nominal) mean income (expressed in GBP) with time. The presented curves are obtained as spline interpolations between actual estimates in 5-year age bins. The shape of these curves is similar to that observed in the U.S. – quasi-logarithmic growth to the peak value and then quasi-exponential fall. The age of transition from growth to fall, i.e. the age of peak mean income, has been increasing with time. If the shape of the mean income curve depends only on real GDP per capita the age of peak in the UK has to follow up the same trajectory as in the U.S., with the GDP per capita as defining parameter.
Figure 6. The evolution of age-dependent mean income between 1999 and 2012. No estimates are available for 2008. The absence is likely related to the 2008 financial crisis. The mean income values are assigned to the midpoints of 5-year bins as shown by circles in the 1999 curve. Age is replaced by work experience. The 2012 curve is above all other curved everywhere. The 1999 curve is the lowermost one except in the large work experience range. Three curves between 2001 and 2003 are very close to each other. Almost all curves are characterized by local fluctuations in the bin between 45 and 49 years of work experience. The curves between 2005 and 2007 are smooth, however.
For the purpose of quantitative analysis, age is replaced by work experience. By definition, personal work experience is equal to the age of a given person less 14 years. The mean income estimates are assigned to the midpoints of the respective work experience bins, as shown for the 1999 curve in Figure 6. The only exception is the youngest and open-ended population bin “under 20 years of age”, where no midpoint can be assigned. In Figure 6, we assign the corresponding mean income value to 2 years of work experience by force and use this estimate only for illustration. The 2012 curve is above all other curves everywhere. The 1999 curve is the lowermost one except in the large work experience range. Three curves between 2001 and 2003 are very close to each other. Almost all curves are characterized by local fluctuations of varying amplitude in the bin between 45 and 49 years of work experience. The curves between 2005 and 2007 are smooth, however. The cause of this difference is not clear and we do not consider all possible deviations between the UK and U.S. mean income curves in this age range.
Since individual incomes in different countries are measure in domestic currency one cannot carry out a direct comparison of mean income curves. Scaling to some common currency (e.g. USD) is possible at, say, PPP conversion rates, but in terms of shape comparison this procedure would not differ from the normalization of the mean income curves to their respective maximum values. This was a standard procedure in comparison of U.S. incomes for the period between 1947 and 2011 (Kitov and Kitov, 2013) and we have applied in to the UK data. Figure 7 displays the same curves as in Figure 6 but normalized to their respective peak values. There are two clear observations – the work experience corresponding to the peak mean income increases with time (actually GDP per capita) and the 2012 curve now lies below all other curves before the peak value and above after the peak work experience. We call the age (work experience) corresponding to the peak mean income “critical age” or “bifurcation point” since the behaviour of the mean income curve changes from quasi-logarithmic growth to exponential fall. In this point, the process of income distribution suffers some dramatic changes, and this is not the age of retirement. In the U.S., the critical age was measured between 35 and 40 years of age seventy years ago and currently approaches 60.
Figure 7. Same curves as in Figure 6 with all mean income estimates normalized to the peak mean incomes for the respective years. The growth in the work experience corresponding to the peak value is clearly seen.
In order to estimate the age of peak mean income, Figure 8 presents the central segments of the curves in Figure 7. The normalization procedure results in dimensionless estimates of the average income assigned to the midpoints of the corresponding age bins. The lines drawn through these estimates do not represent actual values of dimensionless mean income except in the midpoints. They are spline interpolations of these estimated values, with the age of the maximum value in the obtained curves likely to be shifted from the midpoint of the bin with the peak value. (Therefore, some curves may be above 1.0.) These estimated maxima are then used to evaluate the shift in the age-dependence mean income. In Figure 8, the 1999 curve (thick blue line) has a larger work experience peak (around 31 years) than the peak age for 2000 and 2001 (dotted lines) - between 28 and 29 years, as well as for 2002 and 2003 (dashed lines) – around 30 years. The curves between 2004 and 2011 are characterized by a gradual increase in the peak age, with the 2012 curve (black line) peaking at approximately 32.5 years of work experience. Therefore, the 1999 curve likely includes some biased estimates and we do not use it in the following quantitative estimates.
Figure 8. The age (work experience) of peak mean income increases with real GDP per capita. The 1999 curve (thick blue line) has a larger work experience peak than those for 2000 and 2001 (dotted lines) around 28 years, as well as for 2002 and 2003 (dashed lines) – around 30 years. The curves between 2004 and 2011 are characterized by gradual increase in the peak age. The 2012 curve (black line) peaks at 32.5 years. Therefore, the 1999 curve likely includes some biased estimates.
Figure 8 demonstrates the evolution of the normalized curves and proves that the work experience corresponding to the peak mean income increases from approximately 28-29 years in 2000 and 2001 to above 32 years in 2012-2013. The estimates of real GDP per capita are $20,207 and $23,017 in 2000 and 2012, respectively. Theoretically, the working experience should increase from 28.5 years to 28.5√(23017/20207)=30.9 years. The estimates of average disposable income reported by the OECD give a slightly larger age growth between 2000 and 2012 - 2.7 years. So, the assumed root square dependence suggests that the theoretical difference between the peak ages has to be approximately 2.4 to 2.7 years. Considering the accuracy of the peak age and GDP/income measurements, the match between the predicted increase of 2 to 3 years and the observed one of approximately 4 years is a good one. For better estimate, one needs a much longer and more accurate time series.
Historically, population in the UK needs more and more time to reach the peak mean income. According to our microeconomic model (Kitov and Kitov, 2013), this effect is caused by increasing sizes of work capital, with the growth proportional to the root square of the real GDP per capita, similar to the Cobb-Douglas production function. This allows higher personal incomes (as well as real GDP per capita) to be achieved by all individuals in a given economy. Basically, the mechanism allowing getting higher incomes consists in decreasing discounting factor counteracting income growth. For a given person, the rate of income discounting is proportional to the attained level of income and inversely proportional to the size of work capital applied by this person. Mathematically, this term leads to a slower relative discounting for incomes earned with the largest work capitals.
One negative outcome of the increasing real GDP per capita is that the relative share of income in the youngest age group is subject to gradual decrease, which is inevitable in the current system of economic and social ties. Figure 9 presents the evolution of the normalized mean income in all age groups; the group “under 20” is not shown. Three youngest age groups: 5 to 9, 10 to 14, and 15 to 19 years of work experience, are characterized by a falling proportion of their mean income since 1999. This trend cannot be reversed in the future if real GDP per capita will be growing. Between 2000 and 2003, the peak work experience shifted from the 25 to 29 years bin to the 30 to 34 years bin. Such a transition happens not often and we are lucky to find it in the UK data. The next transition will be to the 35-39 years bin. One can observe that the proportion of mean income has been also increasing in this group. The peak mean income will likely move into this age group in the next 10 to 15 years, depending on real GDP growth. The proportion of mean income in the elder categories has been increasing as well. The 25-29 years of work experience group lost the peak and joined the category of younger population.
Figure 9. The evolution of mean income in all 5-year age groups normalized to the peak value in the same year. In three youngest age groups (7, 12, and 17 years of work experience), the proportion of mean income has been falling since 1999. The peak work experience shifted from the 25 to 29 years bin to the 30 to 34 years bin between 2000 and 2003. The proportion of mean income has been increasing in the group between 35 and 39 years. The peak will likely move into this age group in the next 10 to 15 years, depending on real GDP growth. The proportion of mean income in the elder categories has been increasing as well.
The increasing age of mean income peak and the decreasing income portion of the youngest population observed in the UK both confirm similar features observed in the mean income distribution in the USA. Therefore, the evolution of personal income distribution in the UK likely follows the same dependence on age as in the USA. As discussed above, in case this dependence is, mathematically, a universal one, the curves in Figure 7 have to repeat similar curves observed in the U.S. in the years defined by GDP per capita.
In paragraph 2.1, we have evaluated that the UK curve for 2012-2013 has to match the U.S. curve for 1992. For this comparison, we used income microdata published by the IPUMS. As before, we have smoothed the annual mean income estimates with a centred MA(9). Figure 10 is the key evidence in favour of universal character of the mean income dependence on real GDP per capita. Despite all differences in sources of data and measuring procedures the shapes of two curves, separated by 20 years full of economic, social, demographic and so on processes and events in the UK as well as country boarders and the intrinsic difference in all aspects of life between the UK and USA, is practically identical! In order highlight the level of similarity between these two curves we added two lines corresponding to 1991 and 1993 in the USA. The 1991 curve deviates from the UK curve, while the 1993 curve is very similar to the 1992 curve. The GDP per capita estimates are $22,875, $23,363, and $23,690 in 1991, 1992, and 1993, respectively. Unfortunately, we do not have any IRS data for 1992. The small discrepancy in two curves in Figure 10 between 25 and 29 years of age could have the same cause as the deviation in Figure 3 – the IRS mean income for younger ages is smaller than that measured by the Census Bureau.
Figure 10. Comparison of the UK mean income curve for 2012-2013 and that observed in the USA in 1992. Microdata provided by the IPUMS are used.
Figure 11. Comparison of the UK mean income curve for 2000-2001 and that observed in the USA in 1984.
For the earliest reliable UK mean income curve (2000-2001) we found the best matching year as well. This is the mean income curve for 1984. Figure 11 compares two corresponding UK and U.S. curves and demonstrates almost the same level of fit. The only difference – two curves deviate at ages above 55. According to the Conference Board, the level of real GDP per capita in the UK in 2000 was $20,207 (1990 US dollars). Almost the same figure was observed in the USA in 1984 - $20,122. Here, we have to stress that the time delay in real GDP per capita between two compared countries plays no role for mean income distributions. Time is just a parameter useful for indexing GDP measurements.
For the UK, we have analysed a relatively short time series of the distribution of mean (tax-related) income with age and found matching distributions in the much longer CPS income dataset available for the USA. The most important result of our analysis is the universal functional dependence of the aggregated income characteristics on real GDP per capita. The UK GDP per capita is lagging by a few thousand USD (in 2014, approximately $9000 as expressed in 1990 USD) behind that for the USA. The shape of the current mean income distribution UK repeats that observed in the earlier 1990s in the USA. This means that one can project the evolution of the mean income distribution in the UK by $9000 ahead. This makes 15 to 25 years depending on the annual growth in real GDP per capita. Having the projection of major features in the personal income distribution one can develop a wise socio-economic policy to mitigate the most damaging effects. Projection beyond the current distribution in the USA is also possible since the evolution of mean income is driven by real GDP per capita only.
For the UK, the distribution of people over income is not available and we could not make any estimation and comparison of the portion of people with higher income, which is the second important indicator we use to characterize the increase in the age when population of developed countries achieves the highest incomes. This portion is most sensitive to age and real GDP per capita, especially in the first few years of work experience. For the USA, we have already demonstrated these effects.