Corollary 3 Marginal Rates of Substitution of the Tax Rates for the Log- Utility Case) Let the utility function of the representative household be logarith-
3.4 Life Cycle Aspects of Income and Wealth
The topic of age is worth mentioning since, as individuals age and gain experience, income grows while asset holdings change as does the type and size of debt holdings. For example, later in life many individuals will have paid off most mortgages related to housing purchases necessitating a change in net worth.
Additionally, some individuals will have acquired more financial assets allowing for greater returns to capital than others for whom the primary source of savings is their income.
Figures10and11display median normalized income (as defined in Sect.3.2) over net worth on they-axis for different income percentiles of the population (noted in the right side legend) based on age for two distinct population groups through time. The first group is the 50th percentile for whom wage income (as defined by
Fig. 10 Lower 50th percentile working-capital ratio
Fig. 11 Upper 50th percentile working-capital ratio
the capital difference ratio in Sect.3.1) constitutes a primary percentage of total income and the second group is that part of the population for whom capital income becomes an increasing percentage of their total income.
Median numbers are used to omit the effects of larger outlying values within the population that do not fully reflect the performance of the vast majority of individuals within the respective income bracket. Additionally, normalized income was used in the numerator so as to smooth the effects of temporary shocks in respondent’s annual earnings. The right hand side of each graph lists the income
brackets of the lowest 50%, middle 40% and top 10% of income earners and the horizontalx-axis reflects the years 1995 through the present.
The biggest discrepancies within each graph are those between the lowest 50th percentile (denoted in blue) and the top 10% (denoted in green). For example, when the blue line grows higher and the green line remains even or decreases. This reflects the normalized income of the lowest 50th percent of the population of primarily wage earners becoming a larger percentage of their net worth while the opposite may be said of the top 10%. The reason is primarily that during economic shocks, the lower percentiles appear to take on more debt for consumption, while easy- money policies raise the asset values held by those in the top 10% of income earners.
Essentially, the spread between these two lines greatly reflects an inequality in the composition and determinants of net worth for these two groups as well as distinctly different spending habits.
One observation in the data is that debt did not dramatically increase during these same times for those in the top 10% of the population while composite risky asset holdings increase with the income grouping relative to other percentiles. A similar finding is postulated in Semmler (2011)33when discussing dynamic portfolio theory and the pension fund problem that, to the extent that income may shield against volatility in asset prices, some may then choose to allocate greater percentages of wealth to risky assets.
It should also be worth noting that as individuals age, they begin to spend more of their net worth, especially during significant economic shocks. This can be seen in the rising normal income-to-net worth line (denoted in green) for the top 10% of older wage earners. In terms of the age designations, the younger workers were aged 20–39, while the middle aged workers were aged 40–59 and the older workers were over the age of 60. Additionally, the capital-difference ratio, outlined in Sect.3.1, was used to determine whether more income was being earned through wages as opposed to capital sources.
The data demonstrates that for the youngest percentiles of earners, accumulated savings in assets is far from its future realized potential since many of the individuals are still in their twenties. However, as one can see, the trends are not quite as pronounced for capital earners of each age group as they are for individuals dependent upon the wage for contributions to the agent’s net worth.
Additionally, it is interesting that, with the exception of the younger wage earners, for all other age groups of both wage and capital earners, the only group to see a CPI adjusted increase in net worth since the 1990s was the top 10% of income earners. Once again, most of this change is due to increases in composite risky asset holdings. Therefore, even if normalized income decreased for the top 10% as well
33The discussion, in section 18.5, specifically involves a dynamic portfolio decision with risky assets and labor income for consideration of the pension fund problem currently facing many retirees. In such a model the low frequency components ofLtmay be estimated using harmonic estimations.
as the bottom 90% the effect on net worth was not as detrimental to financial well- being for those individuals lucky enough to be in the top 10th percentile of income earners.
Finally, it is important to note the changing scale between the percentages reflected in Figs.10 and 11. For example, the incomes tended to rise slightly between wage earners and capital earners based upon the capital-difference ratio used and depicted in Sect.3.1. However, the primary difference between these two groups was their accumulated net wealth. Hence, if normal income increased slightly between equivalent ages between the two groups, net wealth increased far more dramatically changing the scale of the depicted ratios accordingly. Hence, for example, among capital earners normal income appears to be a far smaller percentage of net wealth than for wage earners, which makes intuitive sense.