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-
3.1 Data Sources, Methodology and Measures
The data used herein is from the Federal Reserve Board’s Survey of Consumer Finance (2013). The following empirical sections utilize first the data for survey
23Brunnermeier and Sannikov (2014) have devoted a considerable part of their study to this issue.
24See Sects.3.2and3.3and also Cynamon and Fazzari (2016).
25For a further elaboration on the aggregateqt;see Brunnermeier and Sannikov (2014, sect. 2).
26Data from the 2013 SCF as well as links to the data used herein may be found on the Board’s public website at www.federalreserve.gov/econresdata/scf/scfindex.htm. Additional scripts to download all micro data in R programming language, are available at the following url:https://github.com/ajdamico/asdfree/tree/master/Survey%20of%20Consumer%20Finances
observations for the wage income covering the years 1989–2013. A second further breakdown of the data in Sect.3.3is utilized for the normalized income variable covering the years 1995–2013. Wage income is analyzed according to the lower 80th percentile and top 20th percentile split discussed in the previous theoretical model.
Additional analysis of empirical trends, in Sects.3.3, 3.4, and 3.5, utilize the normalized income variable as a classifier which is available for survey years 1995–
2013. This is done in conjunction with our categorization of wage earners and capital earners via the determination of a capital difference variable consisting of the difference between wage incomes and capital incomes as a percentage of the sum total of incomes. It should be noted that all appropriate figures are CPI adjusted according to the Federal Reserve’s published figures. It was necessary for example, to adjust the component parts of net wealth in such a manner that comparisons would hold across the time period in question while variables such as age, marital status, etc. would remain unchanged.27
The capital difference ratio was created by determining the types and sources of income. The wage income variable was slightly limiting in SCF data as it would not account for employment transitions and various other sources of working income that are relevant for additional portions of the population. Hence, the more comprehensive use of normalized income allowed for greater partitioning of observations for empirical analysis and visualization of potential trends in the data sets.
The capital difference ratio utilized the component portions of total income to determine the difference between wage incomes and capital incomes as a percentage of the total sum of these parts. The absolute value was taken since variables in SCF data may turn negative due to outgoing cash flows such as alimony and this analysis is focused on the total impact each income source had on the sum total of individual’s incomes. Additionally, the purpose is to determine what gains/losses come from what type of source as a percentage of the whole and then look at the weighted percentiles within society.
Capital Difference RatioD ABS.Working Incomes/ABS.Capital Incomes/
ABS.Working C Capital Incomes/
with
Working Incomes D .WagesCSocial Security Retirement Income/ Capital IncomesD.Business Farm IncomeCInterest DividendsCCapital Gains/
27All CPI adjustments followed precisely those used by the Federal Reserve in publishing the triennial bulletin “Changes in U.S. Family Finances from 2010 to 2013”, associated with the Survey of Consumer Finances and within the provided SAS code used for the publication.
Density 0.000.050.100.150.200.250.30
1 0.789 0.474 0.158 0.158 0.474 0.789 1 Fig. 3 Histogram of the capital difference ratio
The capital difference variable can be viewed as a histogram in which the number fluctuates from positive one to negative one with most individuals receiving their income from working wages. Therefore, Fig.3displays the majority of observations as maintaining a ratio closer to 1 as expected since most individuals work for a living. The few cases of a value of 0, were excluded and found to be extremely uncommon in the sample data. The sample density is demonstrated on they-axis, while thex-axis displays the capital difference ratio.
Figure3can be thought of as showing that when the population is broken down into primarily wage earners as opposed to capital earners the individuals will occupy a position within the range from 0 to 1 on the histogram. However, if individuals primarily earn income from capital sources then they will occupy a position ranging from below 0 to negative 1. All members within society then oscillate within the1 toC1scale of this variable. Clearly, one can see from the SCF data that most of society will make their incomes from standard wages identified by a value primarily approaching +1.
Density 0.000.050.100.150.200.250.30
0 0.105 0.211 0.316 0.421 0.526 0.632 0.737 0.842 0.947
Fig. 4 Histogram of capital income to total income
Another interesting observation utilized for corroboration of the previous find- ings is to simply look at the ratio of capital income-to-total income. In this ratio, one may observe the distribution on a scale from 0 to C1, which makes greater intuitive sense visually. Figure4displays the results for this second societal trend in SCF data. The ratio of capital income-to-total income was derived based on the previous equations as follows.
Capital to Income RatioD ABS.Capital Incomes/
ABS.Working C Capital Incomes/
As one can see from Fig.4, the majority of the population rests within a lower placement on the capital-to-total income histogram. The largest distribution is located towards but slightly above 0 on the histogram while substantially fewer individuals exist towards a capital-to-total income ratio of +1. The logic for this finding is similar to that found in the previous figure. In general, the vast majority of people in society work for a living receiving wages and do not receive most of their income from capital sources and investments.
A further breakdown of this variable in society is expanded upon in Sect.3.5.
As we subdivide the data through the years this variable provides a more dramatic visualization of changes in capital income trends within the U.S. population.
This helps to provide some enlightenment with regard to such trends as the U.S.
approached the housing and financial crises of 2007. As we proceed through the next several empirical sections, we begin to analyze the disparities and greater reliance on capital incomes with regard to changes in individual’s net wealth through the last two decades in modern U.S. economic history with a particular emphasis on the heterogeneous households described in Sect.2.
Fig. 5 Level of top 20% net worth households (left scale) and of bottom 80% of net worth households (right scale)