Income inequality for households: a long biased history of Gini ratio. 2021 revision

The Census Bureau measures incomes and reports the estimates. One of the main questions is income inequality – personal and households. We published a post in 2012 on the bias in the household Gini ratio. Here we revise the previous study with new data.

In 2012, our first point was that the Gini ratio for personal incomes reported by the Census Bureau from the very same data set (CPS ASEC conducted every March) does not change much since 1994. The upper panel in Figure 1 reproduces the Gini ratio from the previous post, which varies from 0.494 to 0.512 – a relatively narrow window. In the lower panel, the dataset is extended to 2019 and the rise from 0.494 in 2007 to 0.524 in 2013 is a challenge for an economic explanation. This is a catastrophic and unexpected change in inequality. The years after the Great Recession (say, after 2010 with G=0.503) were not characterized by some outstanding economic processes or events. These were the years of President Obama.

In another post on January 17, 2021, we reported an unprecedented fall in the share of “compensation of employees” in the total personal income (PI) as reported by the Bureau of Economic Analysis. Figure 2 presents the corresponding curve, which demonstrates the accelerated decrease from 0.660 in 2006Q3 to 0.614 in 2016Q3. The 0.046 drop in the share of income from jobs reported by BEA is synchronized with the personal Gini rise by 0.03. The trough in 2020 related to the COVID-19 pandemic may be an interesting economic experiment for income distribution. Personal income in 2020 does not change much (even increase in Q2 and Q3 against pre-crisis expectations) despite the drop in compensation of employees. The question is where we will find the government social benefits to persons (+2.5 trillion in Q2 and +1 trillion in Q3 compared to the previous year). My current guess – stock market.

Figure 1.  Personal incomes:  Upper panel: Gini ratio evolution between 1994 and 2010 as presented in this post. Lower panel. Gini ratio evolution between 1994 and 2019. Between 2007 and 2013 the Gini ratio raised from 0.494 to 0.524, i.e. by 0.03.

Figure 2.  Ratio of compensation of employees and Personal Income (BEA. Table 2.1. Personal Income and Its Disposition). Quarterly data.  The fall 0.655 in the third quarter of 2006 to 0.614 in 2016Q3.

The upper panel in Figure 3 is borrowed from the previous post and shows the history of Gini ratio for households between 1967 and 2010. (The lower panel extends the period to 2019). We normalized the ratio to its maximum value (0.477 in 2011) in order to show that this inequality measure had risen by 20% since 1967. This dramatic increase was interpreted as harm for the US. In my view, this is just a misunderstanding of the income measurement procedures. Unlike personal incomes, the household income data are collected for entities that can evolve in size in all directions. There are two limit cases: 1) all households may have just one person and then the household Gini is fully equivalent to the personal Gini, which is higher as we can learn from Figure 1; 2) all people represent one household and then the Gini is 0 because there is no inequality for 1 object. For a given personal income distribution, any other combination of people gathering in households should give the Gini between 0 and the personal Gini. Reconfiguring the households’ sizes and personal content for the same population one may change the Gini for the household incomes without changing personal incomes. Therefore, the split of the population into households defines the Gini for a given population and time point. The distribution of the increasing number of people among households, i.e. the distribution of household sizes, and the personal income distribution are changing in time, and the household Gini is evolving in sync with these changes. The Census Bureau’s approach is straightforward – they measure the distribution of the household incomes and calculate the Gini ratio. This ratio is incompatible with the previous years since the distribution of household sizes is changing. Moreover, it is changing in the direction of the split of bigger households into smaller pieces, eventually into the single-person-households. Hence, the household income distribution approaches the personal income distribution and this must be accompanied by an artificial increase in the Gini ratio. This increase is reported as a big problem of American households. This is a definitional problem, however, and has no relevance to real changes in income distribution illustrated in the lower panel in Figure 1.   

The Census Bureau does not explicitly report the distribution of household sizes (in persons) and one has to make an own estimate, which is easy, however. Figure 4 presents (old and new) the total household population (different from the civil population or residential population) and the number of households reported by the CB.  Figure 5 depicts (old and new) the evolution of the average household size since 1967. Actually, it was quite spectacular: from 3.2 in 1967 to 2.49 in 2011. Between 2010 and 2019, the mean household size hovered around the 2.5 level. This constant mean size could be interpreted as the constant household size distribution between 2000 and 2019.

Does it matter for the household income inequality?  As we discussed above, the Gini ratio depends on the size distribution of objects if these are not indivisible persons. Intuitively, more low-income (e.g. one person) households result in a higher Gini ratio. The fall in average size indicates that one gets more and more small households over time and … the Gini ratio increases accordingly. The link between the average household size and the Gini ratio is not linear (as we discussed before, many household size distributions have the same average size) but Figure 6 shows the (old and new) product of the normalized Gini curve for households (see Figure 3) and the curve in Figure 5. This product is an approximation of the constant 1967 household size distribution as if all people in every year after 1967 were distributed in the same household size structure as in 1967. This product compensates the size distribution change but does not compensate the income change in the households, i.e. we do not compensate the process of income gain or loss in the households with time, and we do know that the income distribution for a given household size has been changing with time (see these posts). In Figure 6, we see a corrected (and likely closer to reality) Gini history.  This corrected normalized Gini is not fully compensated for the household size changeover time but tells a different story.

The original Gini ratio for households corrected to the change in the household size distribution is depicted in Figure 7. In 2019, the level is the same as in 1967 – 0.397. The positive shift from 1992 (0.358) to 1993 (0.378) is completely artificial. In 1993, there was a revision to income definition and all time series were subject to dramatic changes. Therefore, the current level is below that in 1967 if to use the 1967 household income definition.

Overall, the Gini ratio for households has not been changing as the CB estimate says because these estimates do not take into account the change in the household size distribution.

As we wrote in 2012, this is a methodological error.  The same logic must be applied to family income distribution.  Another sufferer is the mean income.  Since the size of households has been decreasing the number of households has been growing faster than the total household population.  The mean household income must also be corrected for the changing size.  Figure 8 shows the actual evolution of the mean income.  There was a period of constant mean income between 1996 and 2013 with no significant change in the average household size. Since 2014, the mean income curve has been demonstrating tangible growth.

Figure 3. The evolution of normalized Gini ratio for households. Old and new versions

Figure 4. The evolution of the total household population and the number of households (both in thousands)

Figure 5. The evolution of average household size.

Figure 6. Corrected normalized (see Figure 3) Gini ratio.

Figure 7. Original (Census Bureau) Gini ratio corrected to the change in household size distribution. In 2019, the level is the same as in 1967 – 0.397. The positive shift in 1992 (0.358) to 1993 (0.378) is completely artificial. Therefore, the current level is below that in 1967.

 

Figure 8. The growth of normalized (household) mean income and that corrected for the fall in the household average size.

Is the humanitarian society dying?

The history of social development can be explained as the use of profit making part of population by wealth. Farmers produced a larger part of wealth for centuries supporting sustainable population growth.  “Noble” people had harvested the excess profit of food and primitive technical production before effective industrial-size mechanical tools were invented and workers replaced farmers as the excess profit maker. A few centuries exploitation was hard and the working class produced more and more profit allowing replacement of “noble” by the owners of growing factories – capitalists. To protect property the force of knights was replaced by the “power of law” enforced by bought police and court. (Bought means that their budgets are controlled by the governments where the representatives of wealth prevail.) Mechanisms were relatively simple as demanded high skills including masculine power. Workers were the creators of value but the norm of excess profit was relatively small per working hour and a larger part of population had to be involved in industrial production together with farmers with relatively low but increasing productivity. Education was not a production asset and social life was extremely polarized between a small group of the richest and masses.   

The next step was related to the increasing electric power behind industrial production, which demanded more educated specialists/engineers covering routine processing and further development. Services also started to develop at an accelerating rate in order to sustain the health and productivity of the population part providing the highest input to the excess profit. Specialists, together with highly skilled workers, formed the middle class. Education become the driver of economic growth and fast wealth growth. The skills of an average worker became less profitable asset.  The role of the middle class as social life trend maker was high.  

This golden age was not long, however, compared to the periods of farmers and workers as the prevailing profit makers. Computers changed everything and ordinary line engineers were declassified to average workers. Computer champions became the excess profit makers. Wealth (0.1 per cent of the population) now days gets the highest portion of GDP (GDI) ever. As a result, the household median (real) income has not been increasing since the late 1990s. The excess profit is and economic profit was privatized by the wealthiest part of population. Engineers and specialists (except the most effective and productive) lost their power in social and economic life. Computer geeks are quite different as humans  - less masculine power and more creativity sometimes close to psychic illness. Since these geeks provide an extremely high rate of excess profit as individuals unlike chain (production line) workers and engineers the search of these profit makers includes intensive support of their (sub-) culture sometimes in many cases conflicting with the conservative values of the golden age. The larger part of population is excluded from the interest of the wealth first time since the Greek republics. The clash between the wealth defending the profit makers and the conservative majority slowly recognizing own extinction in the process of economic development is the core conflict of the present.  The modern liberals serve as lubricant to detach the majority from the political and social power. Conservative views are not welcome because they suppress unlimited creativity. It needs more money, well compensated by the highest rate of productivity growth provided by the creative minority.  

I do not know how far this conflict will go in the near future and do not care about the winner. The problem is that the next step is likely related to further shift of the excess profit makers to the most creative people at the border of schizophrenia merged with the AI.

This is the way of wealth, not the humanitarian society. This society is dying every minute when the income share of the richest increases.     

What is the most efficient household size?

In my previous post, the evolution of mean family size was presented. In the same post, I also presented the long-term decrease in the mean household size from 2.89 in 1975 to 2.65 in 2011. The households break into smaller pieces as well as families. Here, we address the question of the most efficient size for a household. I propose to measure the efficiency in terms of income per person for a given household size. This measure might be not conventional but definitely explains the fall in the household size as the consequence of maximum income.

Figure 1 depicts seven curves of income per person (the average income for a given household size divided by the household size) for households of different sizes (10 people for the category 7+) normalized to the average household income (for all households) in a given year. The two people household is as efficient as one person household since 1998.  (Figure 2 depicts the same pattern for American families.)  Not surprisingly, the portion of one person and two people households increases rapidly since the start of measurement in 1975. These are two most efficient (in terms of personal income) household sizes. The portion of smallest households will rise in the future along their long term trends. Income rules!

Figure 1. Income per person for households of different sizes (10 people for the category 7+) normalized to the average household income in a given year.  

Figure 2. Income per person for families of different sizes (10 people for the category 7+) normalized to the average family income in a given year.

 

Figure 3. The portion of households of a given size since 1975.

American future – two people families

The U.S. Census Bureau is full of data. I was digging into the problem of the long term evolution of the household and family mean and median income and found a precious piece of measurements. Since 1950, the CB has been publishing the average size of family. For households, this data series is limited by 1975. Figure 1 shows the evolution of both variables. The family mean size was falling between ~1965 and 1990. (I would guess that the household size experienced a similar drop since 1965.) Since ~1990, there was no change beyond the measurement accuracy: 3.16 in 1988 to 3.16 in 2009 and 3.13 in 2011.

What is the reason behind the falling mean size?  Figure 2 depicts the evolution of the number of families of a given size (from 3 to 7+ ) normalized to the total number of families (from 2 people to 7+) in the USA. Figure 2 demonstrates that bigger families started to break into smaller pieces around 1965. The five people families still on a long term decline, but the share of 6 and 7+ people families stabilized around 1990. An immediate result of the split was the increasing share of 2, 3, and 4 people families between 1963 and 1990. However, the 3 and 4 people families started to break more intensively in 1990 and their shares have been on a negative  trend ever since.

Figure 3 shows the only winner of the breakage process – the two people families. By 2025, a half of American families will consist of 2 people!

Figure 1. The mean size of family and households in the U.S. as reported by the Census Bureau.

 

Figure 2. The shares of families with different sizes.

Figure 3. The share of 2 people families.

The effect of measuring procedure on Gini ratio estimates

The Census Bureau publishes Gini ratio for households as based on the Current Population Surveys conducted every March. Unfortunately, the CPS data are not compatible over time. (Actually, the CB mentions that in footnotes, but this is not the best place for general public and even for experts.) Therefore, the estimates of Gini ratio are biased and cannot be used in order to characterize the evolution of income inequality in the US. At the same time, each estimate is accurate to the extent the data and calculation procedures allow. Here we present the case of changing data granularity in 2009 which affected the estimates of Gini ratio for various household sizes.  

It is well known that the total income increases with time due to the increase in nominal GDP and population growth. The Census Bureau was measuring the household income distribution in $2500 bins with the upper limit of $100,000 since 1994. All households with income above $100,000 were counted in the open-ended ”$100,000 and above” bin. In 1994, there were 6,581,000 households in this bin and the portion of income was only 26%. This is not good for the Gini ratio estimation since one bin cover a quarter of all total income. In 2008, this bin accommodated 51% of total income. Such a bin counting is too crude and it makes the Gini ratio calculations almost worthless. Since the higher incomes are distributed according to the Pareto law, i.e. a power law, the CB can and does calculate the Gini ratio analytically for higher incomes.

In any case, the Census Bureau had to increase the bins to $5000 and the upper limit to $200,000 together with calculation of Gini ratio with bin counting up to $250,000 (the readings in the bins above $200,000 are not published!).   For the convenience of the CB, this change is appropriate. But it induced a step in the Gini ratio time series. Figure 1 displays the jumps for households of various sizes – from one person to seven+ people. Since households with more people have higher incomes one can expect that the portion of households with $100,000+ income increases with household size. The change in bin granularity and the upper limit from 2008 to 2009 has to change this portion and induce a step in the Gini ratio series.  Table 1 lists these portions for 2008 and 2009 as well as their ratios.

Table 1. The portion of households with income above $100,000 in 2008 and $200,000 in 2009.

	2008	2009	ratio
One person	0.054	0.008	6.52
Two people	0.213	0.037	5.69
Three people	0.270	0.048	5.61
Four people	0.339	0.068	4.99
Five people	0.311	0.071	4.36
Six people	0.282	0.057	4.90
Seven people or more	0.278	0.053	5.20

We illustrate the step in Gini ratio using the overall income distribution. The overall Gini was calculated using the Pareto law approximation for the higher incomes and thus is not biased as the estimates of individual household sizes.  Figure 2 depicts three Lorentz curves based on the relevant CB estimates of household income distribution in 1994, 2008, and 2009. One can see a dramatic difference in Lorentz curves in 2008 and 2009. The high income bin with a half of total income makes the 2008 Gini ratio to be highly underestimated compared to the 2009 estimate. Both curves are identical for 85% of population, however. The 1994 curve also coincides with the 2009 one up to the last bin. Table 2 compares our estimates of Gini ratio and those reported by the CB. One can see that the 2008 CB estimate is corrected, but the step of 0.023 well reproduces the step observed for the individual household sizes in Figure 1.

Table 2. The estimates of Gini ratio in this post and those reported by the CB.

	Gini ratio	CB Gini ratio
2009	0.466	0.465
2008	0.443	0.466
1994	0.457	0.456

 

Figure 1. The evolution of Gini ratio for individual household sizes. Notice the step between 2008 and 2009.

Figure 2. The Lorentz curves for household income distribution in 1994, 2008, and 2009, as constructed from the CB income distributions without approximation of the higher incomes by the Pareto law.