The Census Bureau measures incomes and reports figures. Experts discuss
and panic. The fame depends on the claim of disaster with inequality. It must
grow; otherwise economic commenter would lose public power. Who is interested in
the topic when no change is observed? Let’s
try to dig into raw data and find the reason for the observed tendency. Our first
point is that the Gini ratio ( the most famous measure of inequality) 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. Figure 1 reproduces the Gini ratio, which varies from 0.494 to
0.512 – a relatively narrow window.

Figure 1 . Personal incomes: Gini ratio evolution since 1994.

In Figure 2, we present a sad
history of Gini ratio for households. We
intentionally normalized the ratio to its maximum value (0.477 in 2011) in order
to show that this inequality measure has risen by 20% since 1967. This dramatic
increase is interpreted as harm for the US. Unlike personal incomes, the
household data are collected for entities which can evolve in size. (A person always
has a unit size.) The Census Bureau does not explicitly reports the distribution
household sizes and one has to make an own estimate, which is easy, however.
Figure 3 presents the total household population (different from civil population
or residential population) and the number of households reported by the CB. Figure 4 depicts the evolution of the average household
size since 1967. Actually, it was quite spectacular: from 3.2 in 1967 to 2.49
in 2011.

Does it matter for the income inequality? Sure - yes. The simplest ways is a household
split - instead of one big household one gets two smaller households. The Gini
ratio depends of the distribution of sizes. More low-income households result
in a higher Gini ratio. The fall in average size says that one gets more and more smaller
households over time and … the Gini
ratio increases accordingly. There is no linear link between the average size
and the Gini ratio but Figure 5 shows the product of the Gini curve for
households and the curve in Figure 4. Now we see a corrected Gini history. This corrected Gini is not fully compensated
for the household size changeover time but
tells a different story to the educated audience: the Gini for
households has not been changing since the 1970s. In 1993, there was a revision
to income definition and all time series were subject to dramatic chances. This
step is fully artificial.

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

This is a methodological (i.e. unprofessional) mistake.

The
same corerction logic must be applied to the family income distribution - also biased in its current version. Another sufferer is the mean (and aslo median)
income. Since the size of household 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 6 shows the actual evolution of the mean
income (median income is harder to recover). The history is much brighter than many experts
would like to comment on.

Figure 2. The evolution of normalized Gini ratio for households.

Figure 3. The evolution of total household population and the number of
households (both in thousands)

Figure 4. The evolution of an average household size.

Figure 5. Corrected Gini ratio.

Figure 6. The growth of normalized (household ) mean income and that
corrected for the fall in the household average size.

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