In the previous post, we presented the difference in income distributions for household sizes from one person to seven and more people as observed in 1994 and 2007. Unfortunately, there are no Gini ratio estimates in 1994 for specific household sizes. The first year when the Census Bureau reported these estimates was 1998 and here we compare Gini ratios for 1998 and 2007 together with now standard presentations of normalized income distributions. We use 2007 because in 2009 the CB changed the width of income bins to $5000 and increased the high-end limit to $200,000. Therefore, the measurements before and after 2008 are not compatible. Since nominal GDP was higher in 2007 than in 2008 it is reasonable to use 2007 as a reference year.

Again, we do not repeat the technical part which was well described in this post. Briefly, we showed that the household Gini is biased up in 2007 relative to 1994 because the portion of smaller and thus lower income households increased. Accordingly, the average size decreased. To do this, we normalized the household income distribution to the total number of households and corrected the income bins to the total increase in nominal GDP and the change in the total number of households. This operation is similar to that used for the Lorenz curve calculation.

Figure 1 compares Gini ratios in 1998 and 2007. For all sizes except the one-person-households, the Gini ratio slightly fell since 1998. The increase in one-person households might be related to the increase in the portion of population without income (see this post). In any case, the claim of increasing income inequality among households is not supported by these observations. The dispersion of household incomes (with two or more people) has been decreasing. This is the change in size distribution what actually induced the reported increase in the overall Gini ratio. Since the data granularity increased in 2009, the upper open-ended interval for Gini calculations increased to $250,000, and the interpolation within income bins was changed to the Pareto law, one should not compare the years before and after 2008.

Figure 1. Comparison of Gini ratios in various household sizes: 1998 vs. 2007.

As in our previous post, Figure 2 compares the household income distributions (density functions).. There were relatively more small-size households with one and two people in expense of mid-income households of 3 and more people. Not having the 1998 Gini estimates, we may say that the Gini for the small-size households increased and accordingly decreased for the larger households. But the effect of changing dispersion (and thus Gini) in any household size is likely smaller than the effect of larger households split with the creation of an excess of smaller households.

Figure 2. The evolution of income distribution density functions in various household sizes.

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