5.3.2. Incomes of Top 90-95 and 95-99 Percent Record Increasing Dispersion

The incomes of the 90-95 and 95-99 percent revealed an increase in dispersion across states over time. This result contrasts with the previous section where average income and income of top 1 percent both recorded a sharp decrease in dispersion across states over time (except after the mid 1980s). This opposition is suggested twice: once with the coefficient of variation regressed on time (table below), and another time with graphs of the standard deviation (figure below). 34

Table 5.7. Inequality Across States over the Past Century
Dependent variable: CVt(ytop i,t) AI 90-95% AI 95-99% Top 1%
Time coefficients 1,167.4 * 1,550.6* -0.0047 *
* Statistically significant at the 1% confidence level.

The figure below displays income dispersion within the top decile, measured by the coefficient of variation, and the decomposition of its ratio (standard deviations and means are expressed in 2003 dollars).

Figure 5.7. CV, Mean and Standard Deviation Within the Top Decile
Figure 5.7. CV, Mean and Standard Deviation Within the Top Decile

A common point to all three groups is that the increasing portion of the CV curve after the mid-1980s is accounted for by a rise in both the mean and the standard deviation. However, the differences among them lie on the opposition mentioned earlier: Considering the coefficient of variation of the two fractiles of the 90-99 percent interval, one may notice their respective decrease between the mid-1930s and the late 1970s. This downward trend occurred along with a sharp increase in their mean income, but with a slow and smooth rise in their standard deviation. As for the top percentile CV, it experiences a drop between 1939 and 1980 due to opposite trends in the standard deviation (decreasing) and the mean (increasing), the same way the dispersion of average income did (bottom panel of Figure 5.6).

Notes
34.

By definition, the coefficient of variation (CV) divides the standard deviation by the mean, measures the volatility of a series with respect to its mean, and is an index without unit. Why resorting to the CV ratio and thereby complicating the overall economic interpretation of its coefficient? While the standard deviation is sensitive to the addition of a constant, the coefficient of variation is not. For instance, assume a hypothetical standard deviation of income of $2,000 associated with a mean of $3,000 in a given year, thereby depicting a high degree of inequality. Had everyone earned a bonus of $100,000,000 the following year, the standard deviation would drop, suggesting a decline in inequality. Unlike the standard deviation, the coefficient of variation is scale invariant as the constant term cancels out by appearing on both the numerator and the denominator. Therefore, the coefficient of variation is often considered a better measure of income inequality, especially for series displaying different group means across sections or over time.