4.2.2. Trend over Time

Regressions of intra-state inequality on time and state by state yield time coefficients that are summarized in the three plots below.

Figure 4.14. Time Coefficients of Intra-State Inequality Regressions
Figure 4.14. Time Coefficients of Intra-State Inequality Regressions

An alternative way of presenting the results is to resort to the coefficient of variation (CV). By definition, the coefficient of variation divides the standard deviation by the mean, measures the volatility of a series with respect to its mean. The coefficient of variation CVt(ytop i,t / ybar i,t) is here regressed on time to observe the variability of within-state inequality over time. The table below shows that the annual income gaps within states have significantly reduced in magnitude from 1913 to 2003.

Table 4.2. Variability in Within-State Inequality
Dependent variable: CVt (ytopi,t / ybari,t) AI 90-95% AI 95-99% Top 1%
Regressor coefficient: Time -0.0035* -0.0022* -0.0015*
* Statistically significant at the 1% confidence level.

A visual representation of the coefficients of variation illustrates the same result, in a lesser extent for the top percentile (in the right panel):

Figure 4.15. Coefficients of Variations of Intra-State Inequality
Figure 4.15. Coefficients of Variations of Intra-State Inequality