The Gini Index as a measure of income inequality is redundant when using U.S. Census Bureau’s household income statistics, at least at the national and state levels. That Gini index is fully determined and can be replaced by the household income share of the fifth quintile.
The Census Bureau has measured household income since 1967. Over those 47 years it has calculated the Gini index, a widely used measure of income inequality. Here’s a graph of that Gini index from the beginning to the most current data.
You’ve probably already seen a similar graph. But for emphasis, income inequality measured by the Gini index has been increasing on average since 1969. Also note that a step occurred between 1992 and 1993 because of a change in survey methodology related to top-coding.1 Regardless, except for variability the trend is upward, income inequality is getting worse over time.
In spite of its wide use, among the problems with the Gini index is that it’s not readily interpretable. It’s a synthetic index, Thomas Piketty’s designation in Capital in the Twenty-First Century. It’s just a number. You can use it to compare to similarly derived numbers or observe that it’s trending but beyond that (partitioning for example) will most likely require learning new quantitative skills. We can easily do better than that.
Among the Census Bureau’s yearly income statistics are percentage shares of household income by quintiles plus the top five percent. It turns out that over those same 47 years, the percentage share of the top or fifth quintile determines the Gini index.
The R-square value for this relationship is 0.9994 (where 1.0 is perfect determination). In short, the percentage share of the fifth quintile is equivalent to the Gini index. And it’s readily interpretable! For example, in 2013 the fifth quintile was 51.0, that is the top 20% of the income distribution took in 51% of all income for that year. I also looked at the same relationship but over the 50 states for the year 2013. That relationship was similar but with a bit more variability; the R-square was 0.987. I’d expect that kind of relationship to hold for other years as well. I didn’t try it at the county level but except for a further increase in variability due to smaller populations, I’d expect the association to continue to be robust. On the other hand, I have no idea how a similar relationship would perform in other countries that use the Gini (many don’t). However in the U.S., the Census Bureau is the main source of income data including the Gini index and share of income so substituting the top quintile for the Gini is useful because it’s readily available, makes sense, and lends itself to interpretation.
In 2013, the mean income for the top quintile was $185K, compared to average income for the fourth quintile of $84K, a significant difference of $101K. Also, the fifth quintile averaged over the last few years captured 51% of total income compared to a 43% average income share in the beginning of the timeline. As an inequality measure, the percentage share of the highest quintile is accessible and understandable. And it makes sense. The following graph shows the rise of the fifth quintile while the other four quintiles declined, the four being combined in the graph for visual clarity.
Once graphed you can readily see what’s happening. And of course if you want to, you can use the Census tables to break it down further.2
The Gini index is commonly used so you can’t just ignore it. But if you use U.S. income data and need to discern inequality and why it is what it is, you are better served using the percentage income share of the fifth quintile and related data.
- See Daniel H. Weinberg, “A Brief Look at Postwar U.S. Income Inequality,” June 1996, http://www.census.gov/prod/1/pop/p60-191.pdf. Also of interest, the first page shows family income inequality (instead of household) which begins with 1947: from 1947 to circa 1968 inequality declines. ↩
- The data used for the three graphs are avilable here as an Excel spreadsheet. Search terms, what precedes the parentheses, for the original Census tables are: H02AR 2013 (share aggregate income by fifths), H03AR 2013 (mean HH income by fifths), Census H04 2013 (Gini index). State data can be obtained via FactFinder, tables B19081 (mean income) and B19083 (Gini). ↩