Last week, I talked about income inequality and whether top income earners are paying their fair share of taxes. I found that the top decile of income earners hauled in about 44% of income and paid 60% of federal taxes in 2014. Furthermore, the lopsided tax burden on the rich is a direct product of income inequality: simply put, the rich have more money to spend on taxes.

This week, I’m going to go deeper into income inequality by examining the Gini coefficient for pretax and post tax income.

Some background on the Gini coefficient:

It is the most common statistical measure of inequality. While not totally intuitive to calculate, a way to think about the Gini coefficient is some measure of inequality between 0 — no inequality, and 1 — full inequality. A picture demonstrates the intuition best:

The above graph is a cumulative income distribution. On the X axis is the cumulative share of the population arranged from lowest to highest incomes. On the Y axis is the cumulative share of income. The 45 degree line is the Theoretical Line of Equality. If all income in society were equally shared, the cumulative income distribution would look like this. Section B is the actual cumulative income distribution. The Gini coefficient is calculated as A/(A+B). As societal income gets more equal, B approaches the theoretical line of equality, A gets smaller and smaller, and the Gini coefficient approaches 0.

You can use integral calculus to calculate the area under a curve but my calculus is rusty so I just estimated the values of the pre-tax and after-tax Gini coefficients.

Calculating Gini Coefficients in 3 Easy Steps:

- From geometry, we know that the total area of the triangle is .5 (A=1/2 base x height). Thus, A+B=.5.
- Area A = .5 – Area B. We can get Area B using either integral calculus or an approximation method.
- Gini = A/(A+B) = (.5-B)/.5 = 1-2B

I plotted Treasury data to calculate the pre-tax and after-tax Gini coefficients. The pre-tax Gini coefficient is 53 and the after-tax Gini coefficient is 48, indicating some level of income redistribution. Shown graphically:

We can clearly see that taxes reduce inequality in the US, but the after-tax Gini coefficient is still very high for an industrialized country. Compare the US with other G7 nations and we are a clear outlier.

**Reframing “Fair”**

Back to my original question: are the rich paying their “fair share” of taxes? Maybe — they already cover a vast majority of federal tax receipts. Could they afford to pay more? Absolutely. Rather than getting caught up in the fairness trap, what if we reframed taxes from what is fair to pay to what is necessary to fund all our priorities as a society: Healthcare, education, infrastructure, armed forces, a safety net, etc. Clearly we are not making enough investments in these priorities today, but we could and we should.