Income inequality and race

Recently, I had a discussion with a friend about income inequality and how it relates to the racial wage gap.  I found this conversation particularly relevant given the current Democratic primary race, where wealth inequality has been a hot-button issue among the frontrunners.  The logic behind how one affects the other is simple. Certain minorities tend to be poorer on average than whites, so policies that improve income inequality will disproportionately affect minorities and work to close the racial wage gap.  The question at the forefront of our conversation was: exactly how much would policies that fix income inequality also close the racial wage gap?

To get some clarity on the question, I set out to do a simple thought experiment. In it, I first created a hypothetical world with two races and 11,500 people: 10,000 white people and 1,500 black people. I then simulated a sample income distribution using Census Bureau data on income by race (how I created the sample income distribution merits its own article).  The shape of the resulting distribution roughly resembled the real-world distribution of income in the United States:

I constructed the distribution such that the mean income of the white population was $63,362 while the mean income of the black population was $42,495, resulting in a racial income gap of 49%.  This mirrors U.S. census data, which has mean white income at $63,600 and mean black income at $41,347.
To get a simple sense of how unequal a society is, one can start by comparing mean and median income.  A society where mean income is drastically higher than median income is typically characterized by a high degree of inequality — the income distribution is skewed right, and a few people are really wealthy, while most people have below average incomes.  The mean income of my constructed society was $60,640, and the median income was $41,352, suggesting a relatively unequal society. 
However, comparing mean and median income is not a bulletproof way to assess a society’s inequality.  Consider a hypothetical society of 5 people who have incomes of: $1,000, $2,000, $100,000, $198,000, and $199,000.  The mean and median incomes of this society are equivalent ($100,000), but you’d be hard-pressed to characterize it as a fair distribution of income. 

To get around this issue, experts use a metric called the Gini Index to measure the degree of economic inequality in a society.  A Gini index of 0 indicates a perfectly equal society, while a Gini index of 1 indicates a perfectly unequal society.  The Gini index of my 5-person society would be 0.4736, placing it among the top 25 most unequal societies in the world. My initial distribution was constructed to have a Gini index resembling the United States’ own Gini index (refer to my accompanying article to see how I was able to do that).  There are many estimates of the Gini index for the United States, usually ranging between 0.40 and 0.50 (I somewhat arbitrarily used the figure of 0.464 from the Census website). 

Making a Better Society

What if we had a more equal society? Would the disparity in income between races be ameliorated? If so, how much?  
To answer these questions, I considered a transformation that would make American society as equal as one of its more equitable peers.  I chose the G10 country with the lowest Gini index, Belgium, which has a Gini index of 0.277 as my comparison.  I made a transformation: 

new income_i = f_i(old income_i) + c

where f_i is a function such that the new distribution has the same mean income as before and a Gini index of 0.277, and c is a constant calculated to maintain net wealth between the old society and the new society (in practice, I drew a new distribution based on my updated parameters, and mapped it to the old distribution such that everyone’s “rank” in the distribution stayed the same).  The result:

As expected (and by construction), the result is a more equitable society.  Mean income is still roughly $60,000, while the median rose to $54,000. As for the racial pay gap, mean white income fell slightly to $62,000 and black white income rose to $50,000, indicating a gap of 26%, which is roughly half of the initial 49%. So my experiment suggests that adopting an income distribution similar to Belgium would roughly halve the racial wage gap.

 

Another example

So can we definitively say that a transformation to a more equitable society would necessarily imply a halving of the racial wage gap?  Let’s try one more transformation that is a little easier to conceptualize: let’s halve everyone’s distance to the median income (plus a constant c so net wealth is maintained). 

new income_i = (median(old income) - old income_i)/2 + old income_i +c

The result: 

Much like our first transformation, this new transformation preserves the shape of our old income distribution.  And again, the produced society is measurably more equal. By total accident, the resulting Gini index is eerily familiar: 0.276.   As for the racial wage gap, it falls similarly as well — it approximately halves to 25%.  

 

Conclusion

Our little thought experiment has taught us a few things.  First, the United States is a really unequal society. Our Gini index is higher than any of our peers, and it even surpasses that of Russia, China, and India. This is likely being driven by the fact that the rich in the United States are really rich. Second, reducing inequality would go a long way to fixing the disparity in pay between races, but it won’t completely solve the problem.  Short of redistributing wealth so that everyone makes exactly the same, sweeping policies that address wealth inequality won’t eradicate the racial wage gap. Targeted polices that work to level the playing field for minorities like ensuring fair housing or preventing predatory lending practices, which disproportionately target communities of color, are needed to see a real impact.

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