In the debate on inequality, I am a skeptic of how large a problem the issue is. Personally, I tend to believe that worries of inequality only increase when growth is stagnant. In fact, I also believe that there are numerous statistical biases causing us to misidentify stagnation as rising inequality. Most of the debate on inequality is plagued with statistical problems of daunting magnitudes (regional convergence in income, regional price levels, demographic changes, increasing heterogeneity of preferences, increasing heterogeneity of personal characteristics, income not being purely monetary, the role of taxes and transfers etc.)
One of them centers around the use of tax data. This has been the domain of Thomas Piketty and Emmanuel Saez. I can understand the appeal of using tax data since it is easily available and usable. Yet, is it perfect?
A year or two ago, I would have been inclined to simply say “yes” and not bother with the details. Theoretically, taxes should be an “okay” proxy for the income distribution and should follow average income even if at different levels. Yet, after reading the article of Phil Magness and Robert Murphy in the Journal of Private Enterprise, I confess that I am no longer accepting anything as “granted” in the inequality debate. So, I simply decided to chart GDP per capita with the average taxable income per tax unit. Just to see what happens. Both are basically averages of the overall population, they should look pretty much the same (theoretically). The data for the tax units is made available in the Mark W. Frank dataset based on the Piketty-Saez data (see here) and I deflated with both the CPI and the implicit price deflator available at FRED/St-Louis.
The result is the following and it shows two very different stories! Either the GDP statistics are wrong and we have average stagnation (which does not mean that there is no increase in inequality) or the taxable income data is wrong in estimating the trend of living standards and the GDP are closer to reality (which does not that there is no increase in inequality). In the end, there is a problem to be assessed with the quality of the data used to measure inequality.
Notes On Liberty 
[…] Yesterday, my post on the differences in per capita income and total income per tax unit caused so… To their credit, the point can be defended that tax units are not the same as households and the number of tax units may have increased faster than population (example: a father in 1920 filled one tax unit even though his household had six members, but with more single households in the 1960s onwards the number of tax units could rise faster than population for a time). […]