Yesterday, my post on the differences in per capita income and total income per tax unit caused some friends to be puzzled by my results. 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).

The problems regarding the use of tax units instead of households is not new. In fact, it is one of the sticking point advanced by skeptics like Alan Reynolds (see his 2006 book) and, more recently, by Richard Burkhauser of Cornell University (see his National Tax Journal article here).

Could it be that all the differences between GDP per person and income per tax unit are caused by this problem? Not really.

There is an easy to see if the problem is real. Both measures are ratios (income over a population). Either the numerator is wrong or the denominator is wrong. Those who view tax units as the problem argue that the problem is the denominator. I do not agree since I believe that the numerator is at fault. The way to see this is simply to plot total income reported by all tax units and compare this with real GDP. What’s the result?

Even with tax-reported income being deflated with the Implicit Price Deflator (IPD) instead of the consumer price index, we end up with a difference (in 2013) of roughly 3 orders of magnitude between GDP and tax-reported income relative to the 1929 base point. Basically, GDP has increased by a factor of 14.749 since 1929 while IPD-deflated tax-reported income has only increased by a factor of 11.546.

As a result, I do not believe that the problem is the tax unit issue. The problem seems to be that tax data is not capturing the same thing as GDP is!