# Income Inequality: History, Causes, and Solutions

Between 1979 and 2018, real GDP per capita increased by 89.1% A939RX0Q048SBEA while median wages increased just 6.3% LES1252881600Q. We'll call this discrepancy The Gap. What explains it?

## A Didactic Math Note

Suppose X = A * B * C. Suppose ∆X means "% increase in X".

Then, 1+∆X = (1+∆A) * (1+∆B) * (1+∆C)

So, ln(1+∆X) = ln(1+∆A) + ln(1+∆B) + ln(1+∆C)

I implicitly use this observation to determine what "%" of the gap various hypotheses explain.

## Accounting Issues

Maybe laborers are being paid more, but it's via benefits rather than wages. This is also partly true: salaries and wages as a percent of compensation have decreased from 84.8% to 81.3% Table 2.1. This explains 7% of The Gap.

The hawk-eyed reader will also note a definitional foible: the employment-population ratio. At the moment, we are comparing the median full-time wage to wages per capita. If more people are working now (as a percentage) relative to 1979, then that could explain part of The Gap.

The employment-population ratio has increased slightly from 59.9% to 60.4% EMRATIO. I think the worst case scenario is that a X% increase in the employment-population ratio can explain X% of The Gap. In this case the change in the employment-population ratio explains just 1% of The Gap.

Finally, economists use CPI when converting nominal wages to real wages, but they use the GDP deflator when converting nominal GDP per capita to nominal GDP per capita. During this time frame, CPI increased 3.460-fold CPIAUCSL while the GDP deflator increased 2.848-fold USAGDPDEFAISMEI. This accounts for 34% of The Gap.

## Capitalists

The above accounting issues suggest that 42% of The Gap isn't due to underlying economic issues but due to measurement and demographic differences. The Gap was 77.9%, but The True Gap is just 48.0%.

Maybe the owners of capital are making off with all the money rather than the laborers. During the same time period, labor compensation as a percent of GDP decreased from 56.2% to 53.1% Table 2.1. Table 1.1.5.. This explains just 14% of The True Gap.

## Labor Compensation Distribution

This leaves us with 48% of The Gap and 86% of The True Gap to explain. As far as I can tell, the only factor left that we haven't accounted for is the distribution of compensation for labor.

There are lots of theories regarding why the distribution of labor compensation has grown less equal Economic inequality, some are

- The difference in average earnings between various education level is growing.
- Unions are becoming less common.
- The minimum wage is falling relative to inflation/the median wage/the mean wage/GDP per capita.
- Technology is making low-skill jobs obsolete/lower-paying
- The ability to trade freely is causing low-skill jobs to be offshored.
- Some wealthy groups are influencing government policy to make themselves yet richer.

I'm not going to go into which of these is true or how much of the gap they account for - mostly because that kind of analysis is pretty difficult.

## Taxes and Transfers

The measurement of median income we've been using has been pre-tax median income. However, taxes have changed since 1979 and this could affect median post-tax. Fortunately *The Economist* has looked into this Inequality or middle incomes: which matters more?:

In short, they've found that changes in taxes and transfers have caused median household income to *increase* ~22% during the time period.

## Summary

Real GDP-per-capita has increased 1.65% per year over the past 39 years. After accounting for demographic and accounting issues, the median after-tax compensation has grown a bit slower: about 1.31% per year. The reason for the 0.34% gap is almost entirely due to increasing unequal distribution of labor compensation.

## Future Questions

- Why is there such a discrepancy (0.5% per year) between CPI and the GDP deflator?