Median Income vs. GDP

A friend asked me to do this comparison between income and gross domestic product (GDP) per capita. He wondered about the seemingly conflicting claims that GDP is increasing while incomes are stagnating. Those two facts are both contained in this graph.

There are two reasons for this divergence. The first is the difference between median and mean.

Usually, when people speak of an ‘average’ they are speaking of the mean. Means are calculated through the division of one total by another. GDP per capita is a mean. Total GDP is divided by the U.S. population. Medians, on the other hand, require finding the middle value of a ranked series. If you sorted every income in the U.S. from lowest to highest and then found the one in the middle, that is the median.

Means skew high if the values at the top of a ranking are much larger than those further down the series. The mean can increase if the values at the top increase, even if those further down do not change. In fact, the lower values could fall and the mean could still increase if the gains at the top is greater than losses at the bottom. Medians offer a better picture of income changes for those in the middle.

The second reason is that income is only part of GDP. If the non-income components of GDP increase, then GDP per capita would show an increase even if incomes remain stagnant. My next post will show that, in the U.S., this has indeed happened over the last 30+ years.

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