More Means and Medians

There are a couple of threads that I wanted to follow from my previous entry on Means and Medians. One, of course, relates to the weather. The other is this one, on income.

There are (roughly) 300 million people in America. If you take our Gross Domestic Product (GDP) of $14 trillion dollars, and divide by the population, you arrive at a per-capita income of approximately $45,000. We take that value and compare it with the per-capita income of other countries to get a sense of how well off we are – are we rich, or not?

And, by that measure, Americans are rich. A family of four's share of the output of America is $190,000. We're swimming in money, at least according to the mean.

Of course, that's just a measure of how we have to spread our output around. Unless they are extraordinary, most children don't work, and the majority of our seniors are retired. So a more interesting mean might be the amount of our GDP generated by each worker.

According to the census bureau, there are 138 million employed workers. (So, there are several million more potential workers...). That's a convenient number, because it makes the math easy: The average share of the output (the worker per-capita) is $100,000.

A normal distribution about the average would have 50% of American workers making more than $100,000 a year, and 50% making less. If it were fairly tightly bound to the mean, we would be able to say that American's are quite well off. But is that true?

Again, using the census bureau's numbers, the median household income (the mid-point) is $50,000. And since there are more income earners than households, the median worker income is lower still: $45,000 for men, $35,000 for women, and $41,000 overall.

In fact, the top quintile of all households starts at $91,000. So, less than 20% of American households make the per-worker average. And, since to get into the top quintile 77% of the households had two wage earners, that drops the number of workers who approach the national average income to just under 5%.

95% of all American workers make less than the per-capita value!

Therefore, for determining the actual wealth of the 'average' American, neither the per-capita value nor the per-worker share tells us much useful. Much better is the experience of the median family of 4, with an individual share of just $12,500. That's the experience of most of America. Not $45,000.

Now, economists are a pretty smart lot, and they understand that the difference between the mean and the median income in a country has meaning to the people of that country, and to what you can say about it. To help them, they use the Gini Coefficient (read wikipedia for a fuller account) – but it basically tells them the relative distance between the median and the mean.

Ours is a relatively high 45. Compare that with the bulk of Europe (34 for GB and Switzerland, low 30's for Canada, Ireland and Spain, 28 for France, Belgium, Hungary, Germany and Norway). We're only low compared to Argentina (49), Sri Lanka (50), El Salvador (52), Panama (56), Brazil (57) – and I'll leave it to the reader to consider what those nations have in common.

There's a lot more that could be said and investigated. For instance, what is the typical experience of a worker: Do they start low and progress across the median during their career, or do they remain on one side or the other? Where do our elderly lie? (I think we know: Most are below...)

But to maintain a semblance of brevity, I'll just leave you with this thought. Consider how this large income inequality is the gorilla in the room that silently influences every socio-economic discussion we have: From Education to Health Care, from Taxation to Retirement – the experience of the majority of Americans does not match the experience projected by the statistical mean, nor the experience of the planners and policy makers.

Once again, the mean and the median paint very different pictures. The mean says that we are universally rich.

The median exposes the lie.