A Few Thoughts on Inequality by Age Group

The subject of economic inequality has raised a lot of interest lately, with Obama making it the centerpiece of his hold-the-senate campaign, and a book on the subject by an obscure French economist named Thomas Piketty (more on that in a future post) hitting the bestseller lists. While I think this is a fine topic for debate, I have not been very impressed by how informed the debate has gone. One thing I have been disappointed about is that nobody is discussing the terms and what they mean by inequality, everyone is just throwing out terms they don’t understand, particularly with regard to what measures are relevant, and how much inequality is not only expected, but beneficial.

In this I am largely referring to inequality across age groups. Most discussions of this subject just use vague statistics like “the top 1% have X percent of the wealth” or “the top 10% of households have more income than the bottom 50%” without defining who makes up those households. This is particularly troublesome when comparing for long periods of time, when the make-up of the demographics might change significantly and in fact the same people often move between groups at different stages in their lives.

Here is a simple example. Just to keep things easy, we will measure individual income, and leave out children and such in the small fictional country of Elbonia, of Dilbert fame.  Each 10 year period of Elbonians has an equal population of 1,000 citizens. Elbonians enter the workforce at the age of 20. They start at the low, low pay (these are low skilled Elbonians after all) of $10,000 per year, but receive a healthy 50% raise every ten years (not so much on a yearly basis really but it keeps the math easy.)

Oh, and Elbonians have a mandatory retirement system into which they are required to pay 10% of their income, at a 5% interest rate, compounded every 10 years. And when they retire, they get their retirement paid out in 20 equal installments, until they die at the mandatory age of 80 (it is a very strict country).

Now keep in mind, this is a country with absolutely mandatory inequality. Every single person in each demographic gets paid absolutely the same wage and receive exactly the same return on their pension.  There are no Warren Buffetts or impoverished unemployed Appalachians. Now let’s see how the numbers work out.

Age	Income	Savings
20's	$10,000	$0
30s	$15,000.0	$15,000.0
40s	$22,500.0	$45,000.0
50s	$33,750.0	$101,250.0
60s	$5,062.5	$50,625.0
70s	$5,062.5	$0

This is obviously an extremely simplistic representation, but let’s see what happens when we compare the demographics in this completely “equal” society. For simplicity's sake once again, we will assume each 10 year group has the same population.

Age	Percentage of Income	Percentage of Wealth
20's	11%	0%
30s	16%	7%
40s	25%	21%
50s	37%	48%
60s	6%	24%
70s	6%	0%
Average	$15,229	$35,313

Now what we find is that one demographic, those in their 50s, have 37% of the income, and more than those in their 20s, 30s, 60s, and 70s combined! Conversely, if we look at wealth, those in their 50s have nearly half the wealth. Combined, those in their 50s and 60s have over 10 times the wealth of those in their 20s, 30s and 70s, combined. And this is in a country where everyone is on the exact same payscale.

Now what would make this worse? Well, obviously if some Elbonians drew larger paychecks than others, or made more on their investments. But what else would make it worse that had nothing to do with economic inequality as we normally see it? Notice that in our example each demographic is the same size, but in a normal country with a high birthrate there are far more young people than older people, there would also be a greater disparity in income and wealth. Also, if people merely lived longer, and thus were able to work and save longer, there would also be greater disparities. These are not bad things, a growing society with healthy people who live to a long age is supposed to be good, but critics of inequality would fret over this development.

This does not mean, of course, that all inequality is good, but it does mean, that we need to look into the details of things, and realize that changes in life, getting an education, getting married, having a family, saving for retirement, and finally retiring, have a huge influence on these statistics for reasons other than some form of economic discrimination by the rich and powerful, and we need to consider this.