## Monday, September 23, 2013

### More on lifecycle effects on income inequality

I wanted to revisit this post from the other day.  It included this graph, and I am adding the graph below for further analysis.

On both graphs, I should point out that the Census Bureau data I am using combines all incomes over \$100,000, so I have cut off the x-axis at that level.

The point of the first graph was to show how the income distribution within a working-age age group is much more symmetrical than the aggregate, and that the hump of low income households is a product of lifecycle effects.

The second graph here clarifies that point.

This creates a bit of a paradox, because the aggregate income numbers are combining several pools of households with very differently shaped distributions, so the median household income at any given time is inflated by lifecycle effects, which makes the income distribution appear to be more uniform than it is, but the skewed shape of the aggregate distribution and other statistical forms of income inequality will be overstated.

First, on the overstated inequality, the second graph shows the difference in the distribution of incomes between the 15-24 and 65+ age groups and the 40-44 age group.  We can see from this graph how the hump in the aggregate income distribution comes from the young and old age groups.

So, the position of the mode income level below \$20,000 in the aggregate income distribution is not a product of an oversized underclass of working families.  It is the product of very young and very old households which we do not expect to have income.  In this data from 2007, roughly 47% of the bottom quintile and 36% of the 2nd quintile of households stem from generally non-working or lightly working households from the 15-24 and 65+ age groups.

Now, I absolutely don't want to make light of poverty.  But, statistics about the incomes of the bottom third of the income distribution tell us nothing about poverty among households that we expect to have incomes.  In order to discuss actual levels of poverty, we need to account for this distortion.  Especially in the years ahead, as the 65+ age group grows, the bottom quintile of households will be more and more populated with households that aren't poor.

This third graph helps to visualize this and also might help to visualize why the aggregate median income becomes inflated by lifecycle effects.  We can imagine counting up to about \$50,000 to get to the median household.  At that level of income, the head of household is very likely to be between 25 and 65 years old, working full time.  During the year they are measured as the median household, they are very likely to be making more than their average lifetime income, because that average will be brought down by some years when they are very young or very old when they are not working and have very low incomes.  In other words, if that median family could have smoothed their income over their lifetime, they would probably be making less income during the year when they represent the aggregate median household.