Latest episode of Bikini Statistics

Sold by Bartels, debunked by Kling & Roberts:

As I have written here before, looking at slices of the population over time is a very misleading indicator of what happens to particular families over time, particularly when family composition is changing. Arnold Kling makes the same point and does it superbly:

In his new book Unequal Democracy, Larry Bartels writes (p.7),

families at the 20th percentile experienced declining real incomes in 20 of the 58 years...by comparison, families at the 95th percentile have experienced only one decline of 3% or more in their real incomes since 1951.

I have a nit to pick, which is that Census department percentiles are not families.

I do not want to succumb to disconfirmation bias, which is the tendency to find one thing wrong with something you disagree with and then dismiss the whole idea. But I have a hard time buying into stories about income inequality that look at the behavior of census percentiles over time. At the very least, the author ought to be clear that movements in census percentiles are not the same as movements in families. Bartels is the opposite of clear on that point.

Another issue that people raise with Census data is that the basic unit is the household. If a household breaks into two households, due to divorce, average household income plunges by 50 percent, even though nobody's income has changed. Trends in household income tend to look worse than trends in income per person.

Arnold has it exactly right. To get an idea of the magnitudes, here are some numbers:

Here's what has happened to the number of households in the US:

2000 105 million
1990 93 million
1980 81 million
1970 63 million
1960 53 million

So between 1960 and 2000, the number of households has doubled. What happened to population over that same period? Again from the Census:

2000 282 million
1990 250 million
1980 228 million
1970 205 million
1960 181 million

The average American household has gotten a lot smaller:

2000 2.7
1990 2.7
1980 2.8
1970 3.2
1960 3.4

Why did this happen? The obvious answer is that people are having fewer children. That would lower average household size. But that is not much of the story. The real story is a change in the composition of families due to an explosion in divorce in the 60s and 70s. Here's a breakdown of the proportion of total families headed by women:

Year Single Mothers Single Woman w/o kids Total

2000 12.1% 17.2% 29.3%
1990 11.7% 16.8% 28.5%
1980 10.8% 15.4% 26.2%
1970 8.7% 12.4% 21.1%
1960 8.4% 9.8% 18.2%

So over the last half-century, the number of households has increased at a much faster rate than the number of people, mainly because of divorce. That totally contaminates the comparison of percentiles over time and makes it appear that people are falling behind or standing still when in, fact, particular families are seeing their standard of living rise. Arnold calls a nitpick. I call it a massive structural flaw.

Previous BS installment here.

Statistics are like a bikini. What they present is suggestive, but what they conceal is vital--Aaron Levenstein