In the short space of a few hours, my Google Reader has fed me two quick reactions to Larry Bartels' new book Unequal Democracy.

Both pieces I've read take very quick issue with an incredibly overused, abused and misleading stat: The income shares households in terms of population percentiles.

The first reaction is at EconLog by Arnold Kling.

He pulls this quote from Bartels' book:

Bartels:

"...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."

Kling says he has a "nit to pick" with Bartels' numbers:

Suppose that we start out with 20 families, and the 4th-lowest family (the 20th percentile) has an income of $10,000, while the 3rd family has an income of $9500. Next year, suppose that everyone's family income rises by 2 percent, but we add a new family at the bottom of the income distribution, with an income of $6000. As a result, the new 20th percentile is now somewhere between the income of the original 3rd family (now the 4th family out of 21) and the original 4th family (now the 5th family). The income of the 20th percentile goes down, even though the income of every family has gone up.

I've heard this explanation (and then some) before and it makes perfect sense. Tracking changes in percentiles can totally blur realities lurking behind those numbers. Moreover, when it's obvious that the composition of a "family" or "household" changes radically over time, it's very misleading to use that entity for comparative purposes from which to draw conclusions about the income of individuals....or even households.

Being the thoughtful and thorough man I've come to know Kling is, he adds:

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.

Next we move to Russ Roberts at Cafe Hayek. Roberts links to Kling and follows up on Kling's points with data. Roberts is, as always, very thorough in breaking through the facade of numbers to see what lies behind them. In terms of composition, as I mentioned above, he takes great pains to show how the enormous demographic changes in "households" and "families" make the comparisons over time of such dynamic and shifting groups utterly useless and misleading. Roberts has covered this before, BTW.

Some basic stats from Roberts:

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

America is a much different place than in 1960 in many ways. Household size is one of them as Russ points out. This goes further than just this basic breakdown. Looking at more Russ' stats, we also see that number of single moms and women without children is sharply higher. This accounts for some of the average smaller household size. It also means that there are fewer mouths to feed per house or family which, in turn, requires less income.

In conclusion Roberts states all this quick research:

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.

Indeed. Stats often bother depending on what the stat is. That doesn't mean that I'm selective in terms of conclusions...just methodology. The reactions by Kling and Roberts are sound and insightful. They utterly destroy the premise that Bartels in trying convey. Does that mean that Bartels has no good points? Not necessarily. But on this particular, it's clear that he doesn't have the meat to substantiate the point he wants to make.