Arnold Kling  

Income Distribution Reality

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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.

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.

Next, consider what happens when you have millions of families, and you add lots of new families each year. Because new families (immigrants and young families) tend to join the income escalator at the bottom, it should be no surprise that the bottom percentile shows declines more frequently than the top percentile.

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.

I think that if you are going to write a treatise on income inequality in America, you have no choice but to slog through the data sets that track particular families over time, meaning the National Longitudinal Survey and/or the Michigan panel on Income Dynamics. From time to time, I have considered doing the slogging, just because I am highly curious about this issue of family income dynamics vs. the movement in census percentiles. However, I would need a colleague who could help me up the learning curve with the data.

UPDATE: See Bartels' reply in the comments.


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CATEGORIES: Income Distribution



COMMENTS (18 to date)
Richard Pointer writes:

Didn't he take a simple stats class? When you take classes of people and report the descriptive statistics, certain statistical artifacts will be created.

This guy should have been failed in grad school or at the very least whacked on the head a few times.

"Statistics are like bikinis; they are interesting for what they show, but even more interesting for what they cover up." Dr. Abe Rotstein

Brandon Berg writes:

This could also be to some extent an artifact of the aging of the US population. IIRC, the bottom income quintile has the highest average age.

I point out a similar statistical artifact in my post here.

If you've ever been offered a discount for cash, or read about Ebay & Amazon Marketplace sellers getting audited, you would discount the "income" part of his argument-- lots of "income" is disappearing from lower-income tax returns.

This is true especially for person-to-person services and partly encouraged by the phase-out of government benefits at higher income levels. (income from black market activities also don't make offical income reports). To be meaningful in this context, of course, one would have to show a that unreported income is trending upward as a share of overall income during the relevant measuring period. I suspect it is, but not enough to argue that it is.

spencer writes:

Of course you are right that as the population ages the people in the 25-34 year bracket move up to the 35-44 year bracket, etc., etc., etc..

If the US had a "normal" age distribution this would not really matter as at time 1 you would have x% in one age bracket and 10 years later you would still have x% in that bracket. But because of the baby boomers we do not have a normal age distribution.

If you look at the age distribution what you find is that the baby boomers moving through the age distribution alone has a significant impact on mean earnings. In the 1970s the average age of the employees actually fell. But since 1980 the average age of the employed population has been rising.

Because of this changing demographics alone since 1980 the mean real income of families should have risen by five percentage points. If you use the as reported CPI do deflate actual mean real income growth it was less then 5% since 1980. If you deflate by the CPI-R that recalculates the CPI to show what if would have been if the Boskin Commission changes were applied retroactively what you find is that over half of the actual real mean family income increases since 1980 were due to the aging of the population.

So you are completely correct that comparing real family income in 1990 to 200o is not comparing the same families. But the conclusion is just the opposite of what you are implying. The aging of the population actually conceals that real mean earnings has actually been weaker then what the aggregate data implies.

spencer writes:

Again, you are right about households.

But Census also publishes the data on income, etc, by family where you do not have the distortions you are correctly pointing out.

The family data shows about the same trends, so the problems you correctly point out about households does not change the story of weak real income growth.

Correction. I did not refer to my data and spread sheets before writing the comment about demographics on average income.

My calculation were not based on family income.

Rather I did my calculations showing the impact of the baby boomers on wages using real weekly median earnings for individuals, not families. But I'm sure my conclusion for family income are still valid.

I would be happy to send you the excel file.

Matt writes:

You have to explain why we have more poor large immigrant families and fewer large wealthy immigrant families. Your proof is that we are richer than the average nation. Our distribution and the average distribution should converge over time (assuming trade relations with Mars stay stagnant).

Under this assumption, than the author has a bias toward sending wealth there rather than moving poverty here. If that is the author's intent, to move wealth to poor nations, then hey, I am all in agreement.

KipEsquire writes:

Churn is also a factor at the very top of the distribution too.

In any given year a sizeable chunk of the "top 1%" of income earners will be those who enjoyed a one-time exogenous event -- selling a business, cashing in stock options, having a hit music album or just winning the lottery. It is therefore statistically invalid to treat them as an enduring class.

See also, "The Onion."

spencer writes:

Kim -- just like Arnold, you are right about the churn factor you describe.

But do you have any evidence that the trends about the number of people passing through the 1%
like you use in your examples has changed?

Does the churn account for a larger share of the top 1% in 2000 then it did in 1990 or 1970?

Just because there is churn does not invalidate the data. Watch out for the disconfirmation bias Arnold wrote about.

Anonymous writes:

[Comment removed for supplying false email address. Email the webmaster@econlib.org to request restoring this comment. A valid email address is required to post comments on EconLog.--Econlib Ed.]

Phil writes:

Spencer makes a good point, but it should be broadened - claiming that Bartels' measure means nothing because of the shift in the households in each percentile implicitly assumes that these shifts have changed over time. Bartels, after all, is looking at these measures over a 58 year time period. It's true, this is a pretty shoddy measure, but you're criticizing it using a scenario that contradicts his general point, while a perfectly valid criticism of the measure could strengthen or validate his general point. If you're arguing against his general point, do so. If not, you should present multiple scenarios that would disrupt the meaning of this statistic but are reflective of different underlying trends. I know it makes your life harder, but you're smart, so it won't be that much more difficult and it will be far less misleading.

Russ Roberts writes:

Spencer,

It doesn't matter whether you look at households or families. Either way, the rise in the divorce rate enormously distorts the measurement of inequality to the point of meaninglessness. Arnold's point stands.

Me writes:


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spencer writes:

The difference in the growth rate of households and population is only 0.5% annually, not enough to distort the data out of meaninglessness.

spencer writes:

I agree that one of the causes of poverty in recent decades is the growth in single female mothers -- both from divorce and from children born out of wedlock.

But this does not negate the point that these people are out there and are poor. Yes, it does impact the data. But it should impact the data because the data is suppose to reflect reality and the reality is that the number of poor people, families and/or households has grown rapidly.

Ignoring the evidence that these people exist is
trying to distort the data into meaningless.

spencer writes:

The key point is that sometime in the late 1970s growth of mean, mode, average, individuals, household and/or family --- however you organize the data -- real incomes slowed sharply. Every time this is pointed out people like Russ Roberts try to nitpick the data and convince people that the data is inaccurate. But the overwhelming evidence from a wealth of different data series all confirming each other clearly demonstrates that this slowdown occurred. The only people distorting the data are those arguing that the slowdown did not happen.

Larry M. Bartels writes:

Yes, this is a nit. As I say on the same page of my book that you cite, "specific families do not remain at exactly the same point in the income distribution from year to year. Indeed, the specific families included in the Current Population Survey, from which these tabulations are derived, change from year to year. Nevertheless, the data reflect the general economic fortunes of poor, middle-class, and rich families and how they have changed."

The more detailed tracking of individual incomes you propose has been done by Kopczuk, Saez, and Song in a 2007 working paper using social security earnings data. Their conclusion is that fluctuations from year to year in individual incomes have remarkably little impact on trends in inequality.

Even if that was not the case, it is very hard to see how changes in family structure, an influx of new poor families, or short-term income fluctuations could account for the marked contrast I find in income growth patterns under Democratic and Republican presidents. Families do not suddenly appear or splinter when partisan control of the White House shifts from one party to the other. Chapter 2 of my book includes a variety of additional analyses intended to test the robustness of these partisan differences in income growth patterns. They persist (indeed, look slightly larger) after controlling for changes in family structure and workforce participation, immigration, and a variety of other social and economic factors, and/or after allowing for linear or non-linear trends in inequality due to technological change and other unmeasured factors.

JSB writes:

For that matter, it's very hard to see how any real factor could explain these purported differences in income patterns -- there's such a small sample size of Republican and Democratic Presidents, and neither party's policies have stayed the same over the past 50 years. The whole project is spurious.

Steve Roth writes:

I'm wondering--did you get past the first third of page 7?

This book is right up your alley. If you haven't even read it--and since you haven't done more than pick a tiny nit from page 7 (which Bartels answers later on that very page), it seems you haven't--it suggests a serious affliction of (anti-)confirmatory bias...

Bartels' analysis kicks some serious ass. Given the utterly (non-)response and flaccid discussion in the econoblogosphere, this is definitely not the place where people should go to learn economics.

Time to stand up like a principled person and give Bartel's work some critical, clear-eyed, and unbiased attention--even if it forces you to acknowledge that you're wrong about some things.

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