[Retracted] Simpson's paradox strikes again: there is no great stagnation?

by CarlShulman1 min read30th Jul 201251 comments

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ETA: The table linked by Landsburg has been called into serious question by Evan Soltas [H.T. CronoDAS]. I edited the post to leave only the table to provide context for the comment discussion of its status.

Economist Steve Landsburg has a post [H.T. David Henderson] about the supposed stagnation of median wages in the United States in recent decades. In the linked table median wages have risen for: 

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Link description: the source for the numbers in the OP is unclear; it is certainly not the Census data, which does not agree even approximately with these numbers. The Census data shows that the median wage of white non-Hispanic men has stagnated while that of female and some minority median incomes have grown substantially.

Doesn't the census run just once per decade — i.e. 1980, 1990, 2000, 2010? The above table has claimed data from 2005, when the census didn't run. The Department of Labor and other agencies collect income and employment statistics more often, though.

I just added the link summary because I think that bare links aren't very useful. I didn't check anything.

ETA: I should mention that the author does include links to the source of his own numbers.

The Census Bureau has projects that they do between decades, even though "The" Census is only every decade.

According to Thomas Bayes, the analysis isn't quite wrong. Comment reproduced for your convenience:

Based on the census tables that he cites, here’s what I see for 2005 (in 2005 dollars):

All men: $31,725

White men: $32,179

  • Soltas says $31,725, which is the median for all men.

White, not hispanic men: $35,345

Conard says $35,200 for white men, which is very close to the number for white, not hispanic. The number he uses for white women is $19,600. The Census data that Soltas cited shows $19,451.

Based on this quick comparison, I’m not sure that Soltas has discredited Conard’s analysis.

Thomas Sowell makes a similar point about stagnation of "household" income. The demographics of households have changed dramatically, with a large increase in households with single adults, and single non dependent adults. Two incomes make less money than one, so household incomes can look worse.

I don't think this accurately captures any real issues with young dependent adults, but that's just another instance of the problem of summary statistics of heterogeneous aggregates.

Ah, yeah, I looked up the median household income and was slightly surprised it hadn't dramatically increased as you'd naively expect if the OP's explanation is right. Thanks for explaining :)

Is that adjusted for inflation?

This reminds me of reading about something mentioning that the growing gap between the rich and the poor is not the rich getting richer and the poor getting poorer. It's the rich getting richer, the poor getting richer, and a bunch of people immigrating to replace the poor people.

[-][anonymous]9y 2

This reminds me of reading about something mentioning that the growing gap between the rich and the poor is not the rich getting richer and the poor getting poorer. It's the rich getting richer, the poor getting richer, and a bunch of people immigrating to replace the poor people.

Do you have a cite or remember generally where you had read that?

Does only counting the wages of workers make the median less meaningful? For instance raising the workers' median wage could be accomplished by firing all the lowest earners. If non-workers' personal income ($0) in the 80s were included in the calculation the overall median would have been lower. Also, there's roughly 9% unemployment in the U.S. today; what would happen to the median if half of those people got minimum-wage jobs today?

Interesting data.

I have one bone to pick with the original article:

So let’s correct for that. Suppose the 1980 workforce had looked demographically just like today’s,

... then the supply curves would have shifted around and people in each group in the counterfactual 1980's would have been earning a different amount to what they did in the real 1980's.

So can anyone who understands economics help me - is the overall stagnation a supply or demand side thing? The data hint that cheaper labor is entering the workforce and driving wages down, but could it also be that the economy only supports a certain number of jobs, and regardless of how demographics shift around the median wage won't go up?

You're making an unwarranted assumption that the overall stagnation needs a macroeconomic explanation.

Imagine, for a moment, that most of the increase in a workforce happens in low-wage, low-cost-of-living regions. It's entirely possible for average wages to stagnant even as average buying power increases, with no changes to any local costs of living; what mechanism in supply and demand can explain this? Is cheap food entering the country from Mexico and driving the cost of food down? That's the problem with hidden variables.

Instead of looking for an explanation in supply or demand, first you need to look at the hidden variables, and see if there's an inherent explanation there. By asking whether it's a supply or demand issue, you're effectively ignoring the hidden variables, and declaring that the broader statistics are meaningful.

Asking what mechanism in macroeconomics can explain the stagnation is a bit like using the Kidney Stone example used on wikipedia and asking whether maybe doctors aren't sterilizing their equipment properly prior to performing procedure A.

Edit: To clarify exactly why this is the wrong question to ask, this phenomenon is perfectly well described by demand for workers increasing in all sectors, but increasing in some sectors more than others. It's also perfectly well described by demand for workers staying constant (relative to population). It's also perfectly well described by demand for workers declining across all sectors, but decreasing in some sectors more than others. (Absent additional information not present in this data, that is.) That is, you can obtain the same results with relative increases, relative stagnation, and relative decreases in demand for workers. "Supply and demand" in this case is an answer seeking a question.

Upvoted because regardless of the accuracy of the data, it is nice to be reminded of Simpson's Paradox and see an example so that I might think more about it.

Upvoted, especially for the heuristic in the last sentence.

Can you remember what that was?

If you're dealing with statistics averaged from a whole bunch of data, you should check a couple of examples in more detail and see if they match the conclusions you're drawing from the whole data set.

So in this example, checking with a couple of companies to see if their wages really did stagnate.

One heuristic I try to use in making sense of claims about broken-down data is to zoom out to the big picture for a "reality check." [/tongueincheek] Reality doesn't play favorites with big versus small pictures.

That isn't a bad heuristic either! However in practice the aggregate claims about scores are often used to make an argument relying upon internal homogeneity, and I don't see the corresponding "scores are up among all groups so aggregate scores must be higher" often, which would require more information and space.

Is there a link to the original somewhere? I was indifferent to that particular issue ('The great stagnation') but interested in the general theory/background.

Anywhere I could read about it?

any particular individual would be likely to make more

Could this result be explained simply by people joining the workforce at a low wage, working their way up the ladder over the course of their career, and then retiring with a higher wage? If that's all that's happening here then it wouldn't seem to contradict the stagnation narrative at all.

But how would we find out whether that hypothesis is correct? And in fact what are the alternative hypotheses?

Even better would be to use more of those omitted variables: age, education, time in the workforce. One could use the General Social Survey for a rough take, using this link. I'd be curious to see the analysis if you'd like to do it.