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

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

Tue, 31 Jul 2012 03:55:04 +1000

Submitted by CarlShulman • 30 votes • 51 comments

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:

51 comments

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

2012-07-31T04:20:45.498092+10:00

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.

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

2012-07-31T07:09:12.110392+10:00

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 :)

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

2012-07-31T07:20:26.161587+10:00

http://esoltas.blogspot.com/2012/07/inaccurate-consequences.html

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

2012-07-31T07:36:58.934813+10:00

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.

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

2012-07-31T07:46:41.482657+10:00

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.

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

2012-07-31T08:15:49.290288+10:00

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.

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

2012-07-31T21:21:35.803415+10:00

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

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

2012-07-31T08:49:14.899396+10:00

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.

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

2012-07-31T09:03:58.404875+10:00

CronoDAS's linked post does indeed reflect the census data. Huh.

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

2012-07-31T10:19:09.998249+10:00

Just checked myself, indeed.

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

2012-07-31T05:29:25.927151+10:00

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?

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

2012-07-31T06:22:35.847255+10:00

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.

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

2012-07-31T05:01:08.846542+10:00

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.

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

2012-07-31T05:08:54.307766+10:00

Yes.

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

2012-07-31T08:43:01.750107+10:00

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?

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

2012-07-31T09:00:06.456440+10:00

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?

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

2012-07-31T12:03:32.974461+10:00

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.

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

2012-07-31T04:07:50.213910+10:00

Upvoted, especially for the heuristic in the last sentence.

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

2012-08-04T02:24:43.460164+10:00

Can you remember what that was?

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

2012-08-04T19:03:49.714583+10:00

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.

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

2012-08-07T00:54:01.764329+10:00

Thanks!

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

2012-07-31T04:41:32.411531+10:00

The error comes more from the map-warping power of political correctness than from the Simpson's paradox.

Edit: look at what happened to the then Harvard President Larry Summers when he discussed why women might be underrepresented in the sciences.

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

2012-07-31T06:00:49.688131+10:00

Simpson's paradox is a simple mathematical explanation for the error, "political correctness" is a complex socially-constructed one intimately tied up with particular political positions. Occam's Razor favors the former, overwhelmingly so.

There is no need to introduce the hypothesis that the error is due to people not agreeing with the particular political views of the Blue Party (which is what the "political correctness" hypothesis states), when simple math suffices to explain it.

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

2012-07-31T09:06:15.012228+10:00

There is no need to introduce the hypothesis that the error is due to people not agreeing with the particular political views of the Blue Party (which is what the "political correctness" hypothesis states), when simple math suffices to explain it.

If the Blue Party has the belief that it's evil to ever think that any non-white racial group is on average worse at anything than white people are and if this belief is one of the most important beliefs of the Blue Party then what there is no need to introduce here is Simpson's paradox.

Steve Landsburg (like myself) is a college professor. The President of his university recently attacked Landsburg on politically correctness grounds. Landsburg's post was an implicit attack on blank slate politically correctness.

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

2012-07-31T09:35:16.935111+10:00

Yes, I understand that you're saying that all Blues hate the truth; that Blues are the opposite of decent people — that they speak lies out of love of deceit; their veins run with corrosive black ichor; they despise all that is good and natural in the world; they invert the ritual of the Mass and perform lewd acts with the consecrated Host; their women dress as men and their men dress as women; they curse crops, cause milk to sour, and make men's penises shrink and vanish. And that only the sacred, knightly courage of the Greens can exterminate the Blue threat, make the land prosperous once again, bring smiles to the faces of the children, and lead us marching joyously into a new age of shining order and righteousness.

I get that. That was all obvious when you said "political correctness", because that's what "political correctness" means — it is an accusation of bad faith. It means "the other side tell lies, and they refuse to allow the truth to be spoken."

What I'm asking you to recognize is that this is a more complicated hypothesis than the Simpson's paradox hypothesis. Politics will pretty much always be more complicated than math, and conspiracy theories always more complicated than mathematical errors. And so they require more evidence.

That's all.

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

2012-07-31T09:43:21.647997+10:00

NO!

I'm not saying that the Blues hate the truth. I'm saying that on one small set of issues the Blues have beliefs independent of the truth.

Politics will pretty much always be more complicated than math

Yes, but in this situation, a situation over which I have a huge amount of local knowledge, politics is the simpler answer.

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

2012-07-31T06:06:41.972282+10:00

Greedy reductionism strikes again. Also the two explanations aren't mutually exclusive.

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

2012-07-31T06:40:44.777423+10:00

Greedy reductionism strikes again.

"Greedy reductionism" implies explaining-away the data on the basis of a reductionist theory; e.g. Skinner's explaining-away of the experience of consciousness.

The only thing being explained away here is the "political correctness" explanation, not the data.

Also the two explanations aren't mutually exclusive.

Conditioning on one of two independently sufficient causes detracts from the other's plausibility.

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

2012-07-31T04:52:52.320650+10:00

How so?

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

2012-07-31T05:16:32.366749+10:00

It is impolite to mention demographic change, especially when racial differences are obvious. "Our increases in income are counteracted by the swelling ranks of poor non-whites" does not make newspaper editors happy.

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

2012-07-31T05:31:13.287614+10:00

But they're not "counteracted" at all. White people's wages have actually increased. You don't have to try very hard to put a positive spin on the fact that everyone is making more money, women are becoming more equal with men, and previously poor non-whites are now finding more jobs. What's not to like?

It seems unlikely to me that people discovered this explanation for the data and then covered it up. More likely that they simply hadn't noticed that Simpson's paradox was in effect (maybe because they never even looked at the demographic data).

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

2012-07-31T05:37:18.630468+10:00

Cowen built a lot on the median income in The Great Stagnation; reading it, there was not a whisper about demographics, though Cowen is a pretty honest author usually (and in fact was the one who publicized this one!).

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

2012-07-31T07:35:16.149653+10:00

Drat, I hat-tipped Cowen instead of David Henderson of Econlog, in an example of the Matthew Effect. http://en.wikipedia.org/wiki/Matthew_effect_(sociology)#Sociologyofscience

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

2012-07-31T07:43:06.045283+10:00

Publicized it, I said, not discovered it. Cowen has a huge readership, and pretty much anyone who ever hears of this will do so because Cowen publicized it; and Cowen knows this, so the honesty argument is still true.

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

2012-07-31T08:01:11.703841+10:00

No, I got it from Henderson's blog, but the source data got lost and reconstructed as Tyler. I haven't seen any Marginal Revolution post publicizing it.

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

2012-07-31T08:09:39.356036+10:00

Whoops, you're right; it was Henderson/EconLog, not Cowen.

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

2012-07-31T05:39:16.959161+10:00

But they're not "counteracted" at all.

They are for the metric of median wages.

There's a similar situation with PISA scores: American students of all races are the highest or second highest scorers of that race. The average American PISA score is mediocre, though, because the US's racial balance is not, say, Shanghai's or Finland's racial balance.

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

2012-07-31T07:49:05.314630+10:00

I'm curious by what steps of reasoning do you pick out the hypothesis of "racial balance" rather than, say, "income inequality"?

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

2012-07-31T08:09:33.984939+10:00

It's not at all clear to me how "income inequality" is a theory that predicts the datapoints I'm discussing here.

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

2012-07-31T08:47:11.124027+10:00

It's not at all clear how "racial balance" is, either. That's why I asked the above, with a link to the relevant Sequences post.

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

2012-07-31T10:00:17.217041+10:00

America has less Europeans than Finland does, and less Asians than Shanghai does, and more Hispanics and Africans than either. Asian Americans and European Americans score better on the PISA than Hispanic Americans or African Americans. I'm using the word "balance" to mean "distribution," not some measure of race relations.

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

2012-07-31T09:20:09.047460+10:00

simply hadn't noticed that Simpson's paradox was in effect

You don't understand academic culture. Steve Landsburg (like myself) is a college professor. Because of political correctness almost no college professor would dare point out what Landsburg just did.

You're underestimating both how good economists are at math and how bad we are at resisting political correctness.

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

2012-07-31T11:30:04.020325+10:00

You don't have to try very hard to put a positive spin on the fact that everyone is making more money, women are becoming more equal with men, and previously poor non-whites are now finding more jobs. What's not to like?

Speaking as a leftist who disapproves of "honesty" and "fairness" to still-living opponents in a culture war... haha, no way! Why the flying fuck would we want a "positive spin" on a competing project, especially the fact that it seems to move towards our own declared preferences? We want people to get unhappy, restless and desperate; that's the only opportunity to really engage their implicit assumptions! Our folks have even been kind of up-front about that, really:

"I come not to bring peace, but to bring a sword" - Matt. 10:34
"...the worst slave-owners were those who were kind to their slaves, and so prevented the horror of the system being realised by those who suffered from it." - Oscar Wilde, The Soul of Man under Socialism
"The first step in community organization is community disorganization." - Saul Alinsky, Rules for Radicals

Of course, it's not very certain how much actual influence hardcore and committed leftists really have over American upper-brow media. Nonetheless, it's fun to pretend that someone like Dumbledore on crack might be behind our ever-present intellectual confusion.

(I'm just making random Aqua vs. Turquoise noises again.)

P.S. I'm so adopting "Dumbledore on crack" as a brief summary of the Frankfurt School to recommend it to HPMOR fans.

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

2012-07-31T16:42:30.939697+10:00

P.P.S. Although the "cultural Marxists'" reputation on the modern Voldemort flank is rather more impressive than that of Dumbledore's - certainly a plan to "destroy the Western civilization" sounds rather bold and badass. Unfortunately for the Right, as shown above, such "destruction" and "subversion" are in fact just an ancient, refined and respected tradition of the Western civilization. It suffuses much of our general cultural outlook and gives it a unique character, I'd say - or, some angry and cyncial observers would say, it comes from an underlying feeling of pride, achievement and triumphalism. Only a culture immensely secure in its own dominance and privilege would try such relatively scathing self-criticism. That's oh so human. I'm not perfectly OK with it, but I'd be even less cool with an openly "white nationalist" or "racially realistic", Apartheid-style thinking.

Also. Why e.g. Carlyle should necessarily be ascribed more merit, cultural or otherwise, than e.g. Susan Sontag is beyond me. They were both fairly talented writers with a clear individual voice, and highly elitist. How certain... contrarian elements can say that all fans of the latter are a traitorous degenerate menace to all that is White, while even a communist wouldn't attack the former because Hitler and Goebbels happened to like him... well, it's pathetic.

[The above is basically bullshit without a good spin behind it.]

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

2012-07-31T09:22:51.594388+10:00

It's not just impolite, it's an act that makes one unclean.

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

2012-08-02T01:28:11.360457+10:00

http://www.washingtonpost.com/blogs/ezra-klein/wp/2012/07/31/wages-arent-stagnating-theyre-plummeting/

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

2012-07-31T07:07:30.780605+10:00

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?

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

2012-07-31T07:12:36.301688+10:00

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.

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

2012-07-31T08:22:44.490718+10:00

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.

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

2012-07-31T08:45:25.070510+10:00

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.

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

2012-08-02T01:34:08.191222+10:00

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?