A great example of Simpson's Paradox: US median wage decline

Since 2000, the median US wage has risen about 1%, adjusted for inflation.

But over the same period, the median wage for:

• high school dropouts,
• high school graduates with no college education,
• people with some college education, and
• people with Bachelor’s or higher degrees

have all decreased. In other words, within every educational subgroup, the median wage is lower now than it was in 2000.

How can both things be true: overall wages have risen, but wages within every subgroup have fallen? This is a great example of Simpson's Paradox. In this particular case, the explanation lies in the changing educational profile of the workforce over the past 13 years: there are now many more college graduates (who get higher-paying jobs) than there were in 2000, but wages for college graduates collectively have fallen at a much slower rate (down 1.2%) than for those of lower educational attainment (whose wages have fallen precipitously, down 7.9% for high school dropouts). The growth in the proportion of college graduates swamps the wage decline for specific groups.

Simpson's Paradox isn't really a paradox at all, it just reflects the fact that your perception of events can change depending on your viewpoint. From the points of view of an economist looking at the national economy, the "headline" rate of overall median wages has slightly increased, largely due to changes in demographics. But from the point of view of a typical individual, wages have declined. The New Statesman says that "it's more accurate to say that wages have fallen in the last thirty years even though the headline figure shows otherwise", but it all depends on your perspective.

Comments

[Phil Simon]

Funny how the paradox has become even more important to understand. Thank pervasive communications and Big Data.

[Robert Young]

Well, thank financial services for distorting the reward system for education. And big data's got nothing to do with it: these numbers are from sample surveys, same as they always have been.

As always, the average of the averages isn't the average of the total.

And, from the point of view of a national "economist", it depends very much where said "economist" sits on the political spectrum. Those of the Right Wing (freshwater) will claim life is better because the median crept up ever so slightly. Those of the Left Wing (saltwater) will claim not only that life isn't better, but that the value of education has declined. I'll leave it to the reader to decide which is the more accurate deduction from the data.

Also, subsequent data (reported in the last week), have shown that wages as a proportion of GDP has declined.
Here: http://www.nytimes.com/2013/08/10/business/economy/us-companies-thrive-as-workers-fall-behind.html?src=recg

[Tim Bates]

Excellent, concrete example, clearly explained!

I think this shows not just that there are frames within which conclusions that are contradictory across frames can be justified (and therefore that users need to ask "what's your frame?" or they will be duped), but also that we should use frame-free perspectives: causal mechanistic perspectives. In this case, we would need to quantify "work".

Frame-free, what has happened is that the value of years of education has declined at the same time as the mean quantity of education has increased. This suggests that the value of a year of school may have declined because the supply of educated workers has increased faster than has the demand for skill AND that the rate of aquisition of education for each worker has increased even fast than the decline in the value of each year. Stated that way, the market and egalitarian accounts are both made clear.

It would be interesting to look along the distribution: are there levels of education that have beaten this trend?