Wage stagnation in the US: more than meets the eye

If you can, always look below the surface of data.

Via the Economist journalist Daniel Knowles comes a good example of why its important to look below the surface of statistics. American economist Steve Landsburg addresses a commonly heard refrain – that the wage of the median worker has barely risen in the past thirty years – and shows that all is not as it seems.

Landsburg cites a book by economist Edward Conard (first chapter, containing what we're talking about, here), which itself cites the Census Bureau. I confess that, without a more specific citation, I can't find the exact data Conard uses, but have found similar enough data (pdf, table A-5) to confirm the overall thrust of the argument.

Conard shows that from 1980 to 2005, median income in the US rose just 3 per cent once inflation is taken into account, from $25,000 to $25,700. 2005 is pre-crash, as well, so this isn't a tale of the recession.

But when you break the data down by race and gender, a very different story appears:

  1980 Median 2005 Median Increase
All Workers 25,000 25,700 3%
White Men 30,700 35,200 15%
Nonwhite Men 19,300 22,300 16%
White Women 11,200 19,600 75%
Nonwhite Women 10,200 16,500 62%

For every single demographic group, there was a much bigger increase in the median wage than we see when the groups are combined. The reason for this is obvious when it's pointed out: demographic change in the US means that there are far more (low-salaried) women and people of colour working now than there were in 2005, which pushes the overall average down.

Landsburg illustrates it with a farmyard analogy:

Imagine a farmer with a few 100-pound goats and a bunch of 1000-pound cows. His median animal weighs 1000 pounds. A few years later, he’s acquired a whole lot more goats, all of which have grown to 200 pounds, while his cows have all grown to 2000. Now his median animal weighs 200 pounds.

A very silly person could point out to this farmer that his median animal seems to be a lot scrawnier these days. The farmer might well reply that both his goats and his cows seem to be doing just fine, at least relative to where they were.

This is almost an example of Simpson's Paradox, a well-known (to stats nerds) effect where the direction of a correlation disappears when that correlation is disaggregated. I was taught it with an example involving racial discrepancies in application of the death penalty:

Sixty per cent of white murderers are executed for their crimes, and fifty per cent of black murderers. Are black people discriminated against in the application of the death penalty?

Now suppose that we break down the murder victims by race as well. We find the common pattern that people tend to attack victims of their own race:

Number of murders where death penalty is applied

White Murderer Black Murderer
White Victim 50/70=71% 25/30=83%
Black Victim 10/30=33% 25/70=36%

What about now? Does it begin to look like black people are discriminated against? In this example, black people are more likely to be executed for the murder of black or white victims; but because the murder of black victims isn't taken as seriously by the courts, the fact that murderers predominantly attack people of their race makes it look like black people are less likely to be executed than white people.

The median income example isn't quite a case of Simpson's Paradox, because there is still a positive increase in wage whether or not the statistics are disaggregated. But it's still an example of a time when it is best to dig beneath the surface.

But there is more to be said on the story of wage stagnation. Because a second claim normally accompanies the belief that US wages have stagnated, and that is that there has been a "decoupling" of wages. Due to rising inequality, the median household wage hasn't risen as fast as the mean wage:

If we've seen that the median wage grows faster when disaggregated, then the solid red line is likely to take a steeper ascent. But what happens to the dashed red line when disaggregated?

Sadly, I cannot find the data required to answer the question. If anyone knows where to look, tell me, and maybe we can put the issue to rest.

An immigrant worker protests in Orlando, Florida. Photograph: Getty Images

Alex Hern is a technology reporter for the Guardian. He was formerly staff writer at the New Statesman. You should follow Alex on Twitter.

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Donald Trump vs Barack Obama: How the inauguration speeches compared

We compared the two presidents on trade, foreign affairs and climate change – so you (really, really) don't have to.

After watching Donald Trump's inaugural address, what better way to get rid of the last few dregs of hope than by comparing what he said with Barack Obama's address from 2009? 

Both thanked the previous President, with Trump calling the Obamas "magnificent", and pledged to reform Washington, but the comparison ended there. 

Here is what each of them said: 

On American jobs

Obama:

The state of our economy calls for action, bold and swift.  And we will act, not only to create new jobs, but to lay a new foundation for growth.  We will build the roads and bridges, the electric grids and digital lines that feed our commerce and bind us together.  We'll restore science to its rightful place, and wield technology's wonders to raise health care's quality and lower its cost.  We will harness the sun and the winds and the soil to fuel our cars and run our factories.  And we will transform our schools and colleges and universities to meet the demands of a new age.

Trump:

For many decades we've enriched foreign industry at the expense of American industry, subsidized the armies of other countries while allowing for the very sad depletion of our military.

One by one, the factories shuttered and left our shores with not even a thought about the millions and millions of American workers that were left behind.

Obama had a plan for growth. Trump just blames the rest of the world...

On global warming

Obama:

With old friends and former foes, we'll work tirelessly to lessen the nuclear threat, and roll back the specter of a warming planet.

Trump:

On the Middle East:

Obama:

To the Muslim world, we seek a new way forward, based on mutual interest and mutual respect. To those leaders around the globe who seek to sow conflict, or blame their society's ills on the West, know that your people will judge you on what you can build, not what you destroy. 

Trump:

We will re-enforce old alliances and form new ones and unite the civilized world against radical Islamic terrorism, which we will eradicate completely from the face of the earth.

On “greatness”

Obama:

In reaffirming the greatness of our nation we understand that greatness is never a given. It must be earned.

Trump:

America will start winning again, winning like never before.

 

On trade

Obama:

This is the journey we continue today.  We remain the most prosperous, powerful nation on Earth.  Our workers are no less productive than when this crisis began.  Our minds are no less inventive, our goods and services no less needed than they were last week, or last month, or last year.  Our capacity remains undiminished.  

Trump:

We must protect our borders from the ravages of other countries making our product, stealing our companies and destroying our jobs.

Protection will lead to great prosperity and strength. I will fight for you with every breath in my body, and I will never ever let you down.

Stephanie Boland is digital assistant at the New Statesman. She tweets at @stephanieboland