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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The Manchester attack will define this election: Broadcasters have a careful line to tread

It's right that the government should be given a chance to respond, but they must not be allowed to use it to campaign.

Every election campaign has its story, its place in the political history of this country. 2017 will forever be known for Manchester and the horror of the attack on Britain's young; and fighting terrorism will be a theme, overt or underlying, of what we see and hear between now and polling day.

The broadcasters have covered the events comprehensively yet sensitively. But they are aware that we're in an election campaign too; and when other news drives aside the carefully-balanced campaign formats, ministerial appearances give them a dilemma.

The fact is that what the Prime Minister and Home Secretary are doing in response to Manchester is newsworthy. It was Theresa May's duty to implement the recommendations of her security advisers on the elevation of the terror alert, and it would have been unthinkable for the news channels not to broadcast her various statements.

But it is also true that, if the bomb hadn't been detonated, Tuesday would have been a day in which the PM would have been under relentless damaging scrutiny for her u-turn on social care. All the opposition parties would have been in full cry across the airwaves. Yet in the tragic circumstances we found ourselves, nobody could argue that Downing Street appearances on the terror attack should prompt equal airtime for everyone from Labour to Plaid Cymru.

There are precedents for ministers needing to step out of their party roles during a campaign, and not be counted against the stopwatch balance of coverage. Irish terrorism was a factor in previous elections and the PM or Northern Ireland secretary were able to speak on behalf of the UK government. It applied to the foot and mouth epidemic that was occupying ministers' time in 2001. Prime ministers have gone to foreign meetings before, too. Mrs Thatcher went to an economic summit in photogenic Venice with her soulmate Ronald Reagan three days before the 1987 election, to the irritation of Neil Kinnock.

There are plenty of critics who will be vigilant about any quest for party advantage in the way that Theresa May and Amber Rudd now make their TV and radio appearances; and it’s inevitable that a party arguing that it offers strength and stability will not object to being judged against these criteria in extreme and distressing times.

So it's necessary for both broadcasters and politicians to be careful, and there are some fine judgements to be made. For instance, it was completely justifiable to interview Amber Rudd about the latest information from Manchester and her annoyance with American intelligence leaks. I was less comfortable with her being asked in the same interview about the Prevent strategy, and with her response that actions would follow "after June", which edges into party territory and would be a legitimate area to seek an opposition response.

When the campaigning resumes, these challenges become even greater. Deciding when the Prime Minister is speaking for the government and nation, or when she is leader of the Conservative Party, will never be black and white. But I would expect to see the broadcast bulletins trying to draw clearer lines about what is a political report and what is the latest from Manchester or from G7. They must also resist any efforts to time ministerial pronouncements with what's convenient for the party strategists' campaign grid.

There might also usefully be more effort to report straight what the parties are saying in the final days, with less spin and tactical analysis from the correspondents. The narrative of this election has been changed by tragedy, and the best response is to let the politicians and the public engage as directly as possible in deciding what direction the nation should now take.

Roger Mosey is the Master of Selwyn College, Cambridge. He was formerly editorial director and the director of London 2012 at the BBC.

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