Comparing Apples to Oranges: Unit Errors in the NYT

Via Atrios, I found this article at the American Prospect, which demonstrates an example of a very
common and very serious math error that's constantly made in the media: unit errors. If you want to
compare two numbers, you need to make sure that they're actually numbers that can be compared. You can't meaningfully compare height in inches to height in centimeters; you can't compare income in dollars
to income in Euro's - to do a meaningful comparison, you need to convert to a common unit.

The specific error pointed out the by Prospect was in the New York Times. The Times published an article discussing politics and economics in Germany. They make some silly arguments about how the Germans don't like goverment economic reforms because they're all a bunch of lazy socialists who like to have the government take care of them. In support of that, they compare the
unemployment rate of Germany to the unemployment rate in the US. And that's where they make their
error: the unemployment rates that they compare don't measure the same thing. It's a slightly
subtle kind of units problem - but it is a units problem.

The German government reports official unemployment numbers using a unit which is "percentage of
employable people with full-time employment". By contrast, the US government reports official unemployment numbers in units of "percentage of people eligible to work with any employment". In the German figures, if you work a part time job 20 hours per week, you're considered unemployed. In the US, if you work a part time job 20 hours per week, you're considered employed. A huge portion of the "unemployed" Germans would be considered employed in the US; or put the other way, a large number of people who are considered employed in the US because they're working part time jobs would be considered unemployed
in Germany because they don't have full-time jobs.

This difference in units is not an unknown or obscure fact. The Organization of Economic
Co-Operation and Development
- which is as close as exists to an official authority on these kinds of
statistics - clearly documents the difference between how different governments report unemployment. They
further provide a standard measure of unemployment, which is almost the same as the US measure. (The
difference is that the US doesn't consider you unemployed if you're employable but not currently looking
for work; the OECD numbers consider anyone eligible for work but not working as unemployed.)

The Times cites the German rate as 9%, compared to the US rate of 5%. But that's comparing apples to oranges. The accurate comparison, of the OECD is 6% in Germany and 5% in the US. Not nearly such a
big difference as the original article makes out.

This kind of error is very common, particularly in reporting about economics. But it's very bad math.


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very true, this is one of my pet peeves with a lot of data that's reported in media, but I just think I'll quibble with the the wording of beginning: you can compare centimeters to inches as you just need to convert between them, this is in contrast to what you describe below where you actually have totally different units.

Well actually percentages are unitless. The problem arose from the details of the metrics which differ. It would make sense to regard a person who works 20 hours/week and 50%employed, and then compute the numbers from there.

There is a lot of information in units, so the risk for confusion is large.

Economics is especially prone for this as money is a proxy for a lot of otherwise incomparable things made comparable by the market mechanism. (Also, here is where the confusion between percent and percent points really flourish.)

Another problems with units that isn't an error but an irritant is when people prefer to conflate different measures for the same variable.

An example is here, where human contamination of diverse Neandertal sequencings is discussed. The number of human-derived alleles in different sequencings are compared in both absolute and relative numbers. (Which brings out different aspects, but should be separated.)

[Seems two explanations best fits observations. Either the alleged contaminations are not serious, or the bone that everyone sequences was from a recent h. neanderthalensis - h. sapiens hybrid. Both are equally likable, if not exactly equally likely, alternatives. :-)]

By Torbjörn Lars… (not verified) on 12 Sep 2007 #permalink

Kudos on a good catch. This kind of inconsistency drives me crazy, especially when trying to build cross-country datasets for econometric analysis.

Dude you can't chop off a significant digit. The rates, as of July 2007, are 6.4% in Germany versus 4.6% in the U.S. I bet the 1.4 million extra people out of work in Germany don't like this difference...

Also, the NYT doesn't actually commit the sin your accusing it of. It doesn't compare the German official number (9%) to the U.S. rate. The only comparison between the two countries is of the salience of terrorism in the electorate (in Germany terror isn't really a hot-button issue).

Germany, by the way, is doing exceptionally well these last few years and Europe in general, too. This improvement has been attributed to economic reforms put into place in countries like France, Italy and Germany. Merkel actually ran on a campaign of economic reform.

So, basically, I'm not sure what you all are yapping about.

(Just kidding about the "yapping" thing, btw. I know exactly what you're yapping about. Economics reporting is generally pretty bad, but this doesn't seem to be a case of it.)

It's much worse than you think. Most journalists here in Ireland are enumerate and can't differentiate between millions of apples and billions of apples. Thank god we are a small country and we hardly ever have to talk about trillions!

By Jonathan O'Connor (not verified) on 12 Sep 2007 #permalink

It is my understanding that the US unemployment numbers deal only with people actively searching for employment, so that people who have given up finding a job are no longer counted. I am not certain that's correct, but have heard it. Are the German numbers similar in that respect?

I am under the impression that the US has such a weak definition of unemployed so that the number seems much lower than it actually is (e.g. for political reasons "Look at how low unemployment is! The economy is doing great!")

It is nice to see that the Germans are more honest. It probably has to do with their vastly superior political system.

Mark, I have to wonder if we're reading the same article. I cannot find any comparison between German and US unemployment in there. In fact, I can find no mention of US unemployment. All I find is a comparison of two German unemployment rates "The unemployment rate has dropped to 9 percent, from 12 percent in 2005".

Because informed people may have some idea what the US unemployment rate is, they should have put in a statement that the Germans use a different metric, but this is not nearly as egregious a mistake as your post describes.

I believe another factor migth be that the US does not count people who are incarcerated. Does Germany?

So I know you were mislead by the American Prospect article, but if you just follow the links in his article, you'll find the New York Times was correct.

I don't know where he gets 6.4% at all. Following the links he provides lists 9.4%.…

Or using OECD's "standardized unemployment rates"
gives 8.2% in Germany vs 4.4% in the US.

I know full well that newspapers make tons of errors, but blogs make tons more.

I've heard, but can't cite a source, that the US unemployment figures assume that someone who is working at 3 jobs concurently counts as 3 people working.

If so, everyone teaching at two colleges or universities at once ("freeway fliers"), and everyone working a seond job at night to make ends meet, hides the data of someone sitting in their underpants watching TV and drinking beer.

In my lifetime, USA has devolved from a default of two married parents, the dad going out to work and the Mom staying home and raising kids, to that being less than 25% of families. The default is both people in a couple working, and still falling short of the rising tide that lifts all multimillionaires.

We've gone from a default 1-job household to a default 2-job household. What's next? 2.5-job household? Which of the couple works the half-time second job? Or is that the eldest child in a sweatshop? Is this the richest country in the world? Where has the wealth of 1.0 to 1.5 workers per couple gone? Surely it can't all have gone to the S&L Bailout, Iraq, Afghanistan, and Halliburton? Surely it has not lowered our average work week, as seems to be the case in much of Western Europe, Australia, New Zealand, and some other postmodern countries? How to compare apples (days of paid vacation) with oranges (number of SUVs and iPhones per household), if that's the tradeoff made differently in USA (or Japan or Canada) and Germany or France? How much of each work week is spent paying for Health Insurance?

And how is self-employment calculated? I know plenty of writers, actors, painters who work full-time in the sense of perfecting their art with arduous practice, and are doing everything they can to make a profit, but are losing money, due to unpredictable actions of editors, film studios, art galleries. The IRS and California Franchise Tax Board has their own arcane assumptions about who is professional and who is engaged in a mere hobby. As a veteran of numerous tax audits, I know that this is a complicated matter. I keep meticulous business records, and arrive with graphs, canceled checks, printouits, and the ability to "do the math" in my head faster than the auditor. I win each time. But my colleagues are not always so fortunate.

If America is to be the land of Opportunity as attracted my immigrant ancestors, then it must realign its tax and employment strategy to reflect the 2007 mix of employment, part-employment, self-employment, independent contractors, freelancers, start-ups, virtual companies, education investment, and internet-based entities of distributed functionality and virtuality. Is a full-time blogger employed or not?

Jonathan Post, you heard wrong. The OECD numbers (e.g. for the U.S. and Germany) come from household surveys that ask questions like "How many people in your home have jobs, are they part-time or full time?"

Here is a FAQ at the American statistics agency charged with counting unemployment here.

Also, in response to Mark P's question about folks that gave up searching for a job. There is a related problem called chronic unemployment and its much worse in Europe than in the U.S. People in Europe spend much more time unemployed looking for jobs. This is primarily because of "their vastly superior political system."

Lastly, I'll just reiterate... The OECD unemployment numbers are comparable... apples to apples. The U.S. has a much lower unemployment rate than the OECD average and Germany in particular.

Thanks for the link to the official FAQ, Will. It sheds light, sort of.

"Individuals are then classified as employed or unemployed by the computer based on the information collected and the definitions programmed into the computer." [GIGO]

"People who are neither employed nor unemployed are not in the labor force."
[A set may be both Open and Closed]

"Not all of the wide range of job situations in the American economy fit neatly into a given category."
[Square Peg, meet Round Hole]

"Persons are classified as unemployed if they do not have a job, have actively looked for work in the prior 4 weeks, and are currently available for work."
[Given up looking after a long frustrating period of sending out hundreds of CVs and getting few or no interviews? You are now an un-person to us]

"Excluded are persons under 16 years of age, all inmates of institutions and persons on active duty in the Armed Forces."
[Child labor, throwing everyone in prison for drug or political charges, or drafting everyone when the Global War on Terror blows up thus solves the unemployment problem]

Yes, I'd rather live in USA than Germany. But DeutcheAerospace made a good impression on me when they interviewed me in Munich, where I was a VIP speaker in both an Aerospace Engineering Conference and a concurrent Science Fiction Film Festival. Gourmet food in the company cafeteria, with decent wine. And there were NO homeless people on the streets of Munich. Well, actually one. A Math professor all of whose family had died in a car crash. Other academics stopped by to ensure that he was well dressed, fed, and conversationally engaged. Are all the homeless people on American urban streets merely, as Ronald Reagan said: "voting with their feet?"

I stand by my contention that US unemployment statistics are misleading, based on erroneous assumptions, and politically mis-used. Nor is there a viable "safety net."

I speak, not just as someone published in refereed mathematical Economics venues, but as someone who volunteered for 2 years at a "one stop" Unemployment Center in Pasadena, counseling unemployed managers, doctors, lawyers, scientists, engineers, systems analysts, researchers, and teachers.

Unless one wears rose-colored White-House glasses, the employment situation is badly broken.

There is precedent for a solution to this: a person who is employed part time could be counted as three fifths of a person.

By Tegumai Bopsul… (not verified) on 14 Sep 2007 #permalink

"Excluded are persons under 16 years of age, all inmates of institutions and persons on active duty in the Armed Forces."

US prison population of 2,1 million, most working-age males;
this reduces unemployment mumber by about a full percent.

My point includes: who is simply not in the databases to begin with?

How many homeless people are there? Estimates differ by an order of magnitude, depending on who is grinding which axe. How many unemployed illegal aliens are there in the USA?

Big error bars here, hence big error bars in the official statistics. This should not be swept under the rug. It leads to "reasonable doubt."

On the opposite end of the spectrum, whenever I see those Forbes lists of richest people in the USA and in the world, I wonder: how rich do you need to be to keep your name off those lists?