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# Averages and Margins: A Teaching Moment

 We Calculate: You Decide... Nowrasteh on Sowell and Immigr...

UPDATE BELOW: OMG. Even economist Paul Krugman screwed up on this one.

A Facebook friend provided a link to the following article from 2009 by John Carney and Vincent Fernando. It's titled "French: The Most Productive People In The World." Carney and Fernando have unintentionally provided a "teaching moment" about marginals versus averages.

Here's one of the key paragraphs:

France has \$36,500 GDP/Capita and works 1,453 hours per year. This equates to a GDP/Capita/Hour of \$25.10. Americans, on the other hand, have \$44,150 GDP/Capita but work 1,792 hours per year. Thus Americans only achieve \$24.60 of GDP/Capita/Hour.

Carney and Fernando argue that the French have figured something out that we harder working Americans have not. They write:
The real message here is that the French are likely some of the most productive people in the entire world.

They're right that the French people who are working are some of the most productive people in the world. But that doesn't mean that the French have something to teach us.

Here's what's going on. The French minimum wage in 2009 was 8.71 Euros per hour. At the exchange rate then of \$1.33 to the Euro, that translates to \$11.58 an hour. That means that people in France whose value of marginal product was less than \$11.58 an hour did not have jobs. So who was left? Only those whose value of marginal product was above \$11.58 an hour. That's how the average wage in France could be so high. The French government lopped off a large portion of the population, the least-productive portion.

In the United States, we could do the same. Have the government raise the minimum wage to, say, \$12 or \$13 an hour and that would lop off the least-productive workers. Then the average wage of the remaining workers would be higher, in fact much higher than the average in France. But, of course, those people who previously worked and now don't would be worse off. Our GDP per working American would be higher but our GDP per American would be lower.

UPDATE: Berry College economics professor Frank Stephenson, one of my favorite letter writers to the Wall Street Journal, e-mailed me with a link to a very similar post he wrote on this same issue in 2005. Guess whom he was criticizing.

CATEGORIES: Labor Market

Hana writes:

I would think that the calculation is also based on the notion of full time hours. In France the legal definition of full time is 35 hours per week. Historically in the US it was 40 hours per week. In comparing legal full time employees the US worker therefore puts in 15% more time. With the new ACA definition of full time as 30 hours per week, the productivity of US workers per hour will go up per their calculations.

Edward Boyce writes:

The elimination of the least productive workers from the workforce is clearly seen in the employment rates by age, see this OECD publication.
http://www.oecd.org/std/labour-stats/QES_012013Eng.pdf

Employment rates are similar the 25-54 age bracket - 81% for France and 76% for the US. However French employment rates are much lower in the 15-24 age bracket (29% for France vs. 46% for the US) and the 55-64 age bracket (45% for France vs. 61% for the US). The youngest and oldest potential workers are less productive on average, and France employs fewer of them due to its high minimum wage, generous student welfare and early pensions.

David R. Henderson writes:

@Hana,
I don't think so. They don't go with definitions. They go with actual hours worked and so their estimate is not subject to the problem you state.
@Edward Boyce,

Andrew writes:

Can someone clarify if they are dividing per capita or per worker?

If they are going by per capita, why would it matter if they are not employing the least productive?

The household averages change in my house if I don't include my children in the calculation.

writes:

is it per capita or per worker?

writes:

A problem here is that you are only measuring taxed hours worked.

Jared writes:

If you trust the official measurements, we do have GDP per hour worked for the two countries.

From FRED: http://research.stlouisfed.org/fredgraph.png?g=kSu

France's rate of increase has been fairly constant since 1970. The US's rate was growing slower (but was still larger than France's) until 1985. In 1995, something happened in the US' rate growth (or the measurement thereof) and the US' real gdp per hour worked started gaining on France's until it passed it in...2005?

Andrew writes:

I am even more confused after the update.

Take Mr. Stephenson's example of two identical groups composed of 10 people.

Group A: 5 of 10 labor for 8 hours total and create 100 widgets.

Group B: 6 of 10 labor for 8 hours total and create 100 widgets.

Would anyone here claim that Group B is more productive?

David W writes:

Andrew, it's more like:

A: 5 of 10 work, make 100 widgets; 20 each worker
B: 6 of 10 work, make 114 widgets; 19 each worker

A clearly produces more on average per worker or per hour, B produces more overall. And if they're otherwise identical, the only change is whether person B6 worked and made 14 widgets, and was counted as a worker. Or didn't work, produced nothing, and didn't count in the worker statistics.

Andrew writes:

David W --

Your example brings me back to the original question. Per capita or per worker?

In your example, on a per capita basis, Group B is more productive. As a "collective" the 10 people of Group B make 114 widgets vs 100 widgets for the "collective" of Group A.

John Strong writes:

Looks to me like this is just a classic example of Simpson's Paradox. The French are using a different set of inputs in their productivity measurements. They're not counting all those unemployed, rioting North Africans in the banlieu of Paris.

David W writes:

Andrew, the quote gives both. GDP/capita is higher in the US (44K vs 36K); GDP/hour worked is higher in France (25.10 vs 24.60). My example necessarily simplified things, but it still seems parallel.

Tom West writes:

I have to say that this feels like dueling narratives, chosen mostly by one's beliefs. Run on the left and French higher per hour productivity is a clear signal that Americans work themselves to the bone for decreasing value (with most of that value going to the 1%, naturally). On the other side, We have David's narrative with massive unemployment. (My personal narrative - with a higher minimum wage, employers invest more in their workers training and equipment, boosting GDP per worker. Plus they treat them better because the mere fact of paying them more means they must be more worthy of respect - the endowment effect w.r.t. to people.)

In fact, we can add Canada to the mix, which has a minimum wage of about \$10, *lower* unemployment than the US and *lower* GDP, ruining everyone's narrative.

However, I'm certain both sides will come up with a plausible explanation for Canada that, surprise, fits both their worldviews.

The reality is that there are so many factors (and assumptions) that go into figures like GDP that we are free to construct almost any narrative we like. It's just not wise to confuse our preferred narratives (which are likely one factor) with the sum total of reality.

writes:

David, I think your response to Hana is mistaken. The point is that the minimum wage isn't the only factor that reduces the amount of work done in France. There are laws and powerful unions that work together to reduce both the number of people working and the number of hours they work. If we believe there is diminishing marginal productivity for hours of work (not just for number of workers), then your average-versus-marginal argument follows.

Mark V Anderson writes:

@ Tom West.
Very well written. These numbers don't really mean anything because of so many varying factors and measurement issues.

Hana writes:

@David
I understand, but did not see that analysis in the article. In particular I did not see the actual reported hours worked by individuals. While the following is anecdotal, it may have some bearing on the analysis. (I apologize in advance for the personal perspective, I have worked at more and more senior levels for Japanese companies in their International divisions for the past 30 years). If the hours worked are based on surveys with individuals, the national character will have a large bearing on the reported annual hours worked.

As an example, our senior management in our French divisions all were available through the same hours as our Japanese, European and American divisions. While the official hours may vary, all work well in excess of 50 hours per week.

Additionally while the French, and other European, divisions may brag about their August holidays, all were available for critical company discussions during those times. On the opposite side, few Americans, and no Japanese ever brag about the amount of holiday they receive. My thought being that by culture, French would exaggerate their off-time and other cultures would minimize theirs.

Without knowing how the hours of work data was accumulated, I would not discount a cultural bias toward praising leisure, or work, as plausible explanations for part of the difference.