Miles Kimball posted a link to a relatively old Scott Sumner post that was discussing a Paul Krugman post from 2011. Which means I am only about 3 years behind, which is good, because I would have estimated I was about 5 years behind.

Anyway, Scott's post deals with some facts about France. Namely, while GDP per capita in France is only roughly 70% of the U.S. level, GDP per hour worked is essentially equal to that in the U.S. French workers are just as productive per hour as U.S. workers, but just work fewer hours in aggregate.

There are generally two responses to this. The optimistic one: "The French have made a decision to spend their high productivity by taking more vacations and retiring earlier, leading to lower GDP per capita, but probably higher utility." The pessimistic one: "The French labor system is so mucked up by taxes and regulations that despite being as productive per hour as the U.S., firms do not find it profitable, and workers do not find it desirable, to have more hours provided."

It's non-obvious which view is correct. Scott's post makes two great points, though, about how to think about this. The first is one that I'm not going to deal with here. Comparing France to the U.S. is not an apples to apples comparison. The U.S. is better compared to the EU, or at least Western Europe, as a whole. French productivity looks much worse when compared to New England or the Mid-Atlantic as a region, and only looks good in comparison to the U.S. because the U.S. includes Mississippi and Alabama (which I will arbitrarily call the Sicily and Greece of Europe). It's a great point.

The second idea that Scott talks about is whether we should be impressed by French output per hour being as high as the U.S. In France, the high youth unemployment rate and early retirement rate mean that the employed population is concentrated in the 30-55 age range. If this age range tends to be particularly productive compared to other age groups, then shouldn't French output per hour be much higher than in the U.S., where we employ lots of sub-30 and over-55 workers?

Jim Feyrer has a paper from a few years back that looks precisely at the relationship of age structure and measures of productivity. What he finds is that the most productive group of workers are those aged 40-49. An 1% increase in the number of those workers (holding other age groups constant) is associated with about a 0.2% increase in productivity. Ages 50-plus imply lower productivity, but the statistical significance is low. Ages under 39, though, are significantly negative for productivity. Jim uses these relationships to partly explain the productivity slowdown in the US during the 1970s, when the Baby Boomers were filling up the labor force and were still under 40, meaning they were relatively low productivity.

But the results speak to this French question that Scott poses as well. By employing so few under 39-year-olds, France is essentially only using the very high productivity workers in the economy. Thus their GDP per hour is likely inflated by that fact, and their workers are not necessarily just as productive as those in the U.S. What you'd want is some kind of equivalent measure for the U.S. to make this concrete. What is the age-structure-adjusted GDP per hour worked in the U.S. and France? Based on Jim's results, the U.S. would be ahead in that comparison.

This is related to the well-known result in labor economics that wages rise with labor market experience, but at a decreasing rate. That is, people's wages always tend to rise with experience, but once you hit about 25-30 years of experience (meaning you are somewhere between 40-55 most likely, the increase gets close to zero. You can see a bunch of these wage/experience relationships in a paper by Lagakos, Moll, Porzio, and Qian, who compare the relationship across countries. One of the features of the data is that in rich countries (like France and the U.S.) the wage/experience relationship is really, really steep when experience is below 10 years. In other words, wages are particularly low for people who have little labor market experience, like young workers aged 18-25.

The U.S. tends to employ a lot more 18-25 year olds as a fraction of our labor force than France. Even prior to 2007, unemployment among those under 25 was roughly 20% in France, and only 10% in the U.S., see here. So the U.S. is employing far more workers that have not yet hit the sweet spot in labor market experience and their wages are very low. On the assumption that wages are some indication of how productive workers are, this means that the U.S. employs proportionately more low-productivity workers. So, again, France's measured GDP per hour should really be higher than the U.S. level if in fact France and the U.S. have similar productivity levels.

Scott's point is that we can't take the equivalence between France's and the U.S.'s GDP per hour at face value. This doesn't necessarily mean that the pessimistic view noted above is correct. France could well be making some kind of optimal decision to take lots of leisure time and retirement. But that decision is not one made with the same "budget constraint" as the U.S. - France is very likely not as productive as the U.S.

If you do want to subscribe to the pessimistic viewpoint, then you could argue that not only have French regulations mucked up the labor market, but they have also given the statistical illusion of high productivity. Hence, France is in fact much worse off than the U.S. Even if they fixed their labor market, their GDP per capita would not reach U.S. levels.