Yes, the cyclicalists really won the bet

So, Bryan Caplan won a bet with Tyler Cowen regarding the unemployment rate. Cowen bet that unemployment wouldn't go below 5% at any time between 2013 and 2033. It recently did, so Caplan won the bet 17.5 years before the deadline. Paul Krugman says that this is vindication for cyclical theories of unemployment, as applied to the Great Recession, over structural theories.

Tyler says: Not so fast. Unemployment may be down, but the employment-to-population ratio has barely budged:

He then cites some labor search theory papers, such as this one by Restrepo and this one by Elsby and Shapiro, that describe various situations in which we might see substantial structural unemployment. All in all, Cowen declares that "I feel I'm the one who won the bet." 

So who is right? Caplan and Krugman are mostly right, and possibly completely right. Cowen is at least mostly wrong here.

The reason? Aging. The Great Recession came along just as Baby Boomers were starting to retire, which is why the employment-to-population ratio hasn't recovered. Instead, let's look at the best measure of employment: the employment-to-working-age-population ratio:

As we can see, there has in fact been a strong and steady recovery in employment when we just look at working-age people. About 75% of the employment drop of the Great Recession has been reversed. So if the bet has a "true" winner, or a winner in spirit, it's definitely Caplan.

What about that last 25%? That represents a little over 2 million people. Does that represent increased structural unemployment, possibly due to effects of the Restrepo type, the Elsby-Shapiro type, or others (such as de-skilling)? It might. But it will be a while before we know. So far, correctly measured employment has been on a strong, smooth, steady upward trend. Only if that trend suddenly breaks, and employment flatlines at a level below the previous one, will it be time to reach for structural explanations for the Great Recession.

Interestingly, if we're using employment recovery as our measure of structural-ness, the 2000 recession looks a lot more structural than the Great Recession. The drop in employment-to-working-age-population after 2000 was almost as steep as that of the Great Recession, and there was far less bounceback. The 2000s really were a "lost decade" for U.S. employment. Of course I suspect China trade as the culprit, based on the timing and on the recent Autor-Dorn-Hanson paper. But that is a story for another day.

Regarding the Great Recession, the conclusion is simple: Caplan has earned his $10.

Which, unfortunately, is not even enough to buy 1/2 of a small Zachary's pizza. 

Updates

On Twitter, Ernie Tedeschi shows an alternative measure, the demographically adjusted employment-to-population ratio:

This measure is designed to take into account the changing age composition of the population. My preferred measure, the employment-to-working-age-population ratio, makes no distinction between a 15-year-old and a 64-year-old. This measure does. Aging doesn't just reduce the percentage of total population in the 15-64 bucket, it also shifts the distribution within that bucket.

The "adjustment" in this measure is meant to take that into account. But it will also involve making some assumptions. It probably assumes that the relative likelihood of a a 64-year-old to be employed and a 15-year-old to be employed stay the same over time. In fact, that is not true. In the recovery from the Great Recession, employment rates rose much more strongly among the old than among the young. That means that the "demographically adjusted" employment-to-population ratio will tend to understate the degree of labor market recovery following the Great Recession. For that reason, Ernie's graph shows a slightly less robust recovery than my own, though the basic stories are the same.

But this graph does make me think I was much too quick to label the post-2000 employment stagnation "structural". Maybe a lot of that was just due to aging, as the Boomers approached (but didn't reach) the official retirement age.