Thursday, September 22, 2016

Dietrich Vollrath says "this isn't the service sector productivity you were looking for...."


Dietrich Vollrath - service sector productivity, Roy, Baumol, etc.

This is just so cool:

Alwyn Young published a paper in 2014 on the “cost disease of services” and productivity growth. In short, the cost disease of services is an idea from William Baumol, and it is intended to explain why productivity growth tends to slow down during a structural transformation from manufacturing to services. The idea is that services have low inherent productivity growth compared to manufacturing, mainly because services are often provided in fixed units of time (you can’t get a one-hour massage in less than one hour). Combine that with the fact that services are highly income elastic, meaning we demand more and more of them as we get richer, and labor moves into services over time. Hence the average growth rate of productivity falls because everyone is now working in this low-growth sector. It is certainly one of my leading candidates for an explanation of why productivity growth is relatively low in the last 15-20 years compared to prior periods of time.

Young’s paper questions whether in fact services really do have slower productivity growth than manufacturing. His argument is going to be that we may be falsely under-stating productivity growth in services because we are not accounting for the fact that the labor flowing into services is, compared to existing service workers, relatively bad at doing service work. What looks like low productivity growth is in fact low growth (or negative growth) in average human capital.

At the same time, productivity growth in manufacturing is over-stated because the workers that remains behind in manufacturing as people leave are only the very best workers, and hence the average ability of manufacturing workers (to do manufacturing work) is going up over time. What looks like high productivity growth is in fact high growth in average human capital.

The idea comes from the Roy model (1951), a classic economics paper about the distribution in earnings. At it’s heart, the Roy model is about self-selection. Imagine that each person has some built-in ability to work in manufacturing, and some built-in ability to work in services. There may be some elements of these abilities that are correlated (maybe you are really smart and could figure out how to do either efficiently), but regardless you’ll have a comparative advantage in one of them. Yes, the same idea of comparative advantage as in trade. You may be good at both activities, but relatively speaking you’ll be better at one or the other when I compare you to someone else.

Young works out an exact case of the Roy model where your comparative advantage is positively correlated to your absolute advantage. That is, people who are relatively good at manufacturing are also absolutely good at manufacturing. Let me be specific, because I know I always found these concepts hard to keep straight in my head. My daughter once took a few hockey lessons, but now has been swimming her whole life. She has a comparative advantage in swimming over hockey. I’ve played hockey for a long time, but I never really took swim lessons as a kid, and I’m always worried about losing my contacts in the water, so I know just enough to keep myself from drowning. My comparative advantage is in hockey.

But not only that, our absolute advantages are correlated with our comparative advantages. If we had a swim race, my daughter would win - absolute advantage matches comparative advantage. If we played hockey, I would win - absolute advantage matches comparative advantage. (This wasn’t true a few years ago. Despite my lack of swimming skill, when she was 7 I could still outswim her just because I was bigger. Not any more. But I can still own her on the ice.)

In the Roy model, if there was demand for one swimmer and one hockey player, my daughter would self-select into the swim sector and I would self-select into the hockey sector. Now, if the economy changes and the demand for hockey falls and swimming rises (global warming?), then I will have to switch. This will unambiguously lower the average skill level of swimmers, as I suck.

When comparative advantage and absolute advantage are correlated in a Roy model, any movement of a worker from one sector to another will lower the average skill of the receiving sector, and raise the average skill of the sending sector. If I get moved from hockey to swimming, I lower the average skill of swimmers. The dudes that remain in my hockey league will be the ones who are still better than me (i.e essentially all of them), and so I just raised the average skill level of my league by leaving.

This is the essence of Young’s story, and he shows that if this is how things work, then it has an effect on measured productivity growth in each sector. Just another example of how measured productivity growth is a garbage pile of all the things we don’t know how to keep track of.

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