One of the running themes on this blog is that productivity (called total factor productivity or multi-factor productivity by those in the biz) is basically a garbage dump for all the stuff we do not know how to measure in the real economy.










In the past on this blog, I’ve referred to measured productivity growth as the “residual”, R, and true productivity growth as A. So to be consistent with the blog, but not with Young’s paper, he finds that

where $\hat{R}$ is the growth rate of the residual productivity measure (what you see reported by the BLS) for sector j. So $\hat{R}_{Manuf}$ is the residual productivity measure for manufacturing, as an example. $\hat{A}$ is true productivity growth in sector j. $\hat{s}$ is the growth in the share of labor working in sector j.

$\xi$ is how average worker ability/skill responds to a change in sector j’s share of the labor force. Young establishes empirically that $\xi$ is less than zero. He has his own estimates based on using sector-level data from Europe and the US, and this is consistent with several other estimates drawn from the literature. These estimates come from regressing measured productivity growth, the $\hat{R}$ things from many sectors over many years, on measures changes in labor shares, the $\hat{s}$ things. An important element of this is that Young actually has these labor terms for 60 types of labor, differentiated by gender, age, and education. Thus his estimate of $\xi$ is not just picking up on the fact that perhaps manufacturing workers are older, male, and less educated, for example. It has to be mentioned here as well that Young’s estimates are very imprecise, with standard errors big enough that you cannot reject zero in many cases - his case is really made on the fact that the negative estimates are so consistent across different samples and specifications. So you could easily remain suspicious of these results pending some more precise way of nailing down the value of $\xi$.

The fact that $\xi$ is estimated to be less than zero implies that measured productivity growth in a sector goes down when more labor (of any of the types) is added to the sector. This is consistent with the theoretical case Young discussed within the Roy model of comparative advantage and absolute advantage being correlated. And now that we know $\xi$ is negative, we can see what kind of an effect the Roy effects have on measured productivity.

Take manufacturing, which has a shrinking share of labor, meaning $\hat{s}<0$ for that sector. Combined with $\xi<0$, this means that $\hat{R}>\hat{A}$ for manufacturing. Measured manufacturing productivity growth is higher than true productivity growth. Flip the logic around for services, where $\hat{s}>0$, and you get that $\hat{R}<\hat{A}$. Measured productivity growth is lower than true productivity growth.

Young provides a table where he recovers the true productivity growth rates in each sector. This depends on the value of $\xi$, and his estimates suggest that this parameter is somewhere between -0.5 and -1.0.


Looking at the table, the first row just gives the regularly reported values for productivity growth in the US and the EU for manufacturing and service productivity growth. In the US, manufacturing (goods) has reported productivity growth of 1.57 percent per year, and services only 0.73. However, if Young’s estimate of $\xi$ of -0.5 is right, then in fact true productivity growth is more like 1.10 in manufacturing and 0.84 in services. If -0.75 is right, then services have a small advantage at 0.90 percent per year, manufacturing has 0.87, and they are basically equal. You get a similar pattern for the EU, where manufacturing and services show similar productivity growth once the $\xi$ parameter is big enough in size.

This analysis suggests that perhaps Baumol’s story is wrong. Services may not have a built-in tendency towards slower productivity growth over time. Rather, we are measuring it wrong. Remember that residual productivity measures are junk piles, and what Young is suggesting is that service productivity measurement had a big load of crap dumped on it because of these Roy effects. Manufacturing does not necessarily have better productivity growth, because it also had a big load of crap dumped on it by the Roy effects. If you take Young’s work seriously, then he’s showing you that productivity growth across all sectors is roughly similar over time, and hence there is no need to worry about the shift from manufacturing to services.

Now, what Young doesn’t do is decompose his table by time periods, so we cannot examine the effects when aggregate produtcivity growth was large (the 90’s) and when it was small (the 10’s). Has the Roy effect gotten bigger or smaller over time, or is it unchanged? And these Roy effects don’t necessarily offer any explanation for the aggregate productivity slowdown we’ve seen in the last few decades. Note that adjusting for the Roy effects may make the true aggregate productivity growth rate go up (the EU) or down (the US). The best this table can do is explain that the slowdown wasn’t due to “Baumol effects” of moving into services. But that’s important, because it means that we are not somehow doomed to slower productivity growth just because we’ve moved into services. We’re doomed for entirely different reasons, apparently.

A few other notes about this paper. David Lagakos and Mike Waugh use this same concept to explain why there is such a large gap in productivity between agriculture and non-agriculture in developing countries, and why that gap tends to disappear as countries develop. And that makes me wonder about accounting for productivity growth rates in sectors in the early part of the 20th century, when agriculture was the shrinking sector and manufacturing was growing. Based on Young’s logic, this means we were probably over-stating agricultural productivity growth and under-stating manufacturing productivity growth. So perhaps Bob Gordon’s story of high mid-century productivity growth is even more extreme than I thought?

Last, if you want to learn how to write a lucid economics paper, read this one, or really any of Young’s work. It’s just so coherently organized and explained compared to the vast, vast, vast majority of what gets published.