# Describing the Decline of Capital per Worker

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The last post I did on the composition of productivity growth documented that recently we appear to be using productivity to reduce our capital/worker, as opposed to increasing the growth of output per worker. The BLS measure of ${K/L}$ is actually shrinking in 2011-2013. That is an anomaly in the post-war era, and seems worth digging into further. Here is some more detail on what is driving the negative growth in ${K/L}$.

• Let me start with a correction. I said in the last post that the BLS was including residential capital in their calculation of ${K}$, but that imputed income from owner-occupied housing was not included in ${Y}$, and that seemed strange. The BLS includes tenant-occupied residential capital in their calculation of ${K}$, and tenant-occupied rents as part of their measure of ${Y}$. They exclude owner-occupied residential housing from ${K}$, and imputed owner-occupied rents from ${Y}$. In short, it seems kosher.
• The decline in ${K/L}$ in the last few years is a function of ${L}$ growing faster than ${K}$, but ${K}$ is still growing. The figure below shows the separate growth rates of both ${K}$ and ${L}$ over the last 20 years.

The growth in ${L}$ is relatively large compared to ${K}$. Why is ${L}$ growth so large? This is a composite measure created by the BLS that measures hours worked, and is weighted by worker type (education, etc..). So it is quite possible to have very strong growth in ${L}$ because hours worked of those employed are higher, even though the absolute number of workers is not growing rapidly. Regardless, ${K/L}$ is falling because growth in ${K}$ is relatively slow. But it is not negative.

• Is the slow growth in ${K}$ caused by any particular type of capital? The BLS has separate measures of equipment, structures (think warehouses), intellectual property (think software), land, rental housing, and inventories. We can look and see which, if any, of these are particularly responsible for the slow growth in ${K}$. What I’ve plotted here is the weighted growth rate of each category of capital. The weighting is their share in total capital income, which is how the BLS weights them to add up total capital growth. This makes the different colors comparable in how they influenced the growth of ${K}$ in a given year.

Looking over the last 4-5 years, there was clearly shrinking inventories (grayish/green) and land (red) during the recession. Since then, there has been negative growth in rental housing capital (yellow) over the last 4 years, but this is a really small effect on aggregate ${K}$ growth.

The rest of the categories are growing. But if you compare them to pre-2007 rates, they are all growing slowly. Equipment grew at about 1.8% per year, for example, in 2011-2013, but at 2.6% per year prior to 2007. Structures grew at 0.6% per year 2011-2013, but 1.5% prior to 2007. IP grew at 2.9% 2011-2013, and 5.2% prior to 2007. Rental housing shrinks at 0.6% 2011-2013, and grew at 1.1% prior to 2007. Inventories and land growth rates are roughly similar in the pre-Great Recession and post-Great Recession periods.

The overall decline in ${K/L}$ is thus not driven by any one single category of capital. Even the reduction in rental housing stock is not really that meaningful in absolute size, and it never was that big of a contributor to ${K}$ growth to begin with. This is a broad-based decline in capital growth rates.

What that indicates about the source of this change, I don’t know. I have to think harder on that. It certainly seems to indicate a secular change in investment behavior, though, rather than reallocation away from some category and into another. So explanations that build on a common drop in savings/investment rates are likely to be successful here.

• Because I love you all, I extracted the BLS aggregate labor input data from a PDF, to see what was going on. The figure shows that the BLS labor input measure (the blue bars) contracts sharply in 2008/09, and then has grown at a relatively normal rate of about 2.5% per year since then. This is driven almost entirely by changes in the growth rate of hours (red bars). The growth rate of labor “composition” (green bars) is basically consistently positive over this whole period, but at a low rate of growth. Composition is capturing the quality of labor; think education levels.

In 2011-2013 you can see that the labor input is growing at really robust rates compared to the historical series. This is the strong ${L}$ growth that, combined with the slow growth in ${K}$, is part of the slow growth in ${K/L}$. Why does it appear that labor input is growing so robustly in the BLS data? This is private business sector data only, excluding the government, which is a huge employer and has not been expanding employment much. So the private business sector labor input has been growing robustly, even though the labor input at the national level may not be growing as fast.

• The labor data and capital data seem to indicate that this is some kind of broad slow-down in investment in capital goods, and not some temporary adjustment by one type of capital. This drop occurs exactly when the Great Recession ends, so it seems that the changing financial conditions since then (ZIRP? Credit tightness?) may be responsible, as opposed to something like demographics. If it was demographics, why did all of the sudden after the GR did people decide to stop investing? Did all the Boomers get old all at once?

Whatever the cause, let me just remind everyone that there is no a priori reason that the decline in ${K/L}$ is a bad thing. A perfectly reasonable response to higher productivity is to reduce the use of inputs. But it an an anomaly, and it seems unlikely that everyone decided all at once that they’d like to shed inputs rather than increase output. Whether it has a detrimental long-run effect on growth is not something I can say given the data I’ve got.

## 11 thoughts on “Describing the Decline of Capital per Worker”

1. A detail of something that’s going on here. Don’t for a moment claim that it explains everything but it does explain some of part of it.

“IP grew at 2.9% 2011-2013, and 5.2% prior to 2007.”

That’s also about the time of the start to the shift to Saas.

We can have two economically equal things which are counted differently in the GDP stats.

For example, let’s say that Office is purchased by a company on a two year licence (no idea, could be, isn’t that about the time between upgrades?). That’s capital investment, the spend is amortised over two years, that’s where we get our investment numbers from, corporate accounts.

We can also have Office 365. This is a monthly subscription. This is not capital investment. This is current spending. Thus in a different silo in GDP.

But, obviously, as we’ve got the same people using the same software to do the same things, this is economically equivalent.

Tot up the Saas market and you do get to something that is large enough to change GDP investment stats at the margin.

I do not, for a moment, claim this is everything. But it is something to be aware of. Goldman had a report a couple of months back looking at corporate investment in software. As this was flatlining therefore less capital investment. But with the above, Saas, that’s not obviously a true statement any more.

• That’s a good point. The numbers BLS uses are built on ultimately arbitrary definition s of what is capital, so changes in reporting could have an effect. I’d have to dig deeper to try and figure how big of an influence that has.

2. Isn’t this what one would expect in an economy with tepid growth in demand and wages, and equities markets demanding and rewarding value extraction, including through share buybacks, rather than investment and long-term growth?

3. Hmm. As to your last point, couldn’t it also be that ‘since we can get lots of people to work lots more hours for a very small pay delta, why should we bother investing?’

4. I’m currently reading books and articles on artificial intelligence, primarily machine learning. It’s quite fascinating. But a big question is, if the quality, the capability, of this software skyrockets, how much of this will be captured in an increase in the value of capital as it’s currently measured, with our current metrics.

AI, and even the amazing machine learning that has recently given us the google car and Watson, and far more capable robots, has actually been around for decades, maybe even at least going back to Turning. But just recently we’ve improved it a lot, and gotten far faster better, cheaper, and smaller hardware to run it on, and gigantic data to train/teach it on.

Improvements in this software can, in reality, for what we really want to get at, vault forward the true value of capital, but perhaps not cause much of an increase in sales revenues for it’s inventors, and in our current metrics for capital.

5. My guess is that two big IT-related trends are playing a major part in this: virtualisation (giving much more efficient utilisation of physical servers) and cloud computing (giving massively more efficient use of computer and software capital by sharing across many users). Both would tend to reduce average capital per worker and both have been growing very rapidly over the last few years. Cloud in particular represents a fundamental shift for end user businesses: away from capex towards bought-in services. These are very rational discounted cashflow decisions for the businesses but have interesting implications for measured productivity…

6. Can this be driven by the fall in relative price of certain types of capital?

I take it you measure K in real terms so the issue would be how you deflate it, by something like a GDP price index or by an index of just capital goods? And then, if the second you have the problem of only computers and that type of things getting much cheaper, so you really could have large real investment in that sort of capital showing up as a much smaller amount.

7. I get the point about new IT spending switching from capex to services – I’m in that business. But it does seem like the “equipment” component of capex growth is recovering nicely. What yell out to me, when I look at the decomposition of capital growth chart, are the red “land” and the brown “structures” components. Why did land go to zero two years before the recession – and why is it going there again? Structures is a recovering category – but recovering pretty slowly. Seems like there may still be a big overhang in those categories from the previous boom.