# The Slowdown in Europe via Human Capital

Posted by Dietrich Vollrath on January 09, 2023 · 20 mins read

This is the second part of a deep(ish) dive into the growth slowdown in Europe. The first installment looked at the timing and basics of the slowdown. This post is going to dig into the role of human capital.

### Hit the reset button

Before moving onto human capital in detail, I want to back up and revisit the basic story behind the slowdown. While the first post had some fun figures that I referenced to make some general statements about the origins of the slowdown, reading it back I was unhappy at how ambiguous I was about those statements. I want to put some harder numbers on things and make the cross-country comparisons more clear.

I’m doing a basic breakdown of growth in GDP per capita according to the following

$g_y = g_{Cap} + g_{Human} + g_{Prod},$

where $g_y$ is the growth rate of GDP per capita, $g_{Cap}$ is the contribution of physical capital accumulation, $g_{Human}$ the contribution of human capital, and $g_{Prod}$ the contribution of productivity.

On top of that, I’m now going to add a further breakdown of human capital growth:

$g_{Human} = g_{Educ} + g_{Hours} + g_{LFP} + g_{Aging}.$

I’ll describe the data behind those four components of human capital later in the post. For now, $g_{Educ}$ is the contribution of growth in years of education (and presumably in skills/effectiveness of labor). $g_{Hours}$ is the contribution of changes in average hours worked. $g_{LFP}$ is the contribution of changes in labor force participation, meaning the number of workers relative to the working-age population. $g_{Aging}$ is the contribution of changes in the size of the working-age population relative to the population as a whole. When I say “contribution”, I mean the amount of growth in GDP per capita that can be attributed to that specific component.

This means that overall GDP per capita growth can be broken down as

$g_y = g_{Cap} + g_{Prod} + g_{Educ} + g_{Hours} + g_{LFP} + g_{Aging}.$

Roughly speaking, how important was each component to the slowdown in growth? To answer that I have to be more specific about timing. I’m going to compare the growth rate of GDP per capita in the 20-year period from 1999-2019 to the growth rate in the 20-year period from 1979-1999. This cutoff is arbitrary, yes. I wanted to avoid anything that had an endpoint during the financial crisis (2009-2010). And when you see the data, this breakdown in time period seems to show a similar slowdown across countries.

The data I’m going to show you is the difference in growth rates between those two 20-year windows of time. For GDP per capita, for example, I’m calculating this:

$\Delta g_y = g_{y,1999-2019} - g_{y,1979-1999}$

where $g_{y,1999-2019}$ is the average annual growth rate of GDP per capita from 1999-2019, and a similar definition holds for $g_{y,1979-1999}$ from 1979-1999. Because we observe a slowdown, that $\Delta g_y$ number is going to be negative; the growth rate fell. For each of the components of growth (physical capital, etc..) I’m going to calculate a similar $\Delta$ term for their growth rate.

Here’s the data for the set of European countries and the US that I referenced in the first post. All the numbers here are in percentage point terms.

For Germany (DEU), this says that the growth rate fell by 0.67 percentage points from 1979-1999 to 1999-2019. The remaining terms in the table show where that -0.67 came from. For each of the remaining terms, you can interpret them as “how much would growth have changed from 1979-1999 to 1999-2019 if this was the only thing that changed”.

You also have to be careful in reading this table. The numbers here are not growth rates, they are changes in growth rates. In Germany, for example, the contribution of productivity growth is negative 1.32 percentage points. This does not imply that productivity in Germany fell. It means that the growth rate of productivity was lower in 1999-2019 than in 1979-1999. Productivity kept rising in Germany from 1999-2019, it just didn’t rise as fast as it once did.

Keep this in mind for all the different components of growth. A negative for education doesn’t mean education fell. It means the growth rate of education fell. Education (and presumably skills) kept rising, just at a lower rate than before. A positive for hours doesn’t mean average hours worked went up, it means that the growth rate of hours was higher (i.e. less negative) from 1999-2019 than it was from 1979-1999. Big positives in LFP don’t necessarily mean LFP itself went up, they mean that the growth rate of LFP was higher in 1999-2019 (which could mean LFP grew or just shrunk at a slower rate).

### Differences in the US and Europe

Maybe the most interesting thing to do with the above table is compare the US and Europe. Doing so is what motivate this post and the planned follow-up on productivity. If you look down the first column, you’ll see that Europe and the US had similar growth slowdowns in terms of size. Italy and Spain had more harsh slowdowns, Germany less so. But everyone is roughly in the same boat.

Physical capital’s contribution and education’s contribution look kinda-sorta the same in Europe and the US. It’s the other terms that are quite different.

For the US, the slowdown is mainly a story of labor force particiation, demographics, and hours. The decline in productivity growth in the US is minor by comparison. In Fully Grown I zeroed in on the demographics, in part because I was combining the LFP and Aging components. The data in the table here is also a little different than what I used in Fully Grown (Penn World Tables versus national accounts) so there are going to be slight discrepancies.

In contrast, the story of the slowdown in Europe is about productivity growth and aging, but with substantial offsets coming from LFP and hours. Changes in labor market activity, in general, prevented the slowdown in Europe from being even more devastating.

To give you some idea of how important this offset was, consider a few simple counterfactuals. First, what is the “worst case” growth slowdown for Europe? That would be if the declines due to productivity growth and aging occurred, but the growth contribution of LFP and hours did not change at all (i.e. kept growing at the 1979-1999 rate). Second, what is the “best case” growth slowdown for Europe? That would be if the increases in growth due to LFP and hours occurred, but the growth contribution of productivity and aging did not change at all (i.e. kept growing at the 1979-1999 rate). In both worst and best case scenario, I’ll leave the growth rate change due to physical capital and education as they are.

The table gives you the consequences. The first column is the actual slowdown in growth in each country (e.g. -0.67 percentage points in Germany). The worst case scenario is very bad compared to the actual slowdown. For Germany, rather than losing 0.67 percentage points off the growth rate of GDP per capita, they would have lost 2.55 percentage points off the growth rate because of productivity and aging alone, without labor force changes to offset them. The growth rate of GDP per capita from 1999-2019 in Germany was actually 1.20 percent per year (0.67 pp lower than the 1.87 percent per year from 1979-1999). In the worst case it would have been negative 0.68 percent per year. Living standards in Germany would have literally fallen in the worst case.

In the best case, Germany’s growth rate would have gone up by 1.31 percentage points if only the labor force changes occurred. Rather than 1.20 percent growth from 1999-2019, it would have been 3.18 percent growth in GDP per capita, which is a huge number for a developed country.

The point is that the gross changes in the componenents of growth (productivity, labor force participation, etc..) were massive in Europe between 1979-1999 and 1999-2019. They turned out to offset each other in many cases, so that the net change in the growth rate of GDP per capita was “only” on the order of minus 1 percentage point for most of Europe.

For this post, I’m going to take this breakdown of things as given. But I’ll be honest, the gross movements here are so big, and they offset in just the right way, that I’m nervous this is some kind of data error. I can’t find anything obviously wrong in the code or data I’m using, but it still smells a little off to me. Code and data are linked in the last section of the post, so if someone wants to take a crack at things, be my guest.

### Seeing the changes over time

Given the importance of the human capital elements in both driving (aging) and offsetting (LFP, hours) the growth slowdown, let me give you some more detailed evidence on their growth contributions over time. As I said earlier, I’ll look at productivity in a later post.

First up is the growth rate of labor force participation, $g_{LFP}$. The figure shows the 10-year backward looking average of this for each country.

Consistent with the table, if you look at the period from around 1980 to 2000 these numbers tends to be just at or below zero, so that $g_{LFP} \approx 0$. From around 2000 to 2019 it seems to be that $g_{LFP}$ is around 0.005 to 0.01, or 0.5%-1.0%. Thus the difference in growth rates is around 0.5-1.0 percentage points. This is true even though the financial crisis knocks down $g_{LFP}$ around 2009 for everyone.

Thinking about this in growth rates can be kind of annoying, so here’s a figure with the level of $LFP$ - employees divided by working-age population - for each country over time. No rolling growth rates, no nothing, just the actual meaures of $LFP$ I’m using.

You can see the dip from 1980 to about 2000, and then the steady rise from 2000 to 2019. It’s not massive changes in the ratio we’re talking about here. But a rough sketch would be that $LFP$ fell from about 0.75 in the late 1970s to about 0.65 by the late 1990s, and then has risen back to about 0.75 by 2019. Thus the positive contribution to growth of $g_{LFP}$ that offsets the growth slowdown.

If instead you look at the graph for aging, $g_{Aging}$, you get a tighter picture. Recall that $g_{Aging}$ is measuring the growth rate of the ratio of working-age population to all population.

Here there is a distinct “hump” (especially for Germany) in the period from 1980 to 2000, and then a decline after 2000, and the actual growth rate becomes negative. This generates the negative effets of aging on the growth slowdown seen in the table above. One thing to note here is that the US is not quite like the other countries. The US has a more substantial early bulge in the 1960s (the Baby Boom) and a less pronounced dip later on. In the US the pure effect of aging isn’t really negative until quite recently, but in Europe the negative effects kicked in closer to 2000.

This is another case where the actual level is interesting. The figure above plots the actual ratio of working-age population to total population over time for all the countries. It is …. boring? You can see the rise from mid-1970s to mid-1990s, and then the decline. It doesn’t look very dramatic here, but nevertheless the change in growth rates contributed in a significant way to the growth slowdown. Just to give you a sense of the effect size here, consider the following stylized example. Let’s say in 2000 63% of your population was of working age, but by 2019 it was only 60%, something consistent with this figure. By itself, how much lower would this make GDP per capita? Well, the ratio of potential workers to all population is only 60/63 = 0.95, or 95% of what it was before. So GDP per capita - holding everything else constant - would in 2019 be only 95% of what is was in 2000. That translates to a drag on the growth rate of about -0.003, or about 3/10ths of one percent per year. Doesn’t seem like a lot? Remember that the growth rate on average fell by about 8/10ths of one percentage point during the slowdown. 3/10ths is a pretty big share of 8/10ths.

Last, for hours worked let’s just jump right to the level. The figure shows average (annual) hours worked by country over time. From 1950 right through about 1990 it declines steadily. Let’s call it about 2000-2200 to about 1600-1800. And after 1990 it continues to decline in most countries, but at a much slower rate. The curves here are almost flattening out. The arrest of the decline in hours helped offset the negative effets of aging and productivity during the slowdown.

### Labor markets saved Europe?

What’s the conclusion? What I’d say this data tell us is that labor market changes, particularly in labor force participation, were crucial in offsetting an even worse growth slowdown in Europe. Productivity growth fell a lot, and the aging of the population also pushed towards a substantial drop in the growth rate of GDP per capita. Increases in labor force participation and the levelling out of hours worked arrested some of that drop. The slowdown in Europe is due to productivity and aging. The net effect, however, was not as bad as it could have been because of labor market changes.

The story for Europe is also quite different than for the US. In the US the drop in productivity growth was almost inconsequential. But hours and labor force participation helped contribute to the slowdown, along with aging. If anything, I’d have to revisit Fully Grown with less attention to the aging itself, and more attention to the changes in LFP.

Regardless, you cannot simply port the argument in Fully Grown over to Europe. I’d still argue that the aging aspect of the European slowdown was to some extent a consequence of successes like contraception and women’s rights. But the productivity slowdown in Europe is way beyond what was seen in the US, and could well be something more “wrong” with the economies. As promised, I’ll try to tackle the productivity stuff in the next post.

### Data, Code, and that stuff

As in the initial post, most data comes from the Penn World Tables, and I access that directly using an R package. The script that produces all the figures and tables in the post is here. What’s new in that script is that I pull in OECD data on age structure to do the calculations involving working-age population. The OECD data is stored in a CSV file here. I used a CSV because the OECD package in R takes a long time to download. It means that to use the script you’ll have to edit the working directory to point to wherever you store the data file. The script was for my use, so caveat emptor.

The basic accounting I do is the same as in the prior post. What I added here was the breakdown in human capital. In the prior post I referred to human capital per capita as $h$. Here the definition of that is:

$h = e^{\phi S} \frac{Hours}{Employ}\frac{Employ}{WorkAge}\frac{WorkAge}{Pop}.$

The first term captures the effects of average years of schooling, $S$, through a Mincerian function, $e^{\phi S}$, where $\phi$ is the return to a year of schooling. I am just pulling this $e^{\phi S}$ term directly from the PWT. I’m simplifying my explanation of what they actually do, which involves different returns for different years of education. Their documentation gives you the full details.

Hours/employee is directly from the PWT. The numerator $Employ$ is the number of employees from the PWT, while $WorkAge$ is the number of 20-64 year olds reported by the OECD. $Pop$ is from the PWT. So one possible error in my calculations is that the two sources are distinct. However, the numbers I get for $Employ/WorkAge$ and $WorkAge/Pop$ are reasonable compared to other sources, so I’m pretty okay with that.