Kevin Drum tries to set Matt Yglesias straight, arguing that this logarithmic graph of real GDP demonstrates that growth has not been any slower in the past thirty years than the previous thirty years:

What it mainly demonstrates instead is that it's hard to read changes in small growth rates on a log graph. If we instead go to the BEA data, and compute the CAGR (compound annual growth rate) over the thirty year period 1950-1980, it was 3.63%, while the 30 year period 1979-2009, it was 2.66% (2010 is not available yet). So the last thirty years are a whole percentage point lower growth. And that's despite the earlier period including the very rough years of the 1970s.

Another way to look at it is to compute the ten year CAGR for the decade prior to each year. That looks like this:

You can see that from 1956-1974, there was a period where every 10 year window in that timeframe averaged over 4% growth. Nothing like that has been seen since. And the last 10 years are the worst since WWII.

## Monday, January 24, 2011

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## 11 comments:

Thank you. I've been looking for specifics like this.

The first graph does not show a decline in growth. Is that because somebody just "eyeballed-in" the trend line, do you think? Or is it maybe because population growth slowed in sync with economic growth? Maybe the economy is doing really good, and we just don't know it because the baby boom ended??

Got a link to your spreadsheet for these numbers?

Art

In my view, the simplest way to look at this is to plot the inflation-adjusted per capita GDP vs. year. Such a plot from 1949 to 2010 (using preliminary 2010 data which is up slightly vs. 2009)is quite linear. A linear trend does reflect a declining percentage year over year growth, but certainly does not indicate a cessation of growth.

In a spreadsheet I could take the first and last year values and find a growth rate for the period by binary guessing. But it seems there must be a better way. If CAGR has a name, it must also have a formula... and I'm out of school way too long now to be trusted to think on my own.

From the second graph above, it looks like all we need to bring back growth is to bring back the Viet Nam war.

The so-called "golden age" is dated 1947-1973 or thereabouts, but that 2nd graph only starts around 1960.

Anyway Mike, "A linear trend" that "does reflect a declining percentage year over year growth" contradicts Stuart's post title!

Arthurian,

It all depends on what one means by "faster" growth. Something that grows by the same percentage each year will have an exponential growth pattern. Something that grows by the same amount in absolute terms, e.g. $500 of per capita GDP growth per year, will have a linear trend. The latter is pretty much what we've seen, albeit with fluctuations, since WW-II. It doesn't look to me like there's evidence yet for a clear change in that pattern. However, any hopes that the economy will continue to grow exponentially are looking less and less realistic.

Arthur:

If you have two observations a_1 and a_N that are N years apart, then the CAGR is (a_N/a_1)^(1/N) -1.

Mike:

If a quantity is perfectly linear with time, then the growth rate of that quantity is dropping with time (which is exactly my point).

OK. But I'd argue that since we're using a per capita measure that takes into account population growth, a consistent pattern of linear growth is nevertheless consistent growth.

Mike:

Well, that would be an ideosyncratic definition of growth. Generally we define the growth rate in year N as A_n/A_(n-1)-1, which gives numbers like 3% etc. So constant growth of 3% means that the first year is X, the second year is X*1.03, the third year is X*1.03^2, and so on. That's an exponential, not linear growth. Linear growth will cause the growth rate (as defined above) to drop over time, and, while you could choose your own definition, probably the rest of us will continue to refer to a growth rate that drops over time as "slowing growth".

I may be ideosyncratic, or maybe even an idiot, but I'd be happy if my salary grew at a steady linear rate for 60 years, adjusted for inflation.

Sure, biological systems typically grow exponentially, but they also typically have periods where growth is essentially linear. There are doubtless people who seriously expect the economy to grow forever at an exponential rate, but what we're concerned about is whether the economy, due to energy issues, etc., is stagnating. If real per capita GDP continues to grow at a linear rate, people are still likely to consider that the economy is improving and that things are getting better, at least in material terms. In biological systems linear growth is often followed by no growth or even crash as resource constraints kick in. We may be approaching such an inflection point, but as long as growth remains linear, we aren't there yet.

The distribution of the benefits of this growth, which I think is what Kevin Drum was driving at, is another issue.

Kevin has a response here in which he basically agrees that I have a point, and that he did overstate his case somewhat (though it doesn't obviate the main point he was trying to make about the importance of distribution).

Interesting series of exchanges. Stuart, thanks for the formula.

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