A commenter on my previous post invites me to bet on the idea that economic growth is slowing. I'm going to decline the offer. This isn't (just) because I'm an empty blowhard: I was only raising the possibility of slower growth. Nor is it just because I'm risk-averse: in being scarred by memories of the early 80s recession, I am one of Malmendier and Nagel's Depression Babies (pdf).

Instead, I reject the bet because facts might not suffice to prove or disprove the secular stagnation hypothesis.

Even over a period as long as ten years - to take Matt's suggested time period - average GDP growth will be due in part to luck as well as to fundamental forces. For example, if a recession hits us in 2025, growth will look much better over the next ten years than it would if the recession comes in 2024.

We can quantify this luck by measuring the standard error, which (under some assumptions) is simply the standard deviation divided by the square root of the number of years in our sample. The idea here is that if growth is very volatile then observed average growth over a period is more likely to be due to good or bad luck than it would be if growth were more stable.

So, let's say that GDP grows by an average of 1.5% a year over the next ten years, with a standard deviation of GDP 2.2 percentage points, its volatility since 1973. What would this tell us?

One possibility is that growth has been lower than the 2% per cent per year we saw between 1973 and 2013. This would be evidence for secular stagnation.

But once we consider the standard error, things get complicated. Over a ten year period, the standard error is 0.7 percentage points. Our 1.5% growth might therefore mean simply that true growth was the same between 2014 and 2024 as it was between 1973 and 2013 and that we got unlucky, in drawing more bad years than good out of the hat. Or it might mean that there really has been secular stagnation and the growth rate has halved*.

We can't tell for sure. Such is the volatility of growth that even over longish periods there's lots of noise relative to signal.

This problem is actually even greater if we consider equity returns rather than GDP; a standard deviation of 20 percentage points makes it almost impossible to measure true returns even over long periods.

This doesn't mean the secular stagnation hypothesis is unfalsifiable; if growth averages (say) 3% per year or more over the next ten years, we can be fairly confident it was wrong. My point is simply that facts often don't tell us much.

My point here isn't merely a statistical one, but a political one. When John Landon-Lane and Peter Robertson argued that national government policies couldn't alter long-run growth, they were relying upon this reasoning; the standard error around growth estimates is so big that it's quite possible that most developed economies grow at much the same rate, implying that (except in a very few cases) the effect of national policies is undetectable.

Their point generalizes. Once we consider the noise-signal ratio, claims that government policies have made a big difference for good or ill must be accompanied either by very robust theory or by a big dose of scepticism.

** Over ten years, a drop in the growth rate from 2% to 1% is a big deal. It's a difference of £229 per month to someone with a monthly income of £2000 now. The fact that such a big difference is hard to detect is therefore troubling.*

but isn't bad luck, on the scale that might explain disappointing growth across all OECD economies, visible? I mean there was no missing the financial crisis. We can observe much of what explains the standard deviation of growth rates.

With this bet, you would not be talking about one country, I presume, but 'the developed world' slowing down, and if this set of countries experiences slow growth from say 2015 to 2025 without any really obvious explanation, then isn't the case for stagnation pretty much proven? On the other hand if growth gets back up to 2 per cent on average over that period, pretty much disproven?

Posted by: Luis Enrique | November 04, 2014 at 03:56 PM

The fact that such a big difference is hard to detect is therefore troubling.

I think you meant

The fact that such a big difference is hard to explain/understand is therefore troubling.

Posted by: andrew | November 04, 2014 at 10:33 PM

I can't help wondering if there is no slowdown but rather a growing systematic error in calculating the deflator due to technology.

Measuring qualitative improvement is hard and getting a price series for an object that didn't previously exist impossible. This has always been a problem but based on other evidence would seem to be a growing one

Posted by: Tim Bassett | November 05, 2014 at 04:40 AM

This is probably the proudest moment of my online existence.

I wonder if there is more or less noise in the outcome of a horse race?

Your arguments certainly cast doubt on the reliability of statistical tests. But you have laid out a pretty good set of assumptions about the future distribution of outcomes, so there must be some odds that would make it worth your while? I'm trying to ascertain your degree of certainty through this offer, but I guess your degree of risk aversion (whatever it is) complicates this.

The broader point is that if we had proper liquid futures markets for these kinds of predictions, we might know a lot more about current money-where-your-mouth-is beliefs.

Posted by: Matt Moore | November 05, 2014 at 06:42 AM

The assumption that 10-year variance is 10 times 1-year variance follows only if annual GDP changes, net of trend growth, are independent. Do you think they are?

Posted by: PaulB | November 05, 2014 at 05:18 PM

As I also commented on economistsview: Wait, we don't know now, and we won't know even in ten years. On what time scale is the hypothesis of any use whatsoever then? Is it all just tilting at windmills while in an ivory tower, with a moat?

Posted by: Jeff | November 06, 2014 at 02:08 PM