11 July 2011

The Long Run

The Economist: Free Exchange | R.A. | Long-run growth: A two-hundred year rising tide

My colleague responds to Karl Smith (and by extension to my previous post) on the constancy of the long-run growth trend. Regarding this chart:


He writes:
Mr Smith thinks the Depression and the second world war are merely bumps here deviating from the long-term average, but this graph doesn't tell us that because it doesn't show what long-term growth was before 1929. Essentially the graph shows that annual GDP growth didn't deviate much from its average during the Great Moderation from 1947 to 2007. But we knew that. That's why it's called the Great Moderation. [...]
Well, it turns out there are estimates going back further:


The variation in government policy over this time period was remarkable. And yet the long-run growth rate was almost absurdly constant.

Of course, this line would look very different in some cases. A similar chart for Argentina would not show a more or less unbroken upward line. Policy can make a big difference. But could policy return the slope of the line to its 1950s-60s level? As much as I'd like to believe it could, I'm sceptical.
True, this is spookily constant. But...

(1) How constant is it really? A very small difference in that constant rate of growth is very important over a long horizon. Let's say our productive capacity is $1 right now, and grows at exactly 4.0% annually for 100 years. At the end of the century we'll be producing $50.50 of stuff. If that growth rate falls to just 3.9% then in 2111 we'll be making $45.87 of stuff, or just short of 10% less than we would have with 4.0% growth. If we nudge that growth rate up one tenth of one percent, then we'll be making $55.59, or over 10% more than the baseline.

(1a) That may not seem like a big deal since the people of 2111 will still be so much richer than we are. But I would be pretty pissed at the people of 1911 if we could be 10% richer than we are right now but they said "Eh, who cares about long term growth? It's practically constant! Those 21st century people will be rich anyway."

(1b) If the difference between $45.87 and $55.59 does seem like a lot, then think about it from a temporal perspective. A century or so from now, the people of my "high" 4.1% growth scenario will have access to the same productive capacity about 6 years earlier than their "low" 3.9% growth counter parts. Would you have like to get iPhones or fMRIs or antilock brakes six years earlier than we did? Of course.  And I'd sure rather have nanobots that eat tumors or algae that shit diesel fuel in 94 years rather than 100.

(2) Don't take mean reversion for granted. Just because a trend is consistently stable does not mean that it is automatically stable. When growth drops under trend one reaction is to take a deep breath and remind yourself that growth is stable on the long term, so let's not concern ourselves with long-term growth. The other, in my opinion equally justifiable reaction, is to decide that sub-par growth is a signal that its time to work like the dickens to get it back up to trend.

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