Broadberry and Wallis: A Suggested Interpretation

The Economist reports,

Stephen Broadberry of Oxford University and John Wallis of the University of Maryland have taken data for 18 countries in Europe and the New World, some from as far back as the 13th century. To their surprise, they found that growth during years of economic expansion has fallen in the recent era—from 3.88% between 1820 and 1870 to 3.06% since 1950—even though average growth across all years in those two periods increased from 1.4% to 2.55%.

Instead, shorter and shallower slumps led to rising long-term growth. Output fell in a third of years between 1820 and 1870 but in only 12% of those since 1950. The rate of decline per recession year has fallen too, from 3% to 1.2%.

Tyler Cowen inspired me to find the article.

Set up two random-number generators, each producing a normal distribution. Give generator M a mean of 2.55 and a standard deviation of 1.5, and give generator H a mean of 1.4 with a standard deviation of 3. Take about 100 draws from those two random-number generators, and then separate the results into positive and negative numbers.

Presumably, the negative numbers from generator H will be more numerous and have a more negative average than those from M. The positive numbers from H, although fewer, could turn out to be larger on average than those from M. That is, by truncating the results from H at zero, the larger standard deviation might lead to a higher average for H than for M. If it does not, then tweak the difference in standard deviations between the two generators a bit more.

In other words, you can replicate the Broadberry-Wallis results without the nature of booms or recessions having any causal role. If modern economic growth, M, is higher with a lower annual standard deviation than historical economic growth, H, then you would observe these sorts of results if you arbitrarily select 0 as your dividing point between booms and slumps.

[UPDATE: a reader writes,

1. With the parameters you suggested, the conditional expectation for H is 2.99, whereas the conditional expectation for M is 2.7.

2. To reproduce their results with the Gaussian model, we’d need to have a standard deviation of about 4.16 for (H), and a standard deviation of about 2.2 for situation (M).

I would add that as you go back in history, much of output is agricultural, and subject to annual variation in weather. So variance might well have been higher for that reason.]

3 thoughts on “Broadberry and Wallis: A Suggested Interpretation

  1. I think it would be possible to show this analytically, maybe with a folded normal distribution, maybe just conditionally.

  2. Wait, so when the article says “average growth”, they mean “the average of all years with positive growth, excluding years with negative growth”? Why would that be considered a useful value?

    Isn’t that like saying, “If you don’t count all the years I lost money, I made 40% in the stock market?”

  3. Try doing it with real per capita income and see what you get.

    In the earlier era population growth was much stronger and when you compare per capita income from 1850-1950 to post 1950 you get even stronger growth differences than the plain growth numbers show.

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