What is a catastrophe?

In the previous post, I mentioned two types of catastrophe: cliff-diving and gradual. Suppose the first is a sudden major decrease in output. How much would returns to capital have to decline to get 1% average yearly returns over a century (given 6% “usual” returns)? This is the solution to this problem:

If I got my sums right, this implies about a 99% reduction in returns to capital in the year of the catastrophe.

Now, suppose the catastrophe plays out over a decade. How negative would growth in capital productivity have to be to get an average 1% returns for a century? Doing a similar calculation, returns to capital would have to be about -35% every year for a decade to get average returns that low over the century.

These examples make the catastrophes of the 20th century pale in comparison. In the US in the 1930s, GDP growth was, on average, positive. Austria was the biggest loser during WWII, in terms of GDP, and it only decreased by about 10% a year from 1938 to 1945.

In Weitzman’s calibration, there’s a 1 in 200 chance of having 1% yearly returns over the next century. These examples make this calibration look rather unrealistic.