The case for a low discount rate is stronger than you think. If we are uncertain what is the right discount rate, and we count values in our averaging (rather than averaging discount rates per se), lower discount rates get more weight in the expected value calculation. In his book on catastrophe, Richard Posner writes:
Suppose there’s an equal chance that the applicable interest rate throughout this and future centuries will be either 1 percent or 5 percent. The present value of $1 in 100 years is 36.9 cents if the interest rate used to compute the present value is 1 percent but only .76 cents (a shade over three-quarters of a cent) if it is 5 percent. Now consider the 101st year and remember the assumption that the two alternative discount rates are equally probable. If the interest rate used to discount the future to the present value is 1 percent, then the present value of $1 at the end of that year will have shrunk from 36.9 cents to 36.6 cents. If instead the interest rate used is 5 percent, the present value of .76 cents will have shrunk to about .75 cents. This means that the average present value of $1 at the end of the 101st year will be 18.68 cents, implying an average discount rate of less than 2 percent, rather than 3 percent. The reason is that the more rapid decline in value under the higher discount rate (5 percent) reduces its influence on present value.
The bottom line: If we are unsure what is the right discount rate, in practice that usually means something like a low discount rate.
“If we are unsure what is the right discount rate, in practice that usually means something like a low discount rate.”
Two points:
1. This result depends on the distribution of possible discount rates. If the low values have small probability, the expected discount will be higher.
Example, if we think the discount rate could be 1% with 20% probability and 5% with 80% probability, the average discount in Posner’s example becomes something like 2.5%.
2. This says nothing about the probability of Stern’s almost zero discount rate.
Example, if we think there’s a 20% chance that Stern is right (i.e. .1% discount) and an 80% chance that the discount is something like 2% then the average discount in is close to 1.2%.
It’s just Jensen’s inequality!
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