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## Weitzman’s Gamma Discounting

I was just thinking about the article
“Gamma Discounting”,
Martin L. Weitzman
The American Economic Review, Vol. 91, No. 1 (Mar., 2001), pp. 260-271. Weitzman has a model in which you are unsure of the proper discount rate, and concludes that your discount rate should become small in far future periods. He says the intuition has to do with compound interest. He uses the gamma function for your prior. I think a numerical example works better, though I’m not sure if this is what he’s getting at– he says that using continuous compounding you don’t get his result.

Anyway, here’s the simple idea. Suppose we don’t know whether the interest rate will be 2% or 4%, and these have equal probability. We will get a benefit of \$1 in 100 years. What is it worth in present value?

If the interest rate is 2%, the value is about \$.13. If the interest rate is 4% the value is about \$.02. The expected value is therefore about \$.07. But if the interest rate were a known 3%, the expected value would be about \$.05. Thus, our ignorance results in less discounting.

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