How should one discount future events when they are far into the future and there is uncertainty? This seems to be a rather odd question, given that we have the von Neumann-Morgenstern framework. The reason this is still a valid question is that the choice of a discount rate matters a lot for questions regarding the distant future, such as climate change, and even small changes can lead to dramatically different policy recommendations. Thus uncertainty does not necessarily pertain to uncertain future outcomes, but to uncertain future discount rates. Are they going to remain at historic interest rates? And which interest rates?

Christian Gollier and Martin Weitzman have written several papers with a similar premise but dramatically different results: discretize the space of discount rates and then assign probabilities to each. Then, the "average" discount rate to use should either be the highest or the lowest in the distribution. Now, they sat together and produced a paper that resolved this apparent puzzle. They both forgot about marginal utilities! Suddenly, they remembered von Neumann-Morgenstern and that the objective probabilities they where using needed to be adjusted for the intertemporal ratio of marginal utilities. In other words, they finally are using the standard Euler equation that is the basis of asset pricing. And they find that one should use a rather low discount rate.

PS: How do you get something named after you, or reinforce that it should be named after you? Apparently by repeatedly drawing the attention of the reader to it. Gollier and Weitzman do this in this paper, and it is very annoying, especially when their "puzzles" come from a failure to use the appropriate framework. Oh, and did I mention von Neumann-Morgenstern?

## Thursday, February 4, 2010

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## 5 comments:

I am sometimes amazed how researchers in some fields are completely unaware of standard practices in other that would easily solve some of the challenges they face. You have uncovered an example of that.

Best post of the year so far. Superb.

The Gollier-Weitzman blunder,that would be more appropiate.

Gollier and Weitzman should be ashamed instead of clamoring they have solved a major puzzle.

This paper has received an important award: the 2011 Erik Kempe Award from the European Association of Environmental and Resource Economists . Gollier and Weitzmann's strategy was very successful!

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