Ergodicity in Economics: a Decision theoretic evaluation

Abstract

Peters (2019a) discusses a compound lottery that allegedly reveals a weakness of the way uncertainty is modeled within economics. This note evaluates that example in the light of standard expected utility. I obtain two results. First, using a variant of Rabin (2000) calibration theorem, I show that the paradox Peters obtains only arises because he implicitly assumes an unbounded utility function for money. That when utility is unbounded such paradoxical outcomes can arise is a well-known fact in decision theory, so his contribution on this matter is of limited interest. Second, I use the same example to illustrate Peters' claim that, when applied to compound lotteries, expected utility is based on the implicit assumption that the underlying stochastic process is ergodic. I compare Peters' analysis with the original one due to Samuelson (1971) and show that this claim is unfounded.

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