Friday, September 20, 2013

Empirics under uncertain beliefs are difficult

The typically way we model uncertainty is by assuming economic agents know the stochastic process they are facing, and we call this uncertainty. That is wrong. This should be called risk as probabilities are known. Uncertainty is when those probabilities are unknown. That does not mean the agent is not rational, it is simply that the information set is smaller than what we typically assume.

Nabil Al-Najjar and Jonathan Weinstein point out that the uncertain agent trying to smooth consumption may look like he is excessively precautionary to someone thinking he has known probabilities. They frame it within a Bayesian framework, where beliefs including subjective probabilities are updated with incoming information. This makes it very difficult to do any empirical work, including measuring time preference or risk aversion.

I am surprised, though, the Al-Najjar and Weinstein misunderstand rational expectations. They claim an uncertain agent does not have rational expectations if beliefs over probabilities do not coincide with observed frequencies. This does not need to be if the econometrician has information the agent did not have at the time of the decision. If the agent uses all the available information, then it is still rational expectations. There may be so little that he cannot determine probabilities precisely, unlike perfect foresight on probabilities, like Al-Najjar and Weinstein seem to imply. In any case, this is more about semantics than results.

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