Abstract:
In models where privately informed agents interact, agents may need to form
higher order expectations, i.e. expectations of other agents’ expectations. This paper explores
dynamic higher order expectations in a setting where it is common knowledge that
agents are rational Bayesians. This structure is a natural generalization of full information
rational expectations and allows any order of expectation at any horizon to be determined
recursively. The usefulness of the approach is illustrated by solving a version of Singleton’s
(1987) asset pricing model with disparately informed traders but without assuming that
shocks can be observed perfectly with a lag. In the context of Singleton’s asset pricing
model, we prove that both the impact of expectations on the asset’s price and the variance
of expectations are decreasing as the order of expectation increases. We use these results to
derive a finite dimensional state representation that can be made arbitrarily accurate. The
solution method exploits the Euler-type structure of the asset pricing function and should be
applicable to a variety of settings where privately informed agents optimize intertemporally.
Paper: http://www1.fee.uva.nl/mint/content/agenda/kris.pdf