Resumen de Dynamic Higher Order Expectations
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.
