Looking Backward and Looking Forward

TL;DR

This paper explores the foundational role of filtering in economic models, linking it to conditional expectations and extending its application beyond traditional rational expectations frameworks.

Contribution

It introduces a generalized filtering framework that connects agent behavior with conditional expectations, applicable across various economic models without information loss.

Findings

Filtering corresponds to the existence of a conditional expectation in equilibrium.

The framework generalizes rational behavior to a broader class of models.

Applications of the filtering device extend beyond specific model classes.

Abstract

Filtering has had a profound impact as a device of perceiving information and deriving agent expectations in dynamic economic models. For an abstract economic system, this paper shows that the foundation of applying the filtering method corresponds to the existence of a conditional expectation as an equilibrium process. Agent-based rational behavior of looking backward and looking forward is generalized to a conditional expectation process where the economic system is approximated by a class of models, which can be represented and estimated without information loss. The proposed framework elucidates the range of applications of a general filtering device and is not limited to a particular model class such as rational expectations.