Agents have foresight when they receive information about a random process above and beyond the information contained in its current and past history. In this paper, we propose an information-theoretic measure of the quantity of foresight in an information structure, and show how to separate...

When can structural shocks be recovered from observable data? We present a necessary and sufficient condition that gives the answer for any linear model. Invertibility, which requires that shocks be recoverable from current and past data only, is sufficient but not necessary. This means that...

The literature on belief-driven business cycles treats news and noise as distinct representations of agents' beliefs. We prove they are empirically the same. Our result lets us isolate the importance of purely belief-driven fluctuations. Using three prominent estimated models, we show that...