Cautious expectations

This paper develops a tractable theory of cautious expectations. We impose the constraint that agents have to estimate the optimal weight on information in an otherwise standard class of linear quadratic economies. Within this framework, we show that expectations optimally feature dampened responses to new and prior information. Our theory has several similarities to models of limited attention. However, our theory is crucially consistent with the broad-based predictability of forecast errors and biased, overreactive expectations that have otherwise called into question attention-based models. We illustrate the consequences of our framework in a standard consumption–savings problem, which shows that cautious expectations can help account for empirical evidence on the marginal propensity to consume and amplify precautionary savings.