We propose an active cognition approach to bounded rationality, inwhich agents use a calculation algorithm to improve on the forecastsprovided by a purely adaptive learning rule such as least-squareslearning. Agents' choices of calculation intensity depend on theirestimates of the benefits of improved forecasts relative tocalculation costs. Using an asset-pricing model, we show how morerapid adjustment to rational expectations and forward-lookingbehavior arise naturally when there are large anticipated structuralchanges such as policy shifts. We also give illustrative applicationsin which the severity of asset price bubbles and the intensity ofhyperinflationary episodes are related to the cognitive ability ofthe agents.