This paper analyzes how bounded rationality affects monetary and fiscal policy via an empirically relevant enrichment of the New Keynesian model. It models agents’ partial myopia toward distant atypical events using a new microfounded “cognitive discounting” parameter. Compared to the rational model, (i) there is no forward guidance puzzle; (ii) the Taylor principle changes: with passive monetary policy but enough myopia equilibria are determinate and economies stable; (iii) the zero lower bound is much less costly; (iv) price-level targeting is not optimal; (v) fiscal stimulus is effective; (vi) the model is “neo-Fisherian” in the long run, Keynesian in the short run.