Structural estimates of the standard New Keynesian model are at odds with microeconomic estimates. To reconcile these findings, we develop and estimate a behav- ioral New Keynesian model augmented with backward-looking households and firms. We find (i) strong evidence for bounded rationality, with a cognitive discount fac- tor estimate of 0.4 at quarterly frequency; and (ii) that the behavioral setting with backward-looking agents helps us in harmonizing the New Keynesian theory with em- pirical studies. We suggest that both cognitive discounting and anchoring are essential, first, to match empirical estimates for certain parameters of interest, and second, to obtain the hump-shaped and initially muted impulse-response functions that we observe in the data.