Book excerpt: We introduce behavioral learning equilibria (BLE) into a multi-variate linear framework and apply it to New Keynesian DSGE models. In a BLE, boundedly rational agents use simple but optimal first-order autoregressive (AR(1)) forecasting rules whose parameters are consistent with the observed sample mean and autocorrelation of past data. We study the BLE concept in a standard three-equation New Keynesian model and develop an estimation methodology for the canonical Smets and Wouters (2007) model. A horse race between rational expectations equilibrium (REE), BLE and constant gain learning models shows that the BLE model outperforms the REE benchmark and is competitive with constant gain learning models in terms of in-sample and out-of-sample fitness. Sample autocorrelation learning of optimal AR(1) beliefs provides the best fit when short-term survey data on inflation expectations are considered in the estimation. As a policy application, we show that optimal Taylor rules under AR(1) expectations inherit history dependence, requiring a lower degree of interest rate smoothing than REE.