New simple forms of deviation from rational expectations (RE) are suggested: temporary near-rational expectations (TNRE) and persistent near-rational expectations (PNRE). The medium-scale DSGE model was estimated with the RE, the TNRE and the PNRE. It was estimated with and without observations from the survey's expectations. The quality of the out-of-sample forecasts was estimated. It is shown that near-rational concepts produce the same advantages as learning, without its disadvantages (including the absence of 'learning expectations' reactions on policy change). The influence of the observed expectations on forecasting quality was analysed.