We outline a dynamic stochastic general equilibrium (DSGE) model with extrapolative expectations in asset pricing that we fit to 50 years of quarterly U.S. macroeconomic time series data with Bayesian techniques. We conclude that extrapolative expectations in asset pricing is statistically significant, quantitatively relevant and results in a substantial improvement of the model’s fit to the data. In particular, extrapolative expectations in asset pricing lead to more pronounced hump-shaped responses of the asset price and investment to shocks, and the model matches the degree of persistence observed in asset price data significantly better than the alternative DSGE models that we consider herein, which are the Smets and Wouters (2007) model, including a variant with pre-determined investment expenditures, and the Gilchrist et al. (2009) financial frictions model. Our findings are confirmed by numerous robustness exercises, including different prior assumptions, different sample periods and different time series variables, both excluding asset price data and the use of different asset price measures.