We investigate whether expectations that are not fully rational have the potential to explain the evolution of house prices and the price-to-rent ratio in the United States. First, a Lucas type asset-pricing model solved under rational expectations is used to derive a fundamental value for house prices and the price-rent ratio. Although the model can explain the sample average of the price-rent ratio, it does not generate the volatility and persistence observed in the data. Then, we consider an intrinsic bubble model and two models of extrapolative expectations developed by Lansing (2006, 2010) in applications to stock prices: one that features a constant extrapolation parameter and one in which the extrapolation coefficient depends on the dividend growth process. We show that these last two models are equally good at matching sample moments of the data. However, a counterfactual experiment shows that only the extrapolative expectation model with time-varying extrapolation coefficient is consistent with the run up in house prices observed over the 2000-2006 period and the subsequent sharp downturn.