Subjective housing price expectations, falling natural rates, and the optimal inflation target

U.S. households’ housing price expectations deviate systematically from full-information rational expectations: (i) expectations are updated on average too sluggishly, (ii) expectations initially underreact but subsequently overreact to housing price changes, and (iii) households are overly optimistic (pessimistic) about housing price growth when the price-to-rent ratio is high (low). We show that weak forms of housing price growth extrapolation allow to simultaneously replicate the behavior of housing prices and these deviations from rational expectations as an equilibrium outcome. Embedding housing price growth extrapolation into a sticky price model with a lower-bound constraint on nominal interest rates, we show that lower natural rates of interest increase the volatility of housing prices and thereby the volatility of the natural rate of interest. This exacerbates the relevance of the lower bound constraint and causes Ramsey optimal inflation to increase strongly with a decline in the natural rate of interest.