Subjective Housing Price Expectations, Falling Natural Rates and the Optimal Inflation Target

U.S. households' housing price expectations deviate systematically from rational expectations: (i) expectations are updated on average too sluggishly; (ii) following housing price changes, expectations initially underreact but subsequently overreact; (iii) households are overly optimistic (pessimistic) about capital gains when the price-to-rent ratio is high (low). We show that weak forms of capital gain extrapolation allow to simultaneously replicate the behavior of housing prices and these deviations from rational expectations as an equilibrium outcome. Embedding capital gain extrapolation into a sticky price model featuring 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 the optimal inflation target to increase strongly as the natural rate falls.