Persistence and Cyclical Dynamics of US and UK House Prices: Evidence from Over 150 Years of Data

We propose a modeling approach for the historical series of real and nominal house prices in the United States and the United Kingdom that permits the simultaneous estimation of persistence at zero frequency (trend) and at frequency away from zero (cycle). We also consider the separate cases of a standard I(d) process, with a pole at the zero frequency, and a cyclical I(d) model that incorporates a singularity at a non-zero frequency. We use annual data from 1830 to 2016 for the United States and 1845 to 2016 for the United Kingdom. We find, in general, that the degree of fractional integration associated with the long run or zero frequency is less than one, but greater than 0.5, while the degree of fractional integration associated with the cyclical frequency is greater than zero and less than 0.5. Thus, the long-run component of house prices is nonstationary but mean reverting, while the cyclical component is stationary. This contrasts with the results of the standard model and much of the empirical literature, where the rejection of the unit root seldom occurs. Some policy implications of the results appear in the conclusion.