The evolution of house price distribution

Is the cross-sectional distribution of house prices close to a lognormal distribution, as is often assumed in empirical studies on house price indexes? How does the distribution evolve over time? To address these questions, we investigate the cross-sectional distribution of house prices in the Greater Tokyo Area. We find that house prices (Pi) are distributed with much fatter tails than a lognormal distribution and that the tail is quite close to that of a power-law distribution. We also find that house sizes (Si) follow an exponential distribution. These findings imply that size-adjusted house prices, defined by lnPi - aSi, should be normally distributed. We find that this is indeed the case for most of the sample period, but not the bubble era, during which the price distribution has a fat upper tail even after adjusting for size. The bubble was concentrated in particular areas in Tokyo, and this is the source of the fat upper tail.