On the evolution of the house price distribution

Is the cross-sectional distribution of house prices close to a (log)normal distribution, as is often assumed in empirical studies on house price indexes? How does it evolve over time? How does it look like during the period of housing bubbles? To address these questions, we investigate the cross-sectional distribution of house prices in the Greater Tokyo Area. Using a unique dataset containing individual listings in a widely circulated real estate advertisement magazine in 1986 to 2009, we find the following. First, the house price, Pit, is characterized by a distribution with much fatter tails than a lognormal distribution, and the tail part is quite close to that of a power-law or a Pareto distribution. Second, the size of a house, Si, follows an exponential distribution. These two findings about the distributions of Pit and Si imply that the the price distribution conditional on the house size, i.e., Pr(Pit | Si), follows a lognormal distribution. We confirm this by showing that size adjusted prices indeed follow a lognormal distribution, except for periods of the housing bubble in Tokyo when the price distribution remains asymmetric and skewed to the right even after controlling for the size effect