A mechanism leading bubbles to crashes: the case of Japan's land markets

In this paper we investigate quantitatively statistical properties of ensemble of {\it land prices} in Japan in the period from 1981 to 2002, corresponding to the period of bubbles and crashes. We find that the tail of the distributions of ensembles of the land prices in the high price range is well described by a power law distribution, $ P(S>x) \sim x^{-\alpha} $, and furthermore that as the power-law exponents $ \alpha $ approached to unity, the crashes of bubbles occurred.