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We use house prices (HP) and house price indices (HPI) as a proxy to incomedistribution. Specifically, we analyze sale prices in the 1970-2010 window ofover 116,000 single-family homes in Hamilton County, Ohio, including Cincinnatimetro area of about 2.2 million people. We also analyze HPI, published byFederal Housing Finance Agency (FHFA), for nearly 18,000 US ZIP codes thatcover a period of over 40 years starting in 1980's. If HP can be viewed as afirst derivative of income, HPI can be viewed as its second derivative. We usegeneralized beta (GB) family of functions to fit distributions of HP and HPIsince GB naturally arises from the models of economic exchange described bystochastic differential equations. Our main finding is that HP and multi-yearHPI exhibit a negative Dragon King (nDK) behavior, wherein power-lawdistribution tail gives way to an abrupt decay to a finite upper limit value,which is similar to our recent findings for realized volatility of S\&P500index in the US stock market. This type of tail behavior is best fitted by amodified GB (mGB) distribution. Tails of single-year HPI appear to show moreconsistency with power-law behavior, which is better described by a GB Prime(GB2) distribution. We supplement full distribution fits by mGB and GB2 withdirect linear fits (LF) of the tails. Our numerical procedure relies onevaluation of confidence intervals (CI) of the fits, as well as of p-valuesthat give the likelihood that data come from the fitted distributions.

Exploring Distributions of House Prices and House Price Indices