Exploring Distributions of House Prices and House Price Indices

Abstract

We use house prices (HP) and house price indices (HPI) as a proxy to income distribution. Specifically, we analyze distribution of sale prices in the 1970–2010 window of over 116,000 single-family homes in Hamilton County, Ohio, including Cincinnati metro area of about 2.2 million people. We also analyze distributions of HPI, published by Federal Housing Finance Agency (FHFA), for nearly 18,000 US ZIP codes that cover a period of over 40 years starting in 1980’s. If HP can be viewed as a first derivative of income, HPI can be viewed as its second derivative. We use generalized beta (GB) family of functions to fit distributions of HP and HPI since GB naturally arises from the models of economic exchange described by stochastic differential equations. Our main finding is that HP and multi-year HPI exhibit a negative Dragon King (nDK) behavior, wherein power-law distribution 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&P500 index in the US stock market. This type of tail behavior is best fitted by a modified GB (mGB) distribution. Tails of single-year HPI appear to show more consistency with power-law behavior, which is better described by a GB Prime (GB2) distribution. We supplement full distribution fits by mGB and GB2 with direct linear fits (LF) of the tails. Our numerical procedure relies on evaluation of confidence intervals (CI) of the fits, as well as of p-values that give the likelihood that data come from the fitted distributions.

Keywords

• fat tails
• Dragon Kings
• negative Dragon Kings
• generalized beta distribution
• income distribution