Statistical methods for modeling house prices and indices

Repeat sales techniques are a common approach for modeling house prices. This methodology presumes the previous sale price acts as a proxy for hedonic variables, such as size and number of bedrooms. Capturing the spirit of the repeat sales setup, the proposed model includes the previous price as a predictor of current price. However, the model also includes an adjustment so that the more time which has elapsed between sales, the less useful the previous price becomes. To incorporate this property into the model framework, a two-part, nonlinear model is proposed which consists of a general price index and an autoregressive component (AR). The latter element can be thought of as the result of a latent AR(1) process for each house which is observed only in time periods when sales occur. In the fitting process, all sales contribute to estimating the time effect but only repeat sales factor in the autoregressive coefficient estimate. The resulting index, constructed from the time effects, is therefore more representative of the housing market compared to existing repeat sales models which ignore single sales. Moreover, the proposed model outperforms benchmark models including the S&P/Case-Shiller® model in terms of predictive power when applied to single-family home sales from July 1985 through September 2004 for twenty U.S. metropolitan areas. Finally, an extension to this model is proposed to incorporate local effects. Here, zip code is introduced to the model as a random effect. Predictive performance is further improved with this addition.