A Bayesian Approach to the Construction and Comparison of Alternative House Price Indices

In this paper, a Bayesian framework is proposed to construct and compare alternative house price indices. The six alternative models under comparison are the two-error AR(1) model, the Case-Shiller model, the one-error AR(1) model, the BMN model, the Webb model, and the Goetzmann- Spiegel model. The posterior odds ratio test suggests that the three two-error models perform better than the three one-error models. The Goetzmann-Spiegel model has the highest posterior odds in three out of four cities, and the two-error AR(1) model has the highest posterior odds in San Francisco. The Goetzmann-Spiegel model outperforms the Case-Shiller model in all four cities, suggesting that it is preferable to include the non-temporal return component in the model for constructing price index. Among the three one-error term models, the AR(1) model has the best performance. The BMN model and the Webb model follow in performance, respectively. We define a normalized distance to measure the difference between each pair of return series. It is found that there could be significant discrepancy among alternative return series or index series. Therefore, the choice of alternative models is important