Repeat sales index for thin markets: a structural time series approach

The repeat sales model is commonly used to construct reliable house price indices in absence of individual characteristics of the real estate. Several adaptations of the original model by Bailey et al. (J Am Stat Assoc 58:933–942, 1963) are proposed in literature. They all have in common using a dummy variable approach for measuring price indices. In order to reduce the impact of transaction price noise on the estimates of price indices, Goetzmann (J Real Estate Finance Econ 5:5–53, 1992) used a random walk with drift process for the log price levels instead of the dummy variable approach. The model that is proposed in this article can be interpreted as a generalization of the Goetzmann methodology. We replace the random walk with drift model by a structural time series model, in particular by a local linear trend model in which both the level and the drift parameter can vary over time. An additional variable—the reciprocal of the time between sales—is included in the repeat sales model to deal with the effect of the time between sales on the estimated returns. This approach is robust can be applied in thin markets where relatively few selling prices are available. Contrary to the dummy variable approach, the structural time series model enables prediction of the price level based on preceding and subsequent information, implying that even for particular time periods where no observations are available an estimate of the price level can be provided. Conditional on the variance parameters, an estimate of the price level can be obtained by applying regression in the general linear model with a prior for the price level, generated by the local linear trend model. The variance parameters can be estimated by maximum likelihood. The model is applied to several subsets of selling prices in the Netherlands. Results are compared to standard repeat sales models, including the Goetzmann model.