Repeat Sales Index for Real Estate Prices: a Structural Time Series Approach

The repeat sales model is commonly used to construct reliable price indices in absence of individual characteristics of the real estate. Several adaptations of the original model of Bailey, Muth and Nourse (1963) are proposed in literature, but all of them have in common that they use a dummy variable approach for measuring the price index. The main drawback of these approaches is that the price levels for the different time periods are supposed to be independent. In the model proposed in this article, the dummy variables are replaced by a structural time series model, in this case a local linear trend model in which both the level and slope can vary over time. The main advantages of this approach are that it is a robust method and that it 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 to predict the price level based on previous information, so even for 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, induced 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.