For most people, purchasing a house is a major decision. Once purchased, the house will by far be the most important asset in the buyer's portfolio. The development of its price will have a major impact on the buyer's wealth over the life cycle. It will, for instance, affect her ability to obtain credit from commercial banks and therefore influence her consumption and savings decisions and opportunities. The behavior of house prices is therefore of central interest for (potential) house buyers, sellers, developers of new houses, banks, policy makers or, in short, the general public.
An important property of houses is that they are different from each other. Hence, while houses in the same market (i.e., the same city, district or neighborhood) will share some common movements in their price there will at all times be idiosyncratic differences due to differences in maintenance, design or furnishing. Thus, the average or median price will depend not only on the general tendency of the market, but also on the composition of the sample. To calculate a price index for real estate, one has to control explicitly for idiosyncratic differences. The hedonic approach is a popular method for estimating the impact of the characteristics of heterogenous goods on their prices.
The statistical model used in this chapter tries to infer the common component in the movement of prices of 1502 single-family homes sold in a district of Berlin, Germany, between January 1980 and December 1999. It combines hedonic regression with Kalman filtering. The Kalman filter is the standard statistical tool for filtering out an unobservable, common component from idiosyncratic, noisy observations. We will interpret the common price component as an index of house prices in the respective district of Berlin. We assume that the index follows an autoregressive process. Given this assumption, the model is writable in state space form.
The remainder of this chapter is organized as follows. In the next section we propose a statistical model of house prices and discuss its interpretation and estimation. Section 13.4 introduces the data, while Section 13.5 describes the quantlets used to estimate the statistical model. In this section we present also the estimation results for our data. The final section gives a summary.