There is increasing evidence that aggregate housing price are predictable. Despite this, a random walk in time and independence in space are two maintained hypotheses in the empirical models for housing price measurement used by government agencies and by commercial companies as well. This paper examines the price discovery process in individual dwellings over time and space by relaxing both assumptions, using a unique body of data from the Singapore private condominium market. We develop a model that tests directly the hypotheses that the prices of individual dwellings follow a random walk over time and that the price of an individual dwelling is independent of the price of a neighboring dwelling. The model is general enough to include other widely used models of housing price determination, such as Bailey, Muth, and Nourse (1963), Case and Shiller (1987) and Redfearn and Quigley (2000), as special cases. The empirical results clearly support mean reversion in housing prices and also diffusion of innovations over space. Our estimates of the level of housing prices, derived from a generalized repeat sales model, suggest that serial and spatial correlation matters in the computation of price indices and the estimation of price levels. The finding of mean reversion may suggest that housing prices are forecastable and that excess returns are possible for investors. We use the monthly price series derived from condominium sales to investigate this issue. We compute gross unleveraged real returns monthly. When returns are computed from models which assume a random walk without spatial autocorrelation, we find that they are strongly autocorrelated. When returns are calculated from more general models that permit mean reversion, the estimated autocorrelation in investment returns is reduced. Finally, when they are calculated from models permitting mean reversion and spatial autocorrelation, predictability in aggregate investment returns is completely absent.
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