Repeat-Sales Indices

Overview

The aim of the repeat-sales technique is to control for compositional change in the sample of houses that sell through time by considering the sale price of the same property at two distinct points in time. That is, this method limits its sample to observations of properties that sell more than once. Of these observations, assuming no material change in the property between sales, this method overcomes the issue of compositional bias by quite literally holding quality constant.

Bailey, Muth, and Nourse (1963) developed the repeat-sales method as a method of avoiding the heterogeneity concerns of housing data. The estimation technique underlying their model assumes, however, that the dispersion in housing returns is constant across time. Case and Shiller (1987) observe that this is unlikely to be the case. Consider the range of prices you would accept for a property the day after you bought it – is it the same as the range you would accept 20 years after you bought the house?

Along these lines, Case and Shiller (1987) argue that it is likely that price dispersion is related to the length of time between sales. The suggested improvement on the Bailey et al. (1963) model is a generalised least squares regression in which the estimates of the Bailey et al. (1963) model are weighted by a second stage regression that models price dispersion as a function of the time between sales.

Calhoun (1996) extends Case and Shiller’s (1987) model to allow for non-linear time effects in the modeling of price disperision. The logic behind this approach comes from Abraham and Schauman (1991) who show that it is unlikely that the deviation of prices from the index can increase linearly with time forever.

The Chicago Mercantile Exchange S&P/Case-Shiller Home Price Index Futures, listed in June, 2006, are estimated for several US metropolitan regions following the Case and Shiller (1987) and Shiller (1991) methodologies. Over-the-counter derivatives broker, GFI, launched residential property derivatives in October 2006 written on an index constructed from a repeat-sales methodology established by academics at the University of Hong Kong.

Education / Methodology

Construction of the repeat-sales index, as originally espoused by Bailey, Muth, and Nourse (1963), assumes that the return on the same property between two sale dates is a function of the return on the underlying property price index over the same period. Within this method, a logarithmic transformation is applied to create a linear equation in which the price appreciation (or depreciation) of a house between two sales (in log form) is a function of the difference in market index values (in log form) between the second and the first sales of the trade-pair.

Calhoun (1996) controls for heteroskedasticity in the error term by estimating a three-stage weighted regression. In this model, the first stage regression estimates the model of Bailey et al. (1967). Taking the residuals from this model, the second stage regression models these squared deviations on a quadratic function of the time between sales.

The coefficient of the linear time variable is expected to be positive while the squared time variable is expected to have a negative coefficient. This is consistent with the theory that variance in house prices increases with tenure time, but at a decreasing rate.

The third stage regression estimates a weighted form of the first stage regression, using square roots of the predicted dependent values from the second stage regression as weights. This first quarterly time period dummy variable coefficient is restricted to zero in the first and third stage of estimation.

Goetzmann and Spiegel (1995) devise an enhancement to the classical repeat-sales model that attempts to control for aspects of property price appreciation that are unrelated to time. This is motivated by the observation that few properties remain physically unchanged between sales; many are going to experience some level of improvement, be it a fresh coat of paint or an additional storey. In fact, it is estimated that in Australia between 2 and 3 per cent of annual GDP is spent on housing renovations (Hansen, 2006). To measure clean price appreciation, Goetzmann and Spiegel’s (1995) model separates housing price appreciation into two components: that element related to the time between sales, and that which is unrelated to time. By incorporating a constant term in the repeat-sales model, Goetzmann and Speigel (1995) show that the biasing effect of non-temporal appreciation can be corrected.