Risk and Structural Instability in US House Prices

When employing this approach, often used with asset market based studies (Timmermann 2001; Granger and Hyung 2004), specific explanations for identified breaks are rarely provided. This is due to the nature of asset markets, where the market will often react to changes in policy or the economy long before they are implemented or even announced. This makes it difficult to attribute breaks to specific events. In addition, breaks in asset markets can typically occur due to bubbles or swings in investor perceptions, Hall et al. (1997) use this as a general explanation for shifts in regime in their study of housing markets. The alternative approach would involve specifying a particular break based on specific policy changes as originally used by Enders (1988). It is important in this literature, as elsewhere, to avoid spurious interpretation of breaks, which are likely to be the result of complex interactions of effects and not susceptible to simple analysis.

As an alternative the more commonly used Threshold GARCH-M (Glosten et al. 1993) model was also employed to test for positive risk-return trade-off and asymmetry, with broadly similar results. We could also have used a multivariate form of GARCH, but the substantial differences in how the models perform in different cities with respect to the structural breaks and CGARCH specification made this impossible.

This is a standard mean equation in nominal form, as in comparable tests on other assets, as used by Glosten et al. (1993), although other studies have incorporated ARIMA type models and the interest rate in the mean. However, this is beyond the scope of this study.

Note that although it is not done in this paper, it is relatively trivial to condition on observables—in the simplest case by nominating the ‘official’ or ‘widely accepted’ breakdates of each series.

This work generalised the results of Bos and Hoontrakul (2002) who refer to the IT test. For further discussion on the difference of all the tests used in this study see Karoglou (2006a).

For example, the IT is found to be the most sensitive to the existence of volatility breaks for independent and identically distributed data, but suffers severe size distortions for strongly dependent data or for non-mesokurtic distributions. In contrast, the KL and the SAC₂ variants do not exhibit size distortions in these cases but their power is smaller, while SAC₁ does not exhibit size distortions for non-mesokurtic data and although it does for strongly dependent data, its power is higher than KL and SAC₂.

For example, a selection rule could suggest that a breakpoint can be considered only if two tests have identified it; or a breakpoint can be considered only if the resulting segments contain more than 10 observations.

Therefore, they provide the same value even if the observations of each segment are randomly ordered. In contrast, statistics that are based on sequential methods (such as the CUSUM tests) are influenced by the order of the observations.

See Karoglou (2010) for a discussion of non-normality and the presence of structural breaks as well as a more detailed discussion of some of the implications of this type of approach to finding breaks in the variance of a series.

A composite house price index covering the main US cities was also estimated, however there was no evidence of a significant risk-return trade-off or asymmetric adjustment (the results are available from the authors on request). This result reflects the varying nature of risk and the housing market across the US, and that in a composite form the effects tend to cancel each other out. This supports a similar result to Case and Shiller (1989), who found little evidence of any relationship between individual city prices and a composite index