Methodology

How the Housing Thermometer Works

Real-time bubble indicators are computed using the econometric methodology proposed recently in Shi and Phillips (2021). This methodology, known as PSY-IVX, is designed specifically to identify bubbles as they begin to emerge. Housing bubbles are defined as explosive deviations of house prices from underlying market fundamentals. The PSY-IVX approach enables period by period assessment of these deviations from fundamentals so that early detection of emergent explosive dynamics is possible, while accounting for the impact of a broad set of fundamental factors that may affect demand and supply pressures in housing markets. Early quantitative detection of bubble behavior is useful to market participants as well as regulators and commercial banks.

The fundamental factors considered include real mortgage interest rates (nominal mortgage rates less inflation expectations), real rents, real disposal income (proxied by state final demand) for Australian cities, employment for New Zealand regions, and housing supply (proxied by new housing completions for Australia and new housing consents for New Zealand).

The PSY-IVX approach has two steps. The first step decomposes log price-to-rent ratios into fundamental and non-fundamental components. The fundamental component reflects underlying economic and financial conditions that are relevant to the housing market and the determination of house prices. The non-fundamental component is a residual that embodies the impact of speculative behavior in the market. The decomposition is accomplished using a recently developed IVX estimation technique and a reduced-form econometric model that measures the empirical effects of economic fundamentals. This approach allows for complex trending features in the data as well as the interdependencies that are characteristic of many indicators of prevailing economic conditions. The second step applies the PSY explosive detection method to the estimated non-fundamental component, thereby revealing the extent of speculative market behaviour that goes beyond prevailing economic indicators.

For the decomposition, we separate the sample into a training sample (January 2011 to December 2019) and a monitoring sample (from January 2020 onward). The reduced-form regression model is estimated with IVX using data from the training sample, accounting for dependence over time in the data. The estimated model coefficients are used to compute the non-fundamental component in both the training and monitoring samples. For the PSY explosive root test, the minimum window size is set as Tmin = 0.01T0 + 1.8√T0 , where T0 is the number of observations in the training sample. The lag order of the model is selected by BIC with a maximum lag of four. Critical values are obtained from the composite bootstrapping procedure, with the control window being a quarter and the significance level being 95%.

Reference

Shi, S. and Phillips, P.C.B., Diagnosing Housing Fever with an Econometric ThermometerJournal of Economic Surveys, forthcoming.