Resources | International Housing Observatory

International Housing Data

A rapid pace of real house price appreciation by itself does not necessarily imply that real house prices are becoming out of step with fundamentals. Still, we recognize that real house price increases today could become out of step with fundamentals supported instead by the expectation of robust future price increases. If enough buyers share the same beliefs about the future prospects in the housing market, their purchases will help drive current house prices up and validate the expectation that strong house price gains will continue. This self-fulfilling prophecy keeps the housing market misaligned from its fundamentals until enough investors become leery of a bust, the flow of money into housing dries out, and eventually the feared collapse occurs.

An expectations-driven real house price appreciation may lead to a misallocation of resources in the economy and distorted investment patterns. Therefore, monitoring for such episodes of exuberance (booms) and collapse (busts) in housing markets may help avoid a repeat of the economic trauma caused by the international boom-bust housing cycle that preceded the 2008 Great Recession (Pavlidis et al., 2016). We take a look at International housing markets (Mack and Martínez-García, 2011) with the novel Generalized Sup ADF (GSADF) test of Phillips et al. (2015a,b) to detect empirical evidence of exuberance. The latest findings across all international housing markets are summarized in this website.

Detecting Exuberance and Collapses

GSADF Test of Phillips et al. (2015a, b)

The Globalization Institute of the Federal Reserve Bank of Dallas produces an international house price database, which comprises quarterly house price and personal disposable income (PDI) series for a number of countries. All data series begin in first quarter 1975. A detailed description of the sources and methodology can be found in Mack and Martínez-García (2011), which is updated whenever modifications to the database occur.

We select a house price index for each country that is most consistent with the quarterly U.S. house price index for existing single-family houses produced by the Federal Housing Finance Agency. We extend the preferred series for each country back to first quarter 1975 either with historical data or with data from secondary sources. Each country's house price index is seasonally adjusted over the entire sample period with an unobserved components time series model and then rebased to 2005 = 100.

PDI series are quoted in per capita terms using working-age population. Both the house price and PDI series are quoted in nominal and real terms. Real values are computed using the personal consumption expenditure deflator. For each series, we produce a weighted average of all countries in the database, using purchasing power parity-adjusted gross domestic product shares in 2005.

Monitoring Exuberance and Collapses in Housing Markets

An Application to International Housing Markets

Mildly explosive behavior is modeled by an autoregressive process with a root that exceeds unity, but remains within the vicinity of one (Phillips et al., 2015a,b). This represents a small departure from martingale behavior, but is consistent with the submartingale property often used in the asset pricing literature to model self-fulfilling prophecies (rational bubbles). The GSADF test achieves this by recursively implementing a right-tailed ADF-type regression test using a rolling window procedure (Phillips et al., 2015a,b; Pavlidis et al., 2016).

More specifically, the GSADF test considers an ADF regression for a rolling interval beginning with a fraction r1 and ending with a fraction r2 of the total number of observations, with the size of the window being rw = r2 − r1. The parameters in the ADF regression are estimated by ordinary least squares (OLS) and then an ADF statistic is calculated to test the null of a unit-root against the right-sided alternative of mildly explosive behavior.

Phillips et al. (2015a,b) formulated a procedure whereby the ADF statistic is repeatedly calculated for a fixed share r2 of the whole sample and the window size is expanded from an initial fraction r0 to r2. The supremum of this sequence of statistics for each r1 ∈ [0, r2 - r0] is the sup ADF (SADF) statistic. The generalized sup ADF (GSADF) statistic is then constructed from the corresponding sequence of SADF statistics for each r2 ∈ [r0, 1].

The GSADF approach uses a variable window width approach, allowing starting as well as ending points to change within a predefined range [0, r₂-r₀], which enhances the flexibility of the ADF framework to identify consistently, periodically-occurring periods of mildly explosive behavior within a sample. The resulting GSADF statistic can then be used to test the null hypotheses of unit root against its right-tailed mildly explosive alternative by comparing it to its corresponding critical values. Further technical details on the implementation of the GSADF procedure to housing data, specifically for international housing markets, can be found in Pavlidis et al. (2016).

Reporting the Evidence

Statistical significance based on the GSADF procedure can be assessed against critical values obtained under the null hypothesis of no-explosive behavior over the entire testing period. The alternative is that there is at least one speculative period over the sample.

For the identification of exuberance periods, the backward SADF (BSADF) statistic is computed for each r2, which ranges between r0 and 1. The BSADF test for r2 is the supremum of the ADF statistic sequence obtained from subsamples whose ending points are on r2 and starting points vary between 0 and r2-r0. The BSADF statistics are linked to the GSADF statistic in the form of GSADF=sup(BSADF_r2), where the sup is taken over all values of r2. The BSADF statistic sequence is compared with its corresponding critical value sequence for the identification of starting and ending dates of exuberance. See Phillips, et al. (2015ab) for details.

The GSADF test is conducted in the first step. If we reject the null hypothesis of no exuberance, the BSADF test is then employed to identify the bubble origination and termination dates. Test statistics below 95% critical value, but above 90% (or for some just 80%) critical value – indicates that caution seems warranted, but there is not enough evidence to detect mildly explosive behavior at conventional statistical significance levels. Test statistic below 90% (or 80%) critical value – indicates that there is not enough evidence to signal an episode of mildly explosive behavior.

PSYIVX methodology

An application to the price-to-rent ratio

https://housing-fever.com/

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.

HOUSING FEVER

Insights from an
Econometric Thermometer

For the decomposition, we separate the sample into a training sample (until 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 T_min = 0.01T₀ + 1.8√T₀ , where T₀ is the number of observations in the training sample.

Data Sources and Methodology