Episodes of Exuberance in Housing Markets: In Search of the Smoking Gun

Abstract

In this paper, we examine changes in the time series properties of three widely used housing market indicators (real house prices, price-to-income ratios, and price-to-rent ratios) for a large set of countries to detect episodes of explosive dynamics. Dating such episodes of exuberance in housing markets provides a timeline as well as empirical content to the narrative connecting housing exuberance to the global 2008 −09 recession. For our empirical analysis, we employ two recursive univariate unit root tests recently developed by Phillips and Yu (International Economic Review 52(1):201–226, 2011) and Phillips et al. (2015). We also propose a novel extension of the test developed by Phillips et al. (2015) to a panel setting in order to exploit the large cross-sectional dimension of our international dataset. Statistically significant periods of exuberance are found in most countries. Moreover, we find strong evidence of the emergence of an unprecedented period of exuberance in the early 2000s that eventually collapsed around 2006 −07, preceding the 2008 −09 global recession. We examine whether macro and financial variables help to predict (in-sample) episodes of exuberance in housing markets. Long-term interest rates, credit growth and global economic conditions are found to be among the best predictors. We conclude that global factors (partly) explain the synchronization of exuberance episodes that we detect in the data in the 2000s.

Appendix A: Demand Equation for Rental Housing

Consider the maximization of the Stone-Geary utility function with housing units rented, H _t , and consumption of other goods, C _t , i.e.,²⁵

$$U\left( H_{t},C_{t}\right) =\left( H_{t}-\theta_{H}\right)^{\alpha} \left( C_{t}-\theta_{C}\right)^{1-\alpha}, 0<\alpha<1, $$

subject to the intratemporal budget constraint,

$$C_{t}+x_{t}H_{t}=Y_{t}, $$

where the price of the consumption good is normalized to 1. X _t ≡x _t H _t is the housing rents—rental expenditures—paid and x _t the rental rate per unit rented, Y _t refers to disposable income, and α, 𝜃 _H and 𝜃 _C are preference parameters.

From first-order conditions, the Stone-Geary utility function subject to the standard intratemporal budget constraint gives a linear expenditure system where the demand for rental housing takes the following form:

$$ H_{t}=\theta_{H}+\frac{\alpha}{x_{t}}\left( Y_{t}-x_{t}\theta_{H}-\theta_{C}\right), $$

(38)

or in expenditure terms,

$$ X_{t}\equiv x_{t}H_{t}=\alpha Y_{t}+\left( 1-\alpha\right) \theta_{H} x_{t}-\alpha\theta_{C}. $$

(39)

Under the assumption that in equilibrium the units rented are constant (i.e., H _t =H) and normalized to 1, the demand equation that determines housing rents in Eq. 39 reduces to an affine transformation of disposable income (Y _t ), i.e.,

$$ X_{t}=x_{t}=\theta_{F}+\delta Y_{t+1}, $$

(40)

where $\delta \equiv \frac {\alpha }{1-\left (1-\alpha \right ) \theta _{H}}$ and $\theta _{F}\equiv -\frac {\alpha }{1-\left (1-\alpha \right ) \theta _{H}} \theta _{C}$.

B The Panel GSADF Test

The bootstrap procedure consists of the following steps:

• 1. For each country, impose the null hypothesis of a unit root and fit the restricted ADF regression equation,

  $${\Delta} y_{i,t}=a_{i,r_{1},r_{2}}+ \sum\nolimits_{j=1}^{k} \psi_{i,r_{1},r_{2}}^{j}{\Delta} y_{i,t-j}+\epsilon_{i,t}, $$

  to obtain coefficient estimates ($\widehat {a}_{i,r_{1},r_{2}}$, and $\widehat {\psi }_{i,r_{1},r_{2}}^{j}$ for $j=1,\dots ,k$) and residuals ($\widehat {\epsilon }_{i}$).

• 2. Create a residual matrix with typical element $\widehat {\epsilon }_{t,i}$.

• 3. In order to preserve the covariance structure of the error term, generate bootstrap residuals, $\epsilon _{i,t}^{b}$, by sampling with replacement draws from the residual matrix.

• 4. Use the bootstrap residuals and the estimated coefficients to recursively generate bootstrap samples for first differences,

  $${\Delta} y_{i,t}^{b}=\widehat{a}_{i,r_{1},r_{2}}+ \sum\nolimits_{j=1}^{k} \widehat{\psi}_{i,r_{1},r_{2}}^{j}{\Delta} y_{i,t-j}^{b}+\epsilon_{i,t}^{b}, $$

  and for levels,

  $$y_{i,t}^{b}= {\displaystyle\sum\nolimits_{p=1}^{t}} {\Delta} y_{i,p}^{b}. $$

• 5. Compute the sequence of panel BSADF statistics and the panel GSADF statistic for $y_{i,t}^{b}$.

• 6. Repeat steps (3) to (5) a large number of times to obtain the empirical distribution of the test statistics under the null of a unit root.