The Dynamic Relationship Between Housing Prices and the Macroeconomy: Evidence from OECD Countries

Abstract

This paper studies the dynamic relationship among house prices, income and interest rates in 15 OECD countries. We find that any disequilibrium in the long-run cointegrating relationship among these variables is corrected by the subsequent movement in house prices in most of these countries. This error-correction property of house prices implies that most of the variations in house prices are transitory, as compared to the movements in income and interest rates that are permanent, suggesting that the short-run movements in house prices are independent of the movements in income and interest rates. The results suggest that only the permanent movement in house prices, income and interest rates are associated with each other. We also find that the correlation in house price cycles across different OECD countries has changed over time with the highest correlation during the boom period of 1998–2005.

Appendices

Appendix A: State-Space Representation of Multivariate Beveridge-Nelson Trend and Cycle

Based on Morley (2002) we present a state-space representation of the multivariate Beveridge-Nelson trend and cycle. We have the following VECM equations

$$\begin{array}{@{}rcl@{}} \Delta h_{t} &=& \gamma_{10} + \gamma^{h}_{11} \Delta h_{t-1} + \gamma^{y}_{12} \Delta y_{t-1} + \gamma^{r}_{13}\Delta r_{t-1} + \cdots + \gamma^{h}_{17} \Delta h_{t-3} + \gamma^{y}_{18} \Delta y_{t-3}\\[-2pt] &&\qquad + \gamma^{r}_{19} \Delta r_{t-3} + \alpha^{h} \hat{\beta}^{\prime} Y_{t-1} + e_{ht}\\[-2pt] \Delta y_{t} &=& \gamma_{20} + \gamma^{h}_{21} \Delta h_{t-1} + \gamma^{y}_{22} \Delta y_{t-1} + \gamma^{r}_{23}\Delta r_{t-1} + \cdots + \gamma^{h}_{27} \Delta h_{t-3} + \gamma^{y}_{28} \Delta y_{t-3} \\[-2pt] &&\qquad+ \gamma^{r}_{29} \Delta r_{t-3} + \alpha^{y} \hat{\beta}^{\prime} Y_{t-1} + e_{yt}\\[-2pt] \Delta r_{t} &=& \gamma_{30} + \gamma^{h}_{31} \Delta h_{t-1} + \gamma^{y}_{32} \Delta y_{t-1} + \gamma^{r}_{33}\Delta r_{t-1} + \cdots + \gamma^{h}_{37} \Delta h_{t-3} + \gamma^{y}_{38} \Delta y_{t-3}\\ &&\qquad + \gamma^{r}_{39} \Delta r_{t-3} + \alpha^{r} \hat{\beta}^{\prime} Y_{t-1} + e_{rt} \end{array} $$

The Beveridge-Nelson cycle is defined as

$${Y^{c}_{t}} = -[E({\Delta} Y_{t+1}|I_{t}) + E({\Delta} Y_{t+2}|I_{t}) + {\ldots} + E({\Delta} Y_{t+k}|I_{t}) + \ldots] $$

where I _t is the information available at time t. The state space representation of the above model is as follows:

$$\left[ \begin{array}{c} \Delta h^{\ast}_{t} \\[-2pt] \Delta y^{\ast}_{t} \\[-2pt] \Delta r^{\ast}_{t} \\[-2pt] \Delta h^{\ast}_{t-1} \\[-2pt] \Delta y^{\ast}_{t-1} \\[-2pt] \Delta r^{\ast}_{t-1} \\[-2pt] \Delta h^{\ast}_{t-2} \\[-2pt] \Delta y^{\ast}_{t-2} \\[-2pt] \Delta r^{\ast}_{t-2} \\[-2pt] \beta^{\prime} z_{t} \end{array} \right] \!\!=\!\! \left[ \begin{array}{cccccccccc} \gamma^{h}_{11} & \gamma^{y}_{12} & \gamma^{r}_{13} & \gamma^{h}_{14} & \gamma^{y}_{15} & \gamma^{r}_{16} & \gamma^{h}_{17} & \gamma^{y}_{18} & \gamma^{r}_{19} & \alpha^{h} \\[-2pt] \gamma^{h}_{21} & \gamma^{y}_{22} & \gamma^{r}_{23} & \gamma^{h}_{24} & \gamma^{y}_{25} & \gamma^{r}_{26} & \gamma^{h}_{27} & \gamma^{y}_{28} & \gamma^{r}_{29} & \alpha^{y} \\[-2pt] \gamma^{h}_{31} & \gamma^{y}_{32} & \gamma^{r}_{33} & \gamma^{h}_{34} & \gamma^{y}_{35} & \gamma^{r}_{36} & \gamma^{h}_{37} & \gamma^{y}_{38} & \gamma^{r}_{39} & \alpha^{r} \\[-2pt] 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\[-2pt] 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\[-2pt] 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\[-2pt] 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0\\[-2pt] 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0\\[-2pt] 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0\\[-2pt] \gamma^{h}_{101} & \gamma^{y}_{102} & \gamma^{r}_{103} & \gamma^{h}_{104} & \gamma^{y}_{105} & \gamma^{r}_{106} & \gamma^{h}_{107} & \gamma^{y}_{108} & \gamma^{r}_{109}& \gamma^{\ast} \end{array} \right] \left[ \begin{array}{c} \Delta h^{\ast}_{t-1} \\[-2pt] \Delta y^{\ast}_{t-1} \\[-2pt] \Delta r^{\ast}_{t-1} \\[-2pt] \Delta h^{\ast}_{t-2} \\[-2pt] \Delta y^{\ast}_{t-2} \\[-2pt] \Delta r^{\ast}_{t-2} \\[-2pt] \Delta h^{\ast}_{t-3} \\[-2pt] \Delta y^{\ast}_{t-3} \\[-2pt] \Delta r^{\ast}_{t-3} \\[-2pt] \beta^{\prime} z_{t-1} \end{array} \right] \!\!+\!\! \left[ \begin{array}{c} e_{ht} \\ e_{yt} \\ e_{rt} \\[-2pt] 0 \\[-2pt] 0 \\[-2pt] 0 \\[-2pt] 0 \\[-2pt] 0 \\[-2pt] 0 \\ e_{zt} \end{array} \right] $$

where $\gamma ^{h}_{10i} = \gamma ^{h}_{1i}-\beta _{1}\gamma ^{h}_{2i}-\beta _{2}\gamma ^{h}_{3i}, \gamma ^{\ast } = 1+\alpha ^{h}-\alpha ^{y}-\alpha ^{r},$ and e _{z t} = e _{h t} −β ₁ e _{x t} −β ₂ e _{r t} and the starred letters represent the mean adjusted variable. In matrix form the state space form can be written as

$${\Delta} Y^{\ast}_{t} = F {\Delta} Y^{\ast}_{t-1} + e^{\ast}_{t} $$

where eigenvalues of the matrix F are less than unity in modulus. Then the cycle of the i ^th component of vector $Y^{\ast }_{t}$ can be written as (i,i)^th element of the matrix $-(F+F^{2}+F^{3}+ ---) \ast {\Delta } Y^{\ast }_{t}$ which is equivalent of (i,i)^th element of matrix $-F(I-F)^{-1} \ast {\Delta } Y^{\ast }_{t}$. The trend component is computed by subtracting the cyclical component from the corresponding variable.

Appendix B: Robustness Check - Long-Term Interest Rates

As a robustness check, we also test our results using long-term interest rates. The table below reports the cointegrating vector estimates and the t-value from DOLS (Panel A) and the adjustment coefficient from the VECM model (Panel B) in case of cointegrating relationship between real house prices, real personal income, and real long-term interest rates.

Country	Constant	t-value	RPDI	t-value	RINT	t-value
Panel A: DOLS: long-term interest rates
Australia	−5.627	−18.08	2.185	30.26	0.021	3.66
Belgium	−0.936	−0.84	1.238	5.17	−0.087	−6.73
Canada	−4.657	−14.30	2.015	28.31	−0.003	−0.66
Denmark	−7.872	−2.01	2.699	3.20	−0.003	−0.09
Finland	−5.816	−6.64	2.238	11.74	0.038	3.25
France	−3.409	−6.25	1.744	14.21	−0.040	−4.79
Ireland	−4.113	−13.06	1.877	24.37	−0.021	−4.53
Italy	−8.901	−4.93	2.927	7.44	0.010	1.43
Netherlands	−7.089	−5.65	2.534	9.39	−0.047	−2.82
New Zealand	−6.217	−13.95	2.317	23.25	0.001	0.20
Norway	−0.716	−0.37	1.198	2.93	−0.016	−0.41
Spain	−7.928	−22.13	2.682	33.63	0.013	1.07
Sweden	−1.141	−0.94	1.268	4.95	−0.064	−4.41
U.K.	−2.035	−6.05	1.426	18.41	−0.027	−2.71
U.S.	1.124	4.21	0.730	11.34	−0.015	−2.58
Panel B: VECM: Long-Term Interest Rates
Australia	−0.009	−0.44	0.033	1.99	0.782	1.02
Belgium	−0.042	−3.68	−0.006	−1.19	−0.535	−1.26
Canada	−0.082	−3.07	−0.021	−1.26	0.989	1.08
Denmark	−0.033	−2.32	0.002	0.20	−0.097	−0.14
Finland	−0.048	−1.62	0.029	2.17	3.918	3.71
France	−0.021	−2.72	−0.002	−0.45	−0.204	−0.53
Ireland	−0.042	−3.45	−0.008	−0.76	1.158	1.12
Italy	−0.020	−1.81	−0.001	−0.12	2.191	2.54
Netherlands	−0.016	−2.23	0.000	0.04	−0.186	−0.31
New Zealand	−0.019	−1.31	0.033	3.58	0.730	0.69
Norway	−0.066	−4.81	−0.015	−1.74	−0.853	−1.28
Spain	−0.048	−3.11	−0.003	−0.44	0.656	0.86
Sweden	−0.035	−2.38	−0.018	−2.04	−3.510	−3.12
U.K.	−0.024	−2.03	−0.006	−0.76	−0.926	−1.92
U.S.	−0.031	−3.06	−0.003	−0.34	0.559	0.84