European house price deviation: infectivity and the momentum effect

Figures & data

Figure 1. House price index.

Figure 2. Personal disposable income index.

Table 1. Descriptive statistics of house price index and personal disposable income.

$P$	Belgium	Finland	France	Germany	Ireland
Mean	77.80	75.02	71.04	108.81	52.03
Maximum	122.33	112.15	115.42	126.79	118.69
Minimum	41.96	44.57	43.2	93.04	23.28
Std. Dev.	27.97	23.16	25.48	8.97	28.85
Skewness	0.49	0.33	0.69	0.11	0.73
Kurtosis	1.74	1.57	1.73	2.48	2.22
$P$	Italy	Netherlands	Spain	UK
Mean	77.51	65.99	71.31	60.99
Maximum	108.07	105.13	109.32	115.03
Minimum	53.46	33.2	35.74	26.16
Std. Dev.	15.61	24.58	20.21	29.05
Skewness	0.25	0.21	0.30	0.46
Kurtosis	2	1.48	1.86	1.61
$Y$	Belgium	Finland	France	Germany	Ireland
Mean	90.02	84.06	87.01	89.07	75.11
Maximum	105.05	116.62	105.91	111.97	117.97
Minimum	66.15	51.54	66.12	65.2	48.84
Std. Dev.	11.66	19.92	13.58	14.18	23.38
Skewness	–0.41	0.11	0.07	–0.13	0.31
Kurtosis	1.49	1.83	1.41	1.65	1.40
$Y$	Italy	Netherlands	Spain	UK
Mean	88.89	89.3	85.15	79.96
Maximum	102.98	105.02	101.20	109.38
Minimum	61.94	70.24	66.54	46.98
Std. Dev.	9.90	11.25	11.86	20.8
Skewness	–0.87	–0.20	–0.16	–0.16
Kurtosis	2.88	1.53	1.46	1.48

Notes: $P$ denotes the real house price index, and $Y$ denotes the real personal disposable income index.

Table 2. Unit root tests for variables in levels and in differenced form.

$P$	Belgium	Finland	France		Germany		Ireland
ADF unit root test
Level	0.92 (0.90)	0.57 (0.84)	1.05 (0.92)		0.14 (0.73)		0.46 (0.81)
First difference	–2.97 (0.00)	–4.91 (0.00)	–3.22 (0.00)		–3.22 (0.00)		–3.19 (0.00)
	Italy	Netherlands		Spain		UK
Level	0.01 (0.69)	0.12 (0.72)		–1.00 (0.28)		1.09 (0.93)
First difference	–3.95 (0.00)	–2.25 (0.02)		–9.90 (0.00)		–4.37 (0.00)
$Y$	Belgium	Finland	France		Germany		Ireland
ADF unit root test
Level	2.14 (0.99)	4.92 (1.00)	4.52 (1.00)		4.62 (1.00)		2.72 (1.00)
First difference	–9.44 (0.00)	–6.55 (0.00)	–3.97 (0.00)		–2.36 (0.02)		–3.40 (0.00)
	Italy	Netherlands		Spain		UK
Level	2.01 (0.99)	1.32 (0.95)		1.08 (0.93)		4.48 (1.00)
First difference	–4.67 (0.00)	–10.25 (0.00)		–4.08 (0.00)		–3.29 (0.00)

Notes: $P$ denotes the real house price index, and $Y$ denotes the real personal disposable income index. A.D.F. tests are adopted for testing the null hypothesis of a unit root in the series. The lag length of the unit root models is selected by using the Schwarz information criterion. The entry in parenthesis stands for the p-value.

Figure 3. House price Deviation.

Table 3. Estimations for the equilibrium home price (F.M.O.L.S. estimation).

Belgium		Finland		France
$a_0$	–90.9797*** (0.0000)	$a_0$	–16.6109*** (0.0099)	$a_0$	–76.1843*** (0.0000)
$a_1$	1.8917*** (0.0000)	$a_1$	1.0813*** (0.0000)	$a_1$	1.7144*** (0.0000)
R-squared	0.6505	R-squared	0.8576	R-squared	0.8288
Germany		Ireland		Italy
$a_0$	154.5355*** (0.0000)	$a_0$	–32.1063*** (0.0000)	$a_0$	–16.1271 (0.2776)
$a_1$	–0.5036*** (0.0000)	$a_1$	1.1209*** (0.0000)	$a_1$	1.0646*** (0.0000)
R-squared	0.6052	R-squared	0.8251	R-squared	0.5549
Netherlands		Spain		UK
$a_0$	–116.4640*** (0.0000)	$a_0$	15.3629 (0.4591)	$a_0$	–39.0130*** (0.0000)
$a_1$	2.0533*** (0.0000)	$a_1$	0.6842*** (0.0050)	$a_1$	1.2771*** (0.0000)
R-squared	0.8566	R-squared	0.1455	R-squared	0.8310

Notes: This table shows the estimated results of the long-run relationship between home price index and fundamental variables. The estimated model is:

$P_t^{\mathrm{*}}=a_0+a_1{Y}_t.$

where $P^{*}$ denotes the long-run equilibrium real house price index, and $Y$ denotes the real personal disposable income index. *** indicates significance at the 1% level.

Table 4. Interactions between house price deviations.

	Belgium	Finland	France	Germany	Ireland	Italy	Netherlands	Spain	UK
Belgium	85.6	3.4	2.1	1.3	2.2	0.1	0.3	0	5
Finland	3.3	67.6	1.8	1.8	4	0.7	4.9	0.4	15.7
France	3.6	3.2	66.1	2.8	4.5	0.5	6.8	1.2	11.4
Germany	0.2	0.9	4.6	85.5	2.8	0.9	3.8	0.3	0.8
Ireland	1.5	4.5	1.8	0.4	69.1	1.2	0.2	3.8	17.4
Italy	0.7	0.2	0.4	0.3	0.7	95.5	1.4	0.4	0.5
Netherlands	0.1	0.2	4.4	2.7	2.1	3.2	81.9	1.3	4.1
Spain	0	0.5	0.5	0.4	3.3	0.4	0.5	89	5.4
UK	3.9	7.6	1.8	0.7	12.2	1.6	2.4	1.4	68.5

Notes: This table shows the percentage of house price deviation changes in Country j that can be explained by Country i. Each number in the table represents the effects of the vertical countries on their corresponding horizontal countries.

Figure 4. The components of self-influence.

Figure 5. Infectivity.

Table 5. Infectivity and inflation rate.

	Belgium	Finland		France		Germany		Ireland
$\pi$	–1.51 (0.03)	–3.58 (0.00)		6.53 (0.00)		–6.22 (0.00)		2.10 (0.00)
$\mathrm{Constant}$	3.45 (0.07)	16.48 (0.00)		–13.85 (0.00)		15.77 (0.00)		–16.29 (0.00)
	Italy		Netherlands		Spain		UK
$\pi$	–0.38 (0.31)		3.90 (0.00)		–4.80 (0.00)		4.97 (0.00)
$\mathrm{Constant}$	–6.55 (0.00)		–14.63 (0.00)		28.39 (0.00)		–10.48 (0.00)

Notes: This table shows the estimation results for the relationship between each country’s infectivity and domestic inflation rate. The dependent variable is each country’s impact capacity on house price deviation in other countries, and independent variable ($\pi$) is the inflation rate. The entry in parenthesis stands for the p-value.

Table 6. Momentum effect and inflation rate.

	Belgium	Finland		France		Germany		Ireland
$\pi$	0.51 (0.10)	2.23 (0.00)		1.55 (0.00)		0.17 (0.64)		1.69 (0.00)
$\mathrm{Constant}$	44.87 (0.00)	37.97 (0.00)		44.15 (0.00)		59.68 (0.00)		37.17 (0.00)
	Italy		Netherlands		Spain		UK
$\pi$	–0.78 (0.00)		2.37 (0.00)		1.61 (0.00)		3.26 (0.00)
$\mathrm{Constant}$	54.58 (0.00)		50.56 (0.00)		35.09 (0.00)		30.13 (0.00)

Notes: This table estimates the proportion of house price deviation affected by the domestic housing market, or in other words, the correlation between the persistence of house price deviation caused by the momentum effect and domestic inflation rate. $\pi$ denotes the inflation rate. The entry in parenthesis stands for the p-value.

Table 7. Infectivity of Germany.

	Belgium	Finland	France	Ireland
${\pi }_G$	–2.13 (0.00)	–0.28 (0.43)	–0.10 (0.65)	–1.47 (0.00)
$\mathrm{Constant}$	2.29 (0.00)	3.15 (0.00)	–1.22 (0.01)	5.12 (0.00)
	Italy	Netherlands	Spain	UK
${\pi }_G$	–0.57 (0.00)	–0.58 (0.00)	0.71 (0.01)	–1.81 (0.00)
$\mathrm{Constant}$	2.41 (0.00)	2.00 (0.00)	–4.35 (0.00)	6.38 (0.00)

Notes: This table shows the relationship between the net infecting effect from Germany and the inflation rate of Germany. ${\pi }_G$ denotes the inflation rate of Germany. The entry in parenthesis stands for the p-value.

Table 8. Infectivity of the U.K.

	Belgium	Finland	France	Germany
${\pi }_{\mathit{UK}}$	0.55 (0.00)	4.00 (0.00)	0.97 (0.00)	0.44 (0.00)
$\mathrm{Constant}$	–1.58 (0.00)	–13.00 (0.00)	2.97 (0.00)	–4.40 (0.00)
	Ireland	Italy	Netherlands	Spain
${\pi }_{\mathit{UK}}$	0.35 (0.04)	–2.29 (0.00)	–0.44 (0.01)	1.40 (0.00)
$\mathrm{Constant}$	0.29 (0.61)	7.00 (0.00)	0.23 (0.67)	–2.00 (0.01)

Notes: This table shows the relationship between the net infecting effect from the U.K. and the inflation rate of the U.K. ${\pi }_{\mathit{UK}}$ denotes the inflation rate of the U.K.. The entry in parenthesis stands for the p-value.

Table 9. Infectivity and interest rate.

	Belgium	Finland		France		Germany		Ireland
$i_{\mathit{euro}}-i_d$	1.42 (0.11)	8.00 (0.00)		–5.89 (0.00)		1.10 (0.10)		–1.85 (0.00)
$\mathrm{Constant}$	–2.25 (0.20)	1.61 (0.49)		8.40 (0.00)		1.85 (0.38)		–9.26 (0.00)
	Italy		Netherlands		Spain		UK
$i_{\mathit{euro}}-i_d$	–0.99 (0.01)		1.66 (0.05)		5.75 (0.00)		1.08 (0.02)
$\mathrm{Constant}$	–8.04 (0.00)		–11.52 (0.00)		11.16 (0.00)		3.23 (0.00)

Notes: This table shows the estimation results for the relationship between each country’s infectivity and domestic interest rate. The dependent variable is each country’s impact capacity on house price deviation in other countries, and independent variable ($i_{\mathit{euro}}-i_d$) is the relative interest rate. The entry in parenthesis stands for the p-value.

Table 10. Momentum effect and interest rate.

	Belgium	Finland		France		Germany		Ireland
$i_{\mathit{euro}}-i_d$	0.47 (0.22)	–0.44 (0.08)		–5.63 (0.00)		–0.83 (0.00)		–2.36 (0.00)
$\mathrm{Constant}$	45.30 (0.00)	41.49 (0.00)		55.23 (0.00)		62.13 (0.00)		43.31 (0.00)
	Italy		Netherlands		Spain		UK
$i_{\mathit{euro}}-i_d$	0.22 (0.37)		–0.26 (0.50)		–1.91 (0.00)		–1.27 (0.00)
$\mathrm{Constant}$	51.89 (0.00)		55.39 (0.00)		40.88 (0.00)		39.48 (0.00)

Notes: This table estimates the proportion of house price deviation affected by the domestic housing market, or in other words, the correlation between the persistence of house price deviation caused by the momentum effect and domestic interest rate. Independent variable ($i_{\mathit{euro}}-i_d$) is the relative interest rate. The entry in parenthesis stands for the p-value.