Comparisons of housing price risks between first-time buyer and former owner-occupier markets in England

Figures & data

Figure 1. The performance of the FTB property markets.

Figure 2. The performance of the FOO property markets.

Table 1. Causality tests between the FTB and FOO markets.

	North East		North West		Yorkshire and The Humber		East Midlands		West Midlands
Null Hypothesis	F-Stat.	p-value	F-Stat.	p-value	F-Stat.	p-value	F-Stat.	p-value	F-Stat.	p-value
$r_{\mathit{FOO}}-/\to r_{\mathit{FTB}}$	0.0472	0.9539	0.3789	0.6857	1.0330	0.3601	0.2144	0.8074	3.9475	0.0227
$r_{\mathit{FTB}}-/\to r_{\mathit{FOO}}$	0.8557	0.4284	0.2309	0.7943	0.9056	0.4079	3.7558	0.0271	4.7315	0.0111
Total spillover index	49.0%		48.1%		48.6%		45.2%		49.2%
	East		London		South East		South West		England
Null Hypothesis	F-Stat.	p-value	F-Stat.	p-value	F-Stat.	p-value	F-Stat.	p-value	F-Stat.	p-value
$r_{\mathit{FOO}}-/\to r_{\mathit{FTB}}$	1.3098	0.2749	3.0242	0.0535	0.4352	0.6485	0.3701	0.6917	1.1477	0.3219
$r_{\mathit{FTB}}-/\to r_{\mathit{FOO}}$	8.5401	0.0004	1.3407	0.2668	15.4108	0.0000	3.0575	0.0519	9.1234	0.0002
Total spillover index	46.3%		47.6%		45.2%		46.6%		46.1%

Notes: $r_{\mathit{FTB},t}$ is the regional house price return of the FTB housing markets, $r_{\mathit{FOO},t}$ is the regional house price return of the FOO housing markets. Number in bold denotes statistically significant at 5% level.

Table 2. The VAR-MGARCH-X model.

	North East		North West		Yorkshire and The Humber		East Midlands		West Midlands
Variable	Coefficient	p-value	Coefficient	p-value	Coefficient	p-value	Coefficient	p-value	Coefficient	p-value
Mean model: $r_{\mathit{FTB}}$
$r_{\mathit{FTB},t-1}$	–0.0977	0.8275	–0.4732	0.1412	–0.7792	0.0000	–0.3423	0.0000	0.2093	0.6888
$r_{\mathit{FOO},t-1}$	–0.2077	0.6725	0.2259	0.5337	0.6356	0.0000	0.2807	0.0000	0.1650	0.7483
$C\mathrm{onstant}$	0.0401	0.7599	0.2944	0.0047	0.1912	0.0000	0.3643	0.0000	0.2269	0.0000
Mean model: $r_{\mathit{FOO}}$
$r_{\mathit{FTB},t-1}$	0.3371	0.4243	0.0831	0.7666	–0.2908	0.0000	0.1656	0.0003	0.1671	0.7172
$r_{\mathit{FOO},t-1}$	–0.6381	0.1604	–0.326	0.3076	0.0988	0.0000	–0.2588	0.0000	0.2695	0.5531
$C\mathrm{onstant}$	0.0685	0.5739	0.3004	0.0010	0.2084	0.0000	0.3651	0.0000	0.1959	0.0000
Variance model
$\mathrm{C}\left(1,1\right)$	1.3430	0.0000	0.6606	0.0013	1.0921	0.0000	0.6971	0.0000	0.3752	0.0000
$\mathrm{C}\left(2,1\right)$	1.1929	0.0000	0.5533	0.0015	0.9851	0.0000	0.6227	0.0000	0.3640	0.0000
$\mathrm{C}\left(2,2\right)$	0.1946	0.0000	0.0185	0.6056	0.1469	0.0000	0.2123	0.0000	–0.0125	0.5355
$\mathrm{A}\left(1,1\right)$	0.6091	0.5625	0.8972	0.1225	0.7316	0.0000	0.2501	0.0001	1.9076	0.0007
$\mathrm{A}\left(1,2\right)$	0.1503	0.8791	0.5624	0.2799	0.1085	0.0019	–0.4047	0.0000	1.1626	0.0306
$\mathrm{A}\left(2,1\right)$	–0.6841	0.5552	–0.9064	0.1742	–0.3166	0.0000	–0.3486	0.0003	–1.8483	0.0020
$\mathrm{A}\left(2,2\right)$	–0.1397	0.8966	–0.5834	0.3370	0.2343	0.0000	0.1756	0.0309	–1.0314	0.0684
$\mathrm{B}\left(1,1\right)$	1.8974	0.0056	–1.5040	0.0000	–0.0268	0.0230	0.3853	0.0000	1.9103	0.0030
$\mathrm{B}\left(1,2\right)$	1.8863	0.0036	–2.0188	0.0000	–0.0432	0.0225	0.1019	0.0012	1.6075	0.0151
$\mathrm{B}\left(2,1\right)$	–1.9183	0.0082	2.2701	0.0000	0.2053	0.0000	–0.0521	0.1220	–1.8318	0.0102
$\mathrm{B}\left(2,2\right)$	–1.9709	0.0056	2.6604	0.0000	0.3301	0.0000	0.2582	0.0000	–1.4361	0.0500
$\Delta {\mathit{SPI}}_{t-1}\left(1,1\right)$	0.0784	0.1638	0.0838	0.0009	–0.0755	0.0000	–0.0472	0.0000	–0.0094	0.4595
$\Delta {\mathit{SPI}}_{t-1}\left(2,1\right)$	0.0727	0.2188	0.0609	0.0086	–0.0589	0.0000	–0.0289	0.0013	–0.0144	0.2308
$\Delta {\mathit{SPI}}_{t-1}\left(2,2\right)$	0.0056	0.6542	–0.0214	0.0878	0.0051	0.3632	–0.0136	0.1389	–0.0115	0.0022
$\Delta {lr}_{t-1}\left(1,1\right)$	–0.0393	0.0012	0.0141	0.0758	0.0141	0.0000	0.0037	0.0653	0.0048	0.1272
$\Delta {lr}_{t-1}\left(2,1\right)$	–0.0421	0.0002	0.0084	0.2583	0.0101	0.0000	0.0008	0.7274	0.0015	0.5906
$\Delta {lr}_{t-1}\left(2,2\right)$	0.0127	0.0028	0.0028	0.1489	0.0042	0.0000	0.0018	0.4280	0.0008	0.3977

Notes:$r_{\mathit{FTB},t}$ is the regional house price return of the FTB housing markets, and $r_{\mathit{FOO},t}$ is the regional house price return of the FOO housing markets. $\Delta lr$ and $\Delta \mathit{SPI}$ denote the growth rates in the interest rates and the growth rates in the stock price indices, respectively. Number in bold denotes statistically significant at 5% level.

Figure 3. Time series of macroeconomic variables.

Table 3. Causality tests in mean and in variance.

Region	North East			North West			Yorkshire and The Humber			East Midlands			West Midlands
Null Hypothesis	${\chi }^2(n)$	F–Stat.	p-value	${\chi }^2(n)$	F-Stat.	p-value	${\chi }^2(n)$	F-Stat.	p-value	${\chi }^2(n)$	F-Stat.	p-value	${\chi }^2(n)$	F-Stat.	p-value
Causality in mean
$\mathit{FTB}-/\to \mathit{FOO}$	0.6383		0.4243	0.0881		0.7666	84.5420		0.0000	13.0276		0.0003	0.1312		0.7172
$\mathit{FOO}-/\to \mathit{FTB}$	0.1787		0.6725	0.3874		0.5337	669.2359		0.0000	25.7958		0.0000	0.1030		0.7483
Causality in variance
$\mathit{FTB}-/\to \mathit{FOO}$	10.5680	5.2840	0.0051	46.4106	23.2053	0.0000	17.0841	8.5421	0.0002	25.0588	12.5294	0.0000	14.1453	7.0726	0.0008
$\mathit{FOO}-/\to \mathit{FTB}$	10.5760	5.2880	0.0051	36.0253	18.0127	0.0000	289.5994	144.7997	0.0000	13.6334	6.8167	0.0011	23.5949	11.7974	0.0000
Region	East			London			South East			South West			England
Null Hypothesis	${\chi }^2(n)$	F-Stat.	p-value	${\chi }^2(n)$	F-Stat.	p-value	${\chi }^2(n)$	F-Stat.	p-value	${\chi }^2(n)$	F-Stat.	p-value	${\chi }^2(n)$	F-Stat.	p-value
Causality in mean
$\mathit{FTB}-/\to \mathit{FOO}$	36.3843		0.0000	359.2414		0.0000	336.0437		0.0000	3.5768		0.0586	4.6847		0.0304
$\mathit{FOO}-/\to \mathit{FTB}$	31.3409		0.0000	79.5302		0.0000	0.3863		0.5342	0.1266		0.7220	4.9856		0.0256
Causality in variance
$\mathit{FTB}-/\to \mathit{FOO}$	25.7447	12.8723	0.0000	4.6673	2.3337	0.0969	5.8953	2.9476	0.0525	1.5984	0.7992	0.4497	1.5463	0.7731	0.4616
$\mathit{FOO}-/\to \mathit{FTB}$	13.1587	6.5793	0.0014	5.3874	2.6937	0.0676	42.1074	21.0537	0.0000	0.6296	0.3148	0.7299	0.3808	0.1904	0.8266

Notes: Number in bold denotes statistically significant at 5% level.

Figure 4. Conditional volatilities.

Table 4. Factor risk.

Region	North East			North West			Yorkshire and The Humber			East Midlands			West Midlands
Null Hypothesis	${\chi }^2(n)$	F-Stat.	p-value	${\chi }^2(n)$	F-Stat.	p-value	${\chi }^2(n)$	F-Stat.	p-value	${\chi }^2(n)$	F-Stat.	p-value	${\chi }^2(n)$	F-Stat.	p-value
$\mathit{SPI}-/\to \mathit{FTB}$	1.9385		0.1638	11.0197		0.0009	259.8731		0.0000	21.7454		0.0000	0.5470		0.4595
$\mathit{SPI}-/\to \mathit{FOO}$	0.2006		0.6542	2.9134		0.0878	0.8269		0.3631	2.1903		0.1389	9.4120		0.0022
$lr-/\to \mathit{FTB}$	10.5490		0.0012	3.1521		0.0758	890.6767		0.0000	3.3973		0.0653	2.3259		0.1272
$lr-/\to \mathit{FOO}$	8.9610		0.0028	2.0832		0.1489	37.1986		0.0000	0.6283		0.4280	0.7154		0.3977
$\mathit{risk}\mathrm{}\mathit{factors}$ $-/\to$ $\mathit{connection}$	10.6153	5.3077	0.0050	8.4996	4.2498	0.0143	5319.41	2659.70	0.0000	13.7525	6.8762	0.0010	3.0085	1.5042	0.2222
Region	East			London			South East			South West			England
Null Hypothesis	${\chi }^2(n)$	F-Stat.	p-value	${\chi }^2(n)$	F-Stat.	p-value	${\chi }^2(n)$	F-Stat.	p-value	${\chi }^2(n)$	F-Stat.	p-value	${\chi }^2(n)$	F-Stat.	p-value
$\mathit{SPI}-/\to \mathit{FTB}$	0.0438		0.8342	77.6050		0.0000	0.2176		0.6409	0.7413		0.3892	4.2957		0.0382
$\mathit{SPI}-/\to \mathit{FOO}$	0.0593		0.8076	2.3573		0.1247	435.6737		0.0000	3.0390		0.0813	0.0046		0.9456
$lr-/\to \mathit{FTB}$	17.9862		0.0000	0.2166		0.6416	63.0811		0.0000	5.8657		0.0154	0.3544		0.5516
$lr-/\to \mathit{FOO}$	1.9495		0.1626	16.6422		0.0000	1334.79		0.0000	0.3416		0.5589	21.2408		0.0000
$\mathit{risk}\mathrm{}\mathit{factors}$ $-/\to$ $\mathit{connection}$	20.3390	10.1695	0.0000	53.7258	26.8629	0.0000	71.6657	35.8328	0.0000	5.9764	2.9882	0.0504	6.1559	3.0780	0.0460

Notes: $lr$ and $\mathit{SPI}$ denote long-term interest rate and FTSE 100 stock price index, respectively. The null hypothesis of this table is whether or not the changes in the factor can influence the house price volatility risk. Number in bold denotes statistically significant at 5% level.

Figure 5. Impulse response function of volatilities.

Table

	East		London		South East		South West		England
Variable	Coefficient	p-value	Coefficient	p-value	Coefficient	p-value	Coefficient	p-value	Coefficient	p-value
Mean model: $r_{\mathit{FTB}}$
$r_{\mathit{FTB},t-1}$	–0.1268	0.0070	–0.0999	0.0063	0.3522	0.0000	–0.0837	0.6921	–0.1790	0.3423
$r_{\mathit{FOO},t-1}$	0.2738	0.0000	0.2496	0.0000	–0.0330	0.5342	–0.0658	0.7220	0.4976	0.0256
$C\mathrm{onstant}$	0.2761	0.0000	0.2866	0.0000	0.2617	0.0000	0.4323	0.0000	0.2236	0.0048
Mean model: $r_{\mathit{FOO}}$
$r_{\mathit{FTB},t-1}$	0.3247	0.0000	0.4464	0.0000	1.0305	0.0000	0.4120	0.0586	0.3899	0.0304
$r_{\mathit{FOO},t-1}$	–0.1809	0.0001	–0.2873	0.0000	–0.6273	0.0000	–0.4631	0.0186	–0.0285	0.8799
$C\mathrm{onstant}$	0.2849	0.0000	0.2985	0.0000	0.2667	0.0000	0.4149	0.0000	0.2330	0.0001
Variance model
$\mathrm{C}\left(1,1\right)$	0.7653	0.0000	1.0522	0.0000	0.5742	0.0000	0.5461	0.0001	0.5978	0.0000
$\mathrm{C}\left(2,1\right)$	0.7543	0.0000	1.0164	0.0000	0.5414	0.0000	0.7422	0.0000	0.4733	0.0000
$\mathrm{C}\left(2,2\right)$	0.2640	0.0000	0.2802	0.0000	0.1849	0.0000	0.0263	0.8746	0.1828	0.0000
$\mathrm{A}\left(1,1\right)$	0.3850	0.0000	0.2379	0.0000	0.0757	0.4664	0.2644	0.5077	–0.4067	0.5464
$\mathrm{A}\left(1,2\right)$	–0.1755	0.0173	0.1311	0.0332	0.2288	0.0152	0.2509	0.5499	–0.4386	0.2154
$\mathrm{A}\left(2,1\right)$	–0.2169	0.0003	0.1302	0.0321	–0.2982	0.0023	–0.1544	0.6285	0.3796	0.5519
$\mathrm{A}\left(2,2\right)$	0.3352	0.0000	0.0759	0.2206	–0.0113	0.8956	0.0224	0.9468	0.6063	0.1186
$\mathrm{B}\left(1,1\right)$	0.3378	0.0000	–0.0491	0.4654	–0.0739	0.3612	0.8499	0.0080	0.0632	0.9029
$\mathrm{B}\left(1,2\right)$	0.1507	0.0000	–0.0609	0.3960	–0.0455	0.3627	0.5680	0.2228	–0.0871	0.8397
$\mathrm{B}\left(2,1\right)$	0.0048	0.8545	0.0502	0.4983	0.3174	0.0000	–0.1701	0.6477	–0.0127	0.9745
$\mathrm{B}\left(2,2\right)$	0.1144	0.0014	0.0480	0.5288	0.1953	0.0000	–0.0967	0.8123	–0.0357	0.9188
$\Delta {\mathit{SPI}}_{t-1}\left(1,1\right)$	0.0028	0.8342	–0.0891	0.0000	0.0049	0.6409	–0.0170	0.3892	–0.0310	0.0382
$\Delta {\mathit{SPI}}_{t-1}\left(2,1\right)$	0.0006	0.9623	–0.0658	0.0000	–0.0022	0.8238	–0.0012	0.9628	–0.0329	0.0151
$\Delta {\mathit{SPI}}_{t-1}\left(2,2\right)$	–0.0033	0.8076	–0.0120	0.1247	0.0418	0.0000	0.0193	0.0813	0.0005	0.9456
$\Delta {lr}_{t-1}\left(1,1\right)$	0.0128	0.0000	0.0006	0.6416	–0.0064	0.0000	–0.0128	0.0154	–0.0021	0.5516
$\Delta {lr}_{t-1}\left(2,1\right)$	0.0088	0.0012	–0.0022	0.1023	0.0012	0.0242	–0.0034	0.5364	–0.0031	0.3846
$\Delta {lr}_{t-1}\left(2,2\right)$	0.0048	0.1626	0.0061	0.0000	0.0010	0.0000	0.0029	0.5589	0.0125	0.0000

Notes:$r_{\mathit{FTB},t}$ is the regional house price return of the FTB housing markets, and $r_{\mathit{FOO},t}$ is the regional house price return of the FOO housing markets. $\Delta lr$ and $\Delta \mathit{SPI}$ denote the growth rates in the interest rates and the growth rates in the stock price indices, respectively. Number in bold denotes statistically significant at 5% level.

Appendix Table A1. Descriptive statistics and unit root tests (FTB properties).

House prices (£)	$NE$	$NW$	$Y\mathit{and}H$	$EM$	$WM$	$EA$	$L$	$SE$	$SW$	$\mathit{ENG}$
Mean	104.7203	106.9334	107.3546	108.2444	108.9057	109.2184	104.1831	106.8306	106.2857	106.8274
Maximum	112.5560	122.9881	122.3068	127.6287	130.5055	128.9860	121.7683	123.9709	123.8443	123.0422
Minimum	95.8258	91.0987	91.9798	88.5502	89.5740	83.2366	71.9857	82.0002	88.1557	85.3211
Std. Dev.	4.4978	10.1492	9.4908	13.2106	14.1209	17.0033	16.7966	14.8526	12.0266	13.1953
Skewness	–0.1447	0.0769	–0.0074	–0.0144	0.1560	–0.2736	–0.6888	–0.3825	–0.1457	–0.2958
Kurtosis	1.8678	1.5554	1.5730	1.5354	1.5233	1.4286	1.8841	1.51488	1.4866	1.5406
PP test (Level)	–2.1756 (0.2165)	–0.4115 (0.9020)	–1.1928 (0.6752)	–0.6378 (0.8561)	–0.0924 (0.9465)	–1.2334 (0.6575)	–2.1052 (0.2432)	–1.7116 (0.4223)	–0.3268 (0.9159)	–1.3610 (0.5983)
PP test (Differenced)	–12.9060 (0.0001)	–12.6771 (0.0001)	–11.4557 (0.0001)	–11.4551 (0.0001)	–5.7665 (0.0000)	–10.3178 (0.0000)	–10.1362 (0.0000)	–7.1746 (0.0000)	–10.6777 (0.0000)	–8.0888 (0.0000)

Notes: $NE,$ $NW,$ $Y\mathit{and}H,$ $EM,$ $WM,$ $EA,$ $L,$ $SE,$ $SW,$ $\mathit{ENG}$ are the estimated results using the data from North East, North West, Yorkshire and The Humber, East Midlands, West Midlands, East, London, South East, South West, and England, respectively. PP tests are adopted to test the null hypothesis of a unit root in the series. Intercept is included in the testing equation, and the lag lengths of the unit root models are selected by Schwarz Information Criterion. Entry in parentheses stands for the p-value. Number in bold denotes statistically significant at 1% level.

Appendix Table A2. Descriptive statistics and unit root tests (FOO properties).

House prices (£)	$NE$	$NW$	$Y\mathit{and}H$	$EM$	$WM$	$EA$	$L$	$SE$	$SW$	$\mathit{ENG}$
Mean	104.7004	106.9260	107.3385	108.2808	108.8701	109.0004	104.1549	106.7449	106.0730	106.8903
Maximum	112.6157	123.2043	122.2040	127.7091	130.6202	128.8904	120.7523	123.8199	123.6515	123.2063
Minimum	95.4441	91.8992	92.3147	88.7232	89.9001	82.6013	72.1681	82.3009	88.1605	85.9122
Std. Dev.	4.7026	10.0495	9.3847	13.3037	14.1201	16.7906	16.4804	14.6732	11.7488	13.0310
Skewness	–0.1016	0.1169	0.0145	0.0011	0.1626	–0.2533	–0.6847	–0.3736	–0.1158	–0.2501
Kurtosis	1.7902	1.5648	1.5729	1.5296	1.5325	1.4352	1.8717	1.5236	1.5018	1.5283
PP test (Level)	–1.9229 (0.3206)	–0.3264 (0.9160)	–1.0690 (0.7255)	–0.3957 (0.9047)	–0.0003 (0.9557)	–1.0361 (0.7379)	–2.1438 (0.2283)	–1.6205 (0.4684)	–0.2179 (0.9315)	–1.1481 (0.6941)
PP test (Differenced)	–12.8190 (0.0001)	–11.8384 (0.0001)	–10.9859 (0.0000)	–11.8971 (0.0001)	–5.5446 (0.0000)	–9.9760 (0.0000)	–9.1980 (0.0000)	–8.2021 (0.0000)	–10.7572 (0.0000)	–7.1004 (0.0000)

Notes: $NE,$ $NW,$ $Y\mathit{and}H,$ $EM,$ $WM,$ $EA,$ $L,$ $SE,$ $SW,$ $\mathit{ENG}$ are the estimated results using the data from North East, North West, Yorkshire and The Humber, East Midlands, West Midlands, East, London, South East, South West, and England, respectively. PP tests are adopted to test the null hypothesis of a unit root in the series. Intercept is included in the testing equation, and the lag lengths of the unit root models are selected by Schwarz Information Criterion. Entry in parentheses stands for the p-value. Number in bold denotes statistically significant at 1% level.

Appendix Table A3. Descriptive statistics and unit root tests for the two factors.

Variables	$lr$ (%)	$\mathit{SPI}$ (index)
Mean	1.6636	6748.4126
Maximum	3.2400	7748.7600
Minimum	0.4200	5320.8600
Std. Dev.	0.6442	586.5752
Skewness	0.3229	–0.3513
Kurtosis	2.5578	2.2916
PP test (Level)	–0.9906 (0.7543)	–2.0273 (0.2749)
PP test (Differenced)	–10.7185 (0.0000)	–9.7779 (0.0000)

Notes: $lr$ and $\mathit{SPI}$ denote long-term interest rate and FTSE 100 stock price index, respectively. PP tests are adopted to test the null hypothesis of a unit root in the series. Intercept is included in the testing equation, and the lag lengths of the unit root models are selected by Schwarz Information Criterion. Entry in parentheses stands for the p-value. Number in bold denotes statistically significant at 1% level.