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Applied Economics

ISSN: 0003-6846 (Print) 1466-4283 (Online) Journal homepage: https://www.tandfonline.com/loi/raec20

Modelling house price volatility states in the UK by switching ARCH models

I-Chun Tsai , Ming-Chi Chen & Tai Ma

To cite this article: I-Chun Tsai , Ming-Chi Chen & Tai Ma (2010) Modelling house price volatility states in the UK by switching ARCH models, Applied Economics, 42:9, 1145-1153, DOI: 10.1080/00036840701721133

To link to this article: https://doi.org/10.1080/00036840701721133

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Applied Economics, 2010, 42, 1145–1153

Modelling house price volatility

states in the UK by switching

ARCH models

I-Chun Tsai a , Ming-Chi Chen

b, * and Tai Ma

c

a Department of Finance, Southern Taiwan University of Technology,

Taiwan, ROC b Department of Finance, National Sun Yat-sen University, Taiwan, ROC

c Department of Finance, National Sun Yat-sen University, Taiwan, ROC

This article analyses investment risk in the housing market by examining

volatility properties of house prices for the UK. We use both ARCH and

GARCH models to estimate price conditional heteroscedasticity and find

evidence of a time-varying property in the volatilities of the house price

series. We then use the SWARCH model and find there are three volatility

states in the price series. Our estimations suggest the UK housing markets

are relatively stable and different states do not switch very often. The

magnitude of high price volatility is as high as 20.99 times of the low

volatility for the older housing market and 14 times of the low volatility for

the new housing market. In addition, the older housing market is less

efficient than the new housing market, since the impacts of events on the

volatility state of the older house prices is more lasting than in new housing

market.

I. Introduction

Over the past few decades, sustained growth in house

prices and their recurrent fluctuations around the

growth path seem to be a phenomenon common to

many countries. The risk consideration is now widely

recognized by both theoretical and applied econo-

mists and the modelling of house price behaviour has

attracted much research attention. However, few of

the previous studies on the behaviour of house prices

have emphasized on the behaviour of volatility, which

is usually viewed as the risk of house prices. Empirical

work on the dynamics of the housing market has tried

to capture the short-term adjustment process

(for example, Meen, 1990; Drake, 1993; Malpezzi,

1999). Most of these studies try to model price

behaviour based on the interaction of demand

and supply-side factors using traditional regression

analysis on conditional mean. Thus, most of these

economic models may not provide a satisfactory

performance capturing the boom and bust behaviour

of housing markets. Although highly volatile behaviour in house price

series has been recognized in previous studies, more

research is needed. Typically, we can see that house

prices are always converted to natural logarithms

for empirical tests in previous house price studies

because the heteroscedasticity problem usually occur

in house price regression model. Therefore, volatility

in house prices has to be reduced so that the model will

not violate the assumption of OLS. Some studies have

tried to capture the volatility. Giussani and

Hadjimatheou (1991) and Hendry (1984) have tried

to model the volatility by using nonlinear

*Corresponding author. E-mail: [email protected]

Applied Economics ISSN 0003–6846 print/ISSN 1466–4283 online � 2010 Taylor & Francis 1145 http://www.informaworld.com

DOI: 10.1080/00036840701721133

specifications to capture extreme movements in house prices. Hendry (1984) uses a cubic approximation function, calculated as the cubic term of house price changes. Giussani and Hadjimatheou (1991) use both square and cubic terms to capture rapid adjustment of house prices. Hall et al. (1997) further use a switching error-correction model to estimate UK house prices. Their error-correction model allows error-correction term switches between stable and unstable regimes. These papers might be able to determine the volatility of house price, but they are not able to tell the magnitude and pattern of house price volatility. In previous empirical studies, the price changes or variances and SDs are generally used to present the volatility of price and to determine the price risk of investing assets. Consequently, if we are working on the empirical models that assume variances are constant to estimate the house prices, even though the nonlinear variables are placed in the model, we still cannot fully describe the volatilities of house price and determine the price risk of investing in housing markets.

Because high volatility is very common in financial data, the family of ARCH (Autoregressive Conditional Heteroskedasticity) and GARCH (generalized Autoregressive Conditional Heteroske- dasticity) models (Engle, 1982 and Bollerslev, 1986) are developed and widely applied to modelling the variance of financial variables. These types of models allow the conditional variance of a series to depend on the past realizations of the error process and simultaneously model the time-dependent mean and variance. Because of their excellence in capturing volatility, these types of models are applied to other areas, including housing studies (Dolde and Tirtito- glu, 2002). However, time-series behaviour is always complex and sometimes structural breaks occur. Lamoureux and Lastrapes (1990) argue that the near integrated behaviour of the conditional variances might be due to the presence of structural breaks, which are not accounted for by standard ARCH models. In the housing market, some events such as market crashes, financial liberalization and changes in government policy always have clear effects. Cyclical volatilities in the house price series are also clearly observed. During these abrupt events or cycles, house price behaviour, including volatility behaviour, changes substantially.

Following the work of Hamilton (1989) on switch- ing regimes, Hamilton and Susmel (1994) propose a new ARCH model, the Switch ARCH (SWARCH) model that is time variant and allows for a condi- tional volatility process to switch stochastically among a finite number of regimes. In addition, Bloomfield and Hales (2002) suggest that a regime-

shifting model seems to be a reasonable framework

in which to interpret some market anomalies.

This SWARCH model can incorporate the possibility

of volatility regime switch in the conditional variance

for explaining volatility persistence, a phenomenon

that is commonly observed in the housing market.

Hence, the SWARCH model may be a useful tool

to more realistically explain the time-series property

of house price series. The main purpose of this article is to study

volatility properties of UK house prices. We also compare the volatility properties for both the

older and new housing markets. We use the ARCH

and GARCH model to examine whether the volati-

lities of house prices change over time. We also use

SWARCH model to analyse whether there are

different states of volatility in the price series

that can help us to analyse different states of volatility

and estimate the probabilities of changes in these

states. The article is structured as follows. The next

section describes the applied methodologies.

Section III reviews our data and tests the time-series

properties. Estimation results are reported and discussed in Section IV, and the last section provides

a summary of the main findings and draws some

conclusions.

II. The Switching ARCH Model for House Prices

For capturing volatility of house prices, we

employ the ARCH-type model to model the

volatility of house price changing over time, and

use the SWARCH model to see whether there is

regime shifting in the variance process of house

prices.

Modelling volatility of house prices over time: ARCH and GARCH models

Many economic time series do not have constant

mean and volatility. Engle (1982) shows that it is

possible to simultaneously model the time-dependent

mean and variance. This is the widely known ARCH

model. It allows the conditional variance of a series

to depend on the past realizations of the error process. Bollerslev (1986) extended Engle’s (1982)

original work by developing the GARCH model that

allows for both autoregressive and moving average

components in the heteroskedastic variance. We

briefly illustrate the features of these two models in

the following.

1146 I-C. Tsai et al.

ARCH model. Let yt denote the series of an

asset return. Then the error process obtained from

a first-order autoregression for yt follows ARCH(q)

model and it can be specified as:

yt ¼ a0 þa1yt�1 þ "t

"t ���t�1 � Nð0, htÞ

ht ¼ !0 þ Xq

i¼1

�i" 2 t�i

where q is the number of ARCH terms and ht is the

heteroskedastic conditional variance, which is corre-

lated with the lagged error terms.

GARCH model. If the error process obtained

from a first-order autoregression for yt follows

GARCH(p, q) model, then it can be specified as:

"t �t�1 � Nð0, htÞ ��

ht ¼ !0 þ Xp

i¼1

�iht�i þ Xq

i¼1

�i" 2 t�i

where ht is the heteroskedastic conditional variance,

which is correlated with the lagged error terms and

conditional variance.

Detecting volatility states in the housing market: SWARCH model

Though the ARCH and GARCH models has been

widely applied for modelling variance in financial

series, Lamoureux and Lastrapes (1990) show that

these models may not be appropriate if structural

changes exist in the data. Hamilton and Susmel

(1994) propose a regime-switching ARCH model

(SWARCH model) that allows for the conditional

volatility process to switch stochastically among a

finite number of regimes. The features of the

SWARCH model are briefly described as followed. Let yt denote the series of an asset return, the error

process obtained from a first-order autoregression

for yt follows the SWARCH(K, q) model and it can be

specified as:

yt ¼ a0 þa1yt�1 þ "t

"t �t�1 � Nð0, htÞ ��

"t ¼ ffiffiffiffiffi gst p

ut

ut ¼ ffiffiffiffi ht

p vt

ht ¼ !0 þ Xq

i¼1

�i" 2 t�i

where q is the number of ARCH terms, K is the number of regime states, vt follows Gaussian distribution, st denotes an unobserved random variable and gst are scale parameters that capture the size of volatility in different regimes. In the previous section, we proposed that the volatility of house prices can be large, medium or small, hence, we use the SWARCH(3, q) model in an empirical test of this research, i.e. K¼3. The scale parameter for the first state g1 is normalized at unity with gst � 1 for st¼2, 3, and we also assume g25g3, hence, the state 1 (st¼1) can denote the low-volatility regime, state 2 denotes the medium-volatility regime and state 3 denotes the high-volatility regime. The three-state regime switching is assumed to follow a Markov process.

The switching probabilities between three states follow the transition probabilities, Matrix P:

P ¼

p11 p12 p13

p21 p22 p23

p31 p32 p33

2 6664

3 7775

The row i, column j element of P is the transition probability pij, which denotes the probability of state i switching to state j; for example, if the house prices were in a high-volatility state (st¼3) in the last period, the probability of it changing to a low- volatility state (st¼1) is the row 3, column 1 element of P. Note that pij51 for all i and all j, and every row of P sum to unity, that is pi1þpi2þpi3¼1, for all i, or P1¼1, where 1 denotes an (3�1) vector of 1s. Therefore, only six out of nine transition probability elements of the (3�3) matrix P need to be estimated.

1

Let � denote the lagged term of yt and P{st¼ j; �} denote the long-term probability of st¼ j. Therefore, pðyt, st ¼ j; �Þ ¼ fðytjst ¼ j; �Þ �Pfst ¼ j; �g, and the probability distribution of yt is as follows:

fðyt; �Þ ¼ X3 j¼1

pðyt, st ¼ j; �Þ

The log likelihood function is Lð�Þ ¼PT t¼1 log fðyt; �Þ. The maximum likelihood function

(MLE) is used to estimate the coefficients of this model. Besides, the estimation of the model gives the ‘smoothed probability’, Pt{st¼ j; �}, which provides information about the likelihood that house prices are in a particular volatility state at time t based on the full sample of observations.

2

1 A more detailed description of the regime-switching model can be found Hamilton (1994), pp. 678–681.

2 We use the RATS Version 6 software produced by Estima to estimate all the models in our article.

Modelling house price volatility states in the UK by SWARCH models 1147

III. Data Description

Since, the SWARCH model requires a longer period

of data to have better estimation, we use the UK

nationwide mix adjusted house price data from the

Nationwide Building Society starting from 1952Q4 to

2007Q1. That house price series is the longest

quarterly data available and is derived from the

Nationwide lending data for properties at the post

survey approval stage. We compare older (Olderph)

and new house price (Newph) data to understand

whether there is any different pattern of volatility in

the different markets. These two series are seasonally

adjusted, deflated by retail price index and are

converted to natural logarithms. Table 1 presents a summary of the descriptive

statistics for two house price variables. Table 1

also reports the outcome of tests for stationarity.

The augmented Dickey–Fuller test (Said and Dickey,

1984) and the Phillips–Perron test (1988) both

confirm that two house price variables are I(1).

Evidently, the unit-root hypothesis cannot be rejected

at the 5% significance level for two series in levels.

In addition, tests applied to differenced data favour

the stationary alternative for two series. To avoid the

problem of spurious regression, throughout the

article, we use the first-differenced data to estimate

the empirical models. To observe the volatility of house prices, Fig. 1

plots the quarterly time series of two house prices for

the sample period. We can observe that two price

series have increased during the sample period in

nonmonotonic ways. Two series seems to have changes in volatility states or bubbles in four periods: 1971–1974, 1977–1980, 1988–1990, 2002–2005, when the series are highly volatile. Unlike some studies that discuss the bubble-like behaviour of house prices (e.g. Hall et al., 1997), this article emphasizes on the volatility properties of house prices.

IV. Empirical Results

Does the volatility of house prices change over time?

Before estimating the house price volatility, we need to determinate the mean equation. We use the lagged data of house price as the independent variables, and choose the model that can minimize the value of SBC (Schwartz Bayesian Criterion)

3 to decide the number

of lag terms. Due to considerations about the degrees of freedom, only lags of length 1–8 are tested. The empirical results of different AR models are shown in Table 2.

From Table 2, we see that the AR(1) model for older and new house prices is the most appro- priate because the SBC selection criteria derived from the first-order autoregression model performs better than or the same as other AR models, and

Table 1. Descriptive statistics

Variable Olderph Newph

No. of observations 218 218 Mean 527.33 492.70 SD 283.67 210.88 Skewness 1.53 0.95 Kurtosis 5.12 3.61

Variables in level ADF test 1.24 (1.00) 0.92 (1.00) PP test 1.92 (1.00) 0.96 (1.00)

Variables in differenced ADF test �4.49 (0.00) �7.58 (0.00) PP test �6.68 (0.00) �8.02 (0.00)

Note: Mackinnon (1996) one-sided p-values are reported in parentheses.

200 400 600 800

1000 1200 1400 1600

5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5

OLDER

200 300 400 500 600 700 800 900

1000 1100

5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5

NEW

Fig. 1. House price in the older and new housing markets

3 The two most commonly used model selection criteria are the Akaike information criterion (AIC) and the SBC, However,

the SBC is asymptotically consistent, whereas the AIC is biased toward selecting an overparameterized model. Hence, the SBC is used to decide the number of lag terms in this article.

1148 I-C. Tsai et al.

the AR(1) model is more parsimonious. Hence, we choose the AR(1) model for these two housing

markets. 4

Before we use the ARCH and GARCH models, it

is necessary to test whether or not there are ARCH effects existing in data. We use the formal Lagrange

Multiplier (LM) test for ARCH disturbances pro- posed by Engle (1982) and the results of LM test are

shown in Table 3. The results in Table 3 show that the disturbances

obtained from the first-order autoregression of

two series are autocorrelated. This means the variance (risk) in two house markets are time

dependent. Now we use the ARCH and GARCH models to estimate the variance of two series at a

particular point of time. We estimate three different ARCH and GARCH models to determine the most appropriate model for volatilities of two

housing markets. These are the AR(1)-ARCH(1), AR(1)-ARCH(2), and AR(1)-GARCH(1, 1) models.

The results of these three model estimations are shown in Table 4.

Three ARCH-family models for two series are

estimated and the results are presented in Table 4.

The estimated coefficients of ARCH and GARCH

effects are highly significant in each series. The sum

of ARCH and GARCH coefficients in both

AR(1)-ARCH(2) and AR(1)-GARCH(1, 1) model

are larger than one, suggesting that shocks to the

conditional variance are highly persistent, and these

two models are inappropriate for estimating the

volatilities of two housing markets. Lamoureux and

Lastrapes (1990) argued that high persistence might

reflect regime switch in the variance process.

Therefore, different volatility states might also

occur in these two housing markets. We can verify

this phenomenon from Figs 2 and 3 of the conditional

variances for these models. These two figures appear

to show different states of volatility and several high

volatility states can be seen. Volatilities are smaller

before 1972 but are increasing thereafter.

Consequently, we continue to model these volatility

states by using a SWARCH model.

Does the housing market exhibit different volatility states?

To determine whether or not the conditional volati-

lities of house prices switch stochastically and

to capture the switch points endogenously, we use

AR(1)-SWARCH(3, 1) 5

to estimate the variance

of the housing markets. The results of SWARCH

model estimations are shown in Table 5. From Table 5, we find that older housing market

model has significant state variables (g2 and g3),

suggesting this housing market significantly exhibits

three different volatility states. The coefficient g2 suggests that variance in the medium-volatility state

(st¼2) is more than 2.95 times that in the low-

volatility state. The coefficient g3 suggests that

variance in the high-volatility states (st¼3) is more

than 20.99 (g3) times that in the low-volatility states

(st¼1). Consequently, the differences of volatility

states are very obvious. Following the constraints of

the transition probabilities, pi1þpi2þpi3¼1, for all i,

we can derive that p13¼0, p23¼0.55 and p33¼0.46. Because st is assumed to be governed by a first-

order Markov chain with transition probability pij,

this means different states switch according to the

transition probability. The older housing market has

three significant transition probabilities p11, p22 and

p32 with values of 0.92, 0.45 and 0.54, respectively.

The large value of p11 suggests that low-volatility

Table 3. Results of ARCH-effects test

Lags of length 1 2 3 4

Older house price TR

2 4.90 18.53 21.59 21.58

p-value 0.03 0.00 0.00 0.00

New house price TR

2 7.92 10.74 13.13 13.03

p-value 0.00 0.00 0.00 0.01

Note: *Ho: There are no ARCH effects.

Table 2. The value of SBC estimated by AR models

Model AR(1) AR(2) AR(3) AR(4)

Older house price 7.96 7.99 7.96 7.99 New house price 7.79 7.80 7.81 7.84

Model AR(5) AR(6) AR(7) AR(8)

Older house price 7.96 7.99 8.00 8.03 New house price 7.83 7.86 7.89 7.91

4 The other reason is that the previous SWARCH model research, Hamilton and Susmel (1994), also uses AR(1) specification

for the mean return equation. 5 The sum of ARCH and GARCH coefficients in both AR(1)-ARCH(2) and AR(1)-GARCH(1, 1) model are larger than one,

suggesting these two model are inappropriate for estimating the volatilities of two housing markets. Hence, we choose AR(1)-ARCH(1) to estimate switching of the ARCH model, i.e. AR(1)-SWARCH(3, 1) model.

Modelling house price volatility states in the UK by SWARCH models 1149

state maintains a relatively long time, since we can further estimate the average duration of every state by 1/1�pii and find 12.5, 1.81 and 1.85 quarters for states 1, 2 and 3, respectively. These estimations suggest house prices maintain a low-volatility state for a rather long period of 12.5 quarters. On the contrary, medium and high volatility are rather short with periods of 1.81 and 1.85. The stable period (low-volatility state) is almost 3.5 times as long as the volatile periods (medium-and high-volatility states), which seems to suggest the older housing market is a stable market. These estimations also seem to suggest the housing market is relatively stable compared to other financial markets.

We further examine the new housing market. The results of the new housing market show that there are also two significant state variables, g2 and g3, suggesting there are also three volatility states (high, medium and low) in the new housing market. The variance in medium-volatility state is more than 4.18 times (g2) that in the low-volatility states; while the variance in the high-volatility state is more than 14 times (g3) that in the low-volatility state. Since the transition probabilities p11 and p22 are significant, following the constraints of the transition

Table 4. Empirical results of the ARCH family

ARCH(1) ARCH(2) GARCH(1, 1)

Model Older New Older New Older New

Mean equation a0 1.51 (0.86) 1.45 (0.76) 1.11* (0.56) 0.75 (0.43) 1.19* (0.48) 0.83 (0.48) a1 0.71* (0.05) 0.58* (0.05) 0.71* (0.02) 0.48* (0.04) 0.57* (0.06) 0.46* (0.07)

Variance equation !0 116.09* (10.57) 91.27* (8.83) 26.14* (6.78) 19.39* (4.77) 0.50 (0.59) 0.67 (0.49) �1 0.32* (0.11) 0.35* (0.11) 0.49* (0.11) 0.45* (0.12) 0.21* (0.05) 0.19* (0.03) �2 – – 0.85* (0.18) 0.94* (0.15) – – �1 – – – – 0.84* (0.04) 0.84* (0.02)

Residuals test Q(20) 90.85* 25.26* 55.81* 29.29* 40.11* 34.79* Q

2 (20) 61.16* 37.07 11.61 47.57* 20.31 12.01

Notes: Numbers in parentheses are SEs. Q(20) and Q 2 (20) are the Ljung–Box statistic based on the standardized residuals and

the squared standardized residuals, respectively up to the 20th order. * Indicates significance at the 10% level.

100 200 300 400 500 600 700 800

5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5 ARCH (1)

5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5 ARCH (2)

5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5 GARCH (1,1)

0 400 800

1200 1600 2000 2400

0 100 200 300 400 500 600 700 800 900

Fig. 2. Estimated conditional volatilities for the older

housing market

0 100 200 300 400 500 600 700 800 900

5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5 ARCH (1)

5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5

5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5

ARCH (2)

0 400 800

1200 1600 2000 2400

0 100 200 300 400 500 600 700

GARCH (1,1)

Fig. 3. Estimated conditional volatilities for the new

housing market

1150 I-C. Tsai et al.

probabilities, we also can derive that p13¼0, p23¼0.15 and p33¼0.76.

We can further estimate the average duration of every state by 1/1�pii and have 16.67, 6.67 and 4.3 quarters for states 1, 2 and 3. These estimations suggest the new housing market is more stable than the older housing market, since the duration of low- volatility state is longer in the new housing market. However, when some events occur, the magnitude of volatility will increase and the medium-volatility and the high-volatility state will last 6.67 and 4.3 quarters, respectively, before the market returns to a low-volatility state.

From a shorter duration estimation of states 2 and 3 in the older housing market, it appears that market reaction to information is fast in the older housing market. However, this could be caused by instability of these two volatility states. If we continue to examine the transition probability, we find p23 and p32 (the probability of house price in the medium-volatility state and switching to the high-volatility state) are as high as 0.55 and 0.54, respectively, and they are far larger than p21 and p31 (close to 0). Because of the low probability in p21 and p31, house price volatility does not switch from medium or high volatility to low volatility very often. On the contrary, high volatility and medium volatility switch from one to another very often because a high p32 is found. For the new housing market, when some events occur, although the

durations of medium and high volatility are longer, the transition probabilities p23 and p32 are far lower than those for the older housing market, implying the probability of returning to a low- volatility state is higher in the new housing market. These findings appear to suggest that the older housing market is not efficient and the property market is less efficient than financial market.

The smoothed probabilities of the two housing markets are shown in Figs 4 and 5. It can be seen that before 1972, these two markets were in a low- volatility state because the probabilities of state 1 in the two markets are close to one. However, house price behaviours are very different after 1972. We can see from Fig. 4 that house price barely returns to a low-volatility state and continues to switch between medium and high volatility in the older housing market after 1972. From Fig. 5, we can see that switching among these three states is significant in the new housing market, suggesting this market is more efficient.

V. Conclusion

Recurrent house price fluctuations around the growth path of the housing market seem to be a common phenomena worldwide. This article analyses the UK

Table 5. Empirical results of SWARCH model

SWARCH(3,1)

Model Older house New house

Mean equation a0 0.95 (0.39)** 2.13 (0.56)** a1 0.61 (0.04)** 0.50 (0.06)**

Variance equation !0 13.29 (4.16)** 19.73 (6.16)** �1 0.06 (0.09) �0.01 (0.02)

Transition prob. p11 0.92 (0.07)** 0.94 (0.10)** p21 0.00 (0.11) 0.00 (0.06) p31 0.00 (0.12) 0.05 (0.10) p12 0.09 (0.32) 0.08 (0.20) p22 0.45 (0.24)* 0.85 (0.16)** p32 0.54 (0.31)* 0.19 (0.19)

State variable g2 2.95 (1.68)* 4.18 (1.63)** g3 20.99 (6.78)** 14.00 (4.55)**

Notes: Numbers in parentheses are SEs. * and **indicates significance at the 10 and 5% levels, respectively.

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5

State 1

5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5

State 2

5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5

State 3

0.1

0.2

0.3

0.4

0.5

0.6

0.1

0.2

0.3

0.4

0.5

0.6

Fig. 4. Smoothed probabilities of the older housing market

Modelling house price volatility states in the UK by SWARCH models 1151

house price volatility when changes of volatility state are allowed in the housing market. We use both ARCH and GARCH models to estimate conditional heteroscedasticity of house prices in order to verify time-varying property in the price series. We then use the SWARCH model to estimate volatility states of house prices.

Our findings indicate that the estimated coeffi- cients of ARCH and GARCH effects are highly significant in our sample series, suggesting that the volatility of house price changes over time. Because the shocks to the conditional variance are highly persistent in the ARCH estimation and this high persistence might reflect regime switching in the variance process, we further test whether or not there are different states of volatility by using the SWARCH model.

The volatility states found for the older and new housing markets in the UK are low, medium and high. Our estimations suggest the UK housing markets are relatively stable and different states do not switch very often. The magnitude of high volatility is as high as 20.99 times the low volatility for the older housing market and 14 times the low volatility for the new housing market. Consequently, the differences of volatility states are very obvious. Our results also suggest that the older housing market is less efficient than the new housing market.

Our findings have some implications. First, although different volatility states do not switch very often in the UK housing markets, volatility seems to have increased for past half century (1950–2007). This increase could be caused by the continued liberalization of financial markets. This credit expansion brings more investors into the housing market and also increases speculative activities therein. Returns in the housing market might increase, but investors should be cautious because increased volatility means that the risk in property investment has increased. Secondly, the volatility pattern is similar in older and new housing markets, so investors will not be able to diversify their risk by holding assets in these two markets. Third, our findings suggest the older housing market is less efficient than the new housing market in the UK. This is because builders in the new housing market builders usually hold more information than individuals and can quickly respond to market conditions. To lower volatility and increase efficiency for the older housing market, information exchange for the older housing markets should be enhanced.

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Fig. 5. Smoothed Probabilities of the new housing market

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