英国论文代写-非对称变动对英国房地产价格的影响The asymmetric volatility of house prices in the UK
Abstract
Purpose – The purpose of this paper is to show an indication that the asymmetric volatility between house price movement may account for the defensiveness of the housing market.
Design/methodology/approach – First the UK nation-wide house price data from the last quarter
(Q4) of 1955 to the last quarter of 2005 are used and then the most suitable mean and variance
equations to estimate the conditional heteroscedasticity volatilities of the returns of house prices are
selected. Second, a variable that examines the leverage effect of volatility is incorporated into the
model. The GJR-GARCH model is used.
Findings – The results of the empirical test show that while the lagged innovations are negatively
correlated with housing return, that is when there is bad news, the current volatility of housing return
might decline.
Research limitations/implications – The results indicate that the volatilities between house
prices moving up and moving down are asymmetric.
Practical implications – The results show that there is a defensive effect in the UK housing market
during the data periods used.
Originality/value – Although several articles have documented that there is heteroscedasticity and
autocorrelation in the volatilities of real estate prices, few of those papers have noted one of the most
important advantages of the housing market, its defensiveness, from the viewpoint of volatile
behavior.
Keywords Real estate, Prices, Cyclical demand, Residential property, United Kingdom
Paper type Research paper
Introduction
Over the past few decades, the highly volatile behavior of house price series has been
recognized in a number of studies, and several empirical articles have tried to capture
the short-term adjustment process of house prices (Meen, 1990; Drake, 1993; Heiborn,
1994; Eitrheim, 1995; Abraham and Hendershott, 1996; Malpezzi, 2001, Kapur, 2006).
Most of these studies try to model price behavior based on factors related to the
housing demand and supply, and further use traditional regression for analysis. But,
most of these economic models do not come up with satisfying performance capturing
the volatile behavior of the housing markets.
Several methodologies and models are now being used in order to reduce the
heteroscedasticity problems of house price and estimate this volatile process. For
example, house prices were always converted to natural logarithms in empirical tests
in previous house price studies in order to reduce the heteroscedasticity variance
problems in ordinary least squares (OLS) regression. On the other hand, Hendry (1984)
and Giussani and Hadjimatheou (1990) have tried to model the volatility by using
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27,2
80
Received December 2007
Revised October 2008
Accepted January 2009
Property Management
Vol. 27 No. 2, 2009
pp. 80-90
q Emerald Group Publishing Limited
0263-7472
DOI 10.1108/02637470910946390
non-linear specifications to capture extreme movements in house prices. Hendry (1984)
used a cubic approximation function, calculated as the cubic term of house price
changes. Giussani and Hadjimatheou (1990) used both square and cubic terms to
capture the rapid adjustment of house price.
Because high volatility is very common in financial data, the family of ARCH
(Engle, 1982) and GARCH (Bollerslev, 1986) models were developed and are widely
applied to model 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 various areas,
including housing studies (Dolde and Tirtitoglu, 2002; Miller and Peng, 2006; Tsai et al.,
2008).
However, the volatility characteristic of housing markets might be distinct from
that of other financial markets, and it is surprising that few previous studies have
documented the main features of housing market volatility. However, similar studies
have been done in the securities market, and several articles have indicated that there
is a leverage effect in the volatile behavior of securities; that is, the impact on future
assets’ return when unexpected bad news is announced is larger than when unexpected
good news is made public. Black (1976) pointed out that an unexpected decline of stock
prices can result in an increase of the ratio of debt to equity, leading to an increase in
the financial risk of corporations and eventually a higher fluctuation of securities’
price. But it is not yet known whether there is also a leverage effect in the volatility of
housing market.
The main purpose of this paper is to study the volatility properties of the UK house
price series, in particular, to examine whether or not there is a leverage effect in the
volatility of house prices. To consider the asymmetric volatility, the GJR-GARCH
model is used. Glosten et al. (1993) and Zakoian (1994) suggest a GJR-GARCH model in
which the relation between lagged error term and current volatility may be dependent
on the sign of lagged error. The error is the difference between true value and
estimated value, hence, when lagged error is negative, it means that unexpected bad
news has come out, whereas when lagged error is positive, it indicates good news.
Therefore, the asymmetric volatility model, GJR-GARCH, can measure the concept of
leverage effect empirically. Following the work of Glosten et al. (1993) and Zakoian
(1994), we can determine the important characteristics of the volatile behavior in the
housing market.
This paper is structured as follows. The next section describes the methodologies,
while section three shows a review of our data and tests using time-series properties.
Estimation results are reported and discussed in section four, and the results of
robustness test are showed in section five. The last section provides a summary of the
main findings and draws some conclusions.
Methodology
To capture volatility of house prices, we employed the ARCH-type model to model the
volatility of house price changing over time, and used the GJR-GARCH model to see
whether or not there is a leverage effect in the variance process of house price. These
two kinds of models are discussed below:
Volatility of
house prices
81
Modeling volatility of house prices over time: ARCH and GARCH models
Many economic time-series do not have constant mean and volatility. Engle (1982)
showed that it is possible to simultaneously model the time-dependent mean and
variance through the widely known Autoregressive Conditional Heteroskedastic
(ARCH) model. This allows the conditional variance of a series to depend on the past
realizations of the error process. Bollerslev (1986) extended Engle’s original work by
developing the Generalized Autoregressive Conditional Heteroscedasticity (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.
ARCH model. Let yt denote the return of house price at time t. The error process is
obtained from a first-order autoregression for yt following the ARCH (q) model, and it
can be specified as:
yt ¼ a0 þ a1yt21 þ 1t
1t
V~j t21Nð0; htÞ
ht ¼ v0 þX
q
i¼1
ai12
t2i
where q is the number of ARCH terms, and ht is the heteroskedastic conditional
variance, which is correlated with the lagged error terms.
GARCH model. If the error process obtained from a first-order autoregression for yt
follows the GARCH(p,q) model then it can be specified as:
1t
V~j t21Nð0; htÞ
ht ¼ v0 þX
p
i¼1
biht2iX
q
i¼1
ai12
t2i
where ht is the heteroskedastic conditional variance, correlated with the lagged error
terms and conditional variance.
Asymmetric volatility in the housing market: GJR-GARCH
With the ARCH-type models we have shown above, the heteroskedastic conditional
variance is symmetrically correlated with the lagged error terms. Since it does not
matter whether the lagged error is negative or positive, the relation between the
heteroskedastic conditional variance and the lagged error terms is a constant
coefficient, namely, ai . Hence, those models may not be appropriate for a series that has
asymmetric volatility or one that arises from markets in which there is a leverage
effect. To deal appropriately with the series having asymmetric characteristics, the
Glosten, Jagannthan, and Runkle (GJR)-GARCH model is used. The features of the
GJR-GARCH model are briefly described as follows.
Let yt denote the return of house price at time t. The error process is obtained from a
first-order autoregression for yt following the GJR-GARCH (p, q) model, and it can be
specified as:
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yt ¼ a0 þ a1yt21 þ 1t
1t
V~j t21Nð0; htÞ
ht ¼ v0 þX |
