Price Discovery and Segmentation in the Public and Private Housing
Markets in Singapore
Tien-Foo Sing
Department of Real Estate
National University of Singapore, Singapore
Email: rststf@nus.edu.sg
&
I-Chun Tsai & Ming-Chi Chen*
Department of Finance
National Sun Yat-sen University, Taiwan
Email: mcchen@finance.nsysu.edu.tw
Date: 3 August 2004
Abstract:
Public housing is the largest housing submarket in Singapore. There is also an active
resale public housing market, where public housing dwellers are allowed to trade their
houses after a time-bar of five years from the date of their purchase. This segment of
resale HDB market is liken the private housing submarkets, where housing prices are
more likely to fluctuate in accordance to the market and economic cycles. Using the
STOPBREAK tests proposed by Engle and Smith (1999), the study rejected the
random walk null hypothesis for relative prices in pairs of the HDB resale price and
other private housing prices. The public and private housing market is thus not
segmented. When we further examined whether the STOPBREAK process persist in
other pairs of private housing submarkets, we found weak evidence to suggest the
stratification of the private housing market. We also found that price discovery
processes between the resale HDB housing market and other private submarkets
occurred through at least one cointegrating equation in our vector autoregressive error
correction models (VECM). In the private housing submarkets, we observed
significant and positive price effects from detached submarket to other private
housing submarkets, which may imply that the increase in housing wealth of detached
households, who are less financially constrained, will motivate them to allocate part
of their accrued wealth through investment in other private housing submarkets. The
wealth accrued in detached housing submarket is translated into price increases in
other private housing sector.
Keywords:
Stochastic Permanent Break (STOPBREAK), Price discovery, Market
Segmentation and Stratification.
* Corresponding author. Address: Department of Real Estate, National University of Singapore, 4
Architecture Drive, Singapore 117566. Email: Trststf@nus.edu.sg. Comments are welcome.
Price Discovery and Segmentation in the Public and Private Housing
Markets in Singapore
1.
Introduction
Housing market in Singapore is characterized by a two-tier housing system
comprising a public market and a private market. The public housing market
constitutes about 88% of the housing stocks based on the census statistics in 2000.
The public housing is built by the government via the national housing agency, the
Housing and Development Board (HDB), and allocated to qualified Singaporean
citizen at subsidized prices. Social, demographic and income criteria are put in place
to ensure that housing subsidies are efficiently distributed to eligible citizens.1 These
criteria are only applicable for new flats brought directly from the HDB. The income
ceiling and citizen-only restrictions on resale flat were relaxed in 1989. Private
property owners and single citizen above 35 years were also subsequently allowed to
purchase the resale HDB outside central area for owner occupancy (Phang and Wong,
1997; Phang, 2004). Prices of resale HDB flats are not regulated, but market
determined. Many HDB flat owners have amalgamated and realized substantial
wealth by capitalizing on the difference in the new public housing price and resale
public housing price through upward mobility decision (Lum, 2002; Bardhan, Datta,
Edelstein and Lum, 2003). However, Phang (2004) found no significant evidence to
support the wealth effects created though owning public houses on private
consumption. She attributes the findings to the rigid Central Provident Fund (CPF)2
scheme that disallows the withdrawal of the surpluses accrued in housing wealth to
finance personal consumption.
Private housing market operates in a laisser-faire economic system, where private
housing prices are mainly determined by a function of the demand and supply in the
market. This segment of the market is dominated by few major private developers.
The government’s involvement through the sale of leasehold private residential lands
program and the government linked property companies also helps indirectly to
cushion unnecessary price inflation that may dampen Singaporeans’ dream of owning
private residential properties (Phang, 2001). Unlike the public housing, private
housing units are not only more expensive, they are also differentiated though better
designs, quality of finishes and fully-equipped recreationally facilities. A variety of
housing forms, which include landed houses like detached house, semi-detached
house, terrace, and non-landed houses like condominiums and apartments in various
price ranges, is made available by private developers to meet different aspiration and
preference of potential house buyers. With the exception of landed houses, where
some restrictions are imposed on the foreign ownerships of these properties under the
1
2
Some of these eligibility criteria include, for example, the qualified buyers for 4-room and larger
HDB flats must form a nucleus family upon delivery of the flats. The income ceiling criterion for
the household is set at $8000 per month to make sure that the subsidies are channeled to the target
group of citizens.
The Central Provident Fund (CPF) is a comprehensive pension scheme, which has been expanded
to provide financing for the public housing purchases in 1968, and subsequently for the private
housing purchases in 1981 under the Residential Property Scheme (RPS). (See Ambrose, Chu,
SaAadu, and Sing, 2003 for details)
1
Residential Property Act (Chapter 274),3 all other private non-landed houses are
freely transacted in the market.
The private housing market activities are found to be highly dependent on the lagged
period economic performance (Sing, 2001). The strong gross domestic products
(GDP) growths in the earlier and mid 1990s attracted large influx of foreign capitals
into the private housing sector, especially in the medium and luxury classes of nonlanded private properties. The proportion foreigner ownership in the private nonlanded property stocks was estimated at 13.5% in 1996, but declined to 11.0% in
2Q2004 following the Asian’s financial crisis that has dampened the flow of funds
into the private housing market (Figure 1). Active upgrading market in the lower-end
non-landed property submarket, however, partly mitigated the impact caused by the
exodus of the foreign buyers in the upper segment of the private housing markets in
the post-1997 periods.
[Insert Figure 1]
Over the period from the previous peak in 2Q1996 to 2Q2004, the private residential
property price index published by the Urban Redevelopment Authority (URA)4
dropped by nearly 38%, whereas the HDB resale price index was corrected downward
by only 17.18% over the same period (Figure 2). The unparallel rates of decline in
private and public housing prices narrowed the price gap between the two submarkets in the post-crisis periods. Public housing owners found the upward mobility
to lower-end private residential properties more affordable and less constrained on
their income. More households took the upward path by selling their public houses
and move to private houses. This group of public housing upgraders is identified by
Stein (1995) and Lamont and Stein (1999) as “constrained movers.” In Singapore, the
upward mobility of these constrained movers was not only driven by price volatility
in the private housing market; their decisions are also influenced by the changes in the
HDB prices (Ong, 2000; Lee and Ong, 2003). Ong and Sing (2002) also found further
evidence to support Stein’s (1995) hypothesis in the forms of significant price
discovery process between the private and public housing markets in Singapore.
[Insert Figure 2]
Coinciding with the convergence in prices, the quality disparity between the two submarkets is also reduced with the improvement in the quality of the public housing
units and also the shift by private developers in their product designs towards smaller
units that appeal to the upgraders (Lum, 2002). Quality asides, there is, however, still
a clear hierarchical stratification of housing sub-markets that dictates the upward
mobility path of households. The hierarchical or pyramid structure of housing submarkets is composed of public houses as the base, followed in an ascending order by
3
4
Under the Residential Property Act, foreigners are only allowed to purchase properties with
“condominium” status or apartments with buildings more than six levels. They have to obtain
written approvals from the Controller of Residential Property and Land Dealings to purchase
landed properties.
The Urban Redevelopment Authority (URA) is the national physical planning agency, which is
also tasked to provide property transaction information on private residential property market in
Singapore. The private residential property price indices published by the URA are transaction
based indices compiled from caveats lodged with the Land Registry.
2
lower-end apartments, condominiums, terraces, semi-detached houses and detached
houses at the top of the hierarchy (Lum, 2002; Bardhan, Datta, Edelstein and Lum,
2003). There is a clear differential price structure between different housing strata
over the hierarchy, where prices of properties in one stratum support prices of the
properties in the stratum immediately above it. Prices of new HDB flats, being the
lowest in the housing strata, support the prices of resale HDB flats, which in term
support the prices of non-landed and other landed housing submarket in the strata
above.
The segmentation of the housing markets in this hierarchical structure implies that the
upward mobility for households is not a continuous path. Households, in particularly
the constrained movers, will have to “climb up the ladder” of the hierarchy in a “stepby-step” process. In other words, we will expect the HDB upgraders to make the
immediate mobility choice by purchasing entry-level condominiums, rather than
going directly for detached houses at the top of the hierarchy. Therefore, the intra- and
inter-stratum segmentation in the housing sub-markets, if exists, will suggest that
price discovery will not occur ubiquitously across different segments. The process,
however, will only likely to take place between two housing sub-markets that are
immediately above or below each other in the hierarchical stratum. This paper aims to
test the segmentation and stratification between public resale housing market and
other private housing submarkets, in a hierarchical order from apartment,
condominium, terrace, semi-detached and detached. We would also examine how
price discovery process will occur across various strata of the submarkets, if
segmentation of housing clientele is proven to be significant. The empirical tests of
the long run relationships between the two sub-markets will be conducted using the
stochastic permanent break (STOPBREAK) model proposed by Engle and Smith
(1999). Compared to the traditional conintegration methodology, the STOPBREAK
model is able to explicitly capture permanent breaks in the price series between two
markets.
This paper is organized into six sections. Section I provides the background and
motivation of the study. Section II reviews relevant literature in the households’
upward mobility decision and the priced discovery. Section III gives a brief review of
the housing system and market in Singapore. The testable hypothesis and empirical
methodology are laid down in Section IV. Section V discusses the results of the
empirical tests. Section VI concludes the findings with relevant policy implications.
2.
Literature Review
2.1
Price discovery and Upward Mobility
Price discovery studies in real estate have thus far concentrated on the relationships
between direct real estate and other asset classes including the exchange traded or
securitized real estate. Equity real estate investment trusts (EREITs), which are
widely regarded as the proxy of indirect real estate investment vehicle, were found to
provide positive leading signal to the price generating processes in direct real estate
market (Gyourko and Keim, 1992; Ong, 1994; Barkham and Geltner, 1995). Prices of
securitized real estate reflect the market values of underlying real estate assets (Martin
and Cook, 1991). The results imply that information in one market can be used to
efficiently predict the price changes in another market, despite a time lag between the
responses in the two markets.
3
Liu, Hartzell, Greig and Grissom (1990) use the arbitrage rationality in the asset
pricing framework to link the price discovery process to the existence of market
integration. The define that two markets are deemed to be integrated, if systematic
market risk is the only risk undiversified by holding assets in two markets, investor
should then earn the same risk adjusted expected returns on the two assets. They
found that the United State (US) securitised real estate market was integrated with the
stock market, but the same evidence was not found in the commercial real estate
market. Okunev and Wilson (1997) provided further evidence of market integration
between securitized real estate and stock markets in the US, but they found tha
relationships between the two markets were non-linear. Lizieri and Satchell (1997)
obtained the same conclusion on the integration of the securitized real estate and stock
markets in the UK. In the Australia’s study, the results of Wilson, Okunev and Ta
(1996) showed no conclusive evidence for the integration of the two markets.
Studies on the long-run contemporaneous relationships between securitized and direct
real estate markets in Singapore have also been widely published, but the results were
mixed and inconclusive (Ong, 1994 and 1995; Liow, 1998 and 2001; Sing and Sng,
2003; Sing, 2004). Schwann and Chau (2003) found that the price discovery between
securitized and unsecuritized real estate markets was not stable over time, and the new
effects significant reduced the amount of real estate information conveyed from one
market to another.
Ong and Sing (2002) empirically tested the market integration hypothesis and the
inter-market price discovery process between private and public housing markets in
Singapore. They found significant evidence to support that the two markets were
integrated. Market forces play a significant role in regulating the price information
flows between the two highly differentiated markets. The price discovery process was
also evidenced between the two markets in bi-directional Granger causality tests,
which supported the upward mobility hypothesis in the two housing sub-markets in
Singapore. The results reaffirmed the findings by Ong (2000), which showed that
resale HDB prices will have significant effects on upgraders’ mobility choice. He
computed the theoretical threshold upgradability prices, which was found to have
closely tracked the actual private residential property prices from 1990 to 1998. In
another study of the public households’ upward mobility behavior in Singapore, Lee
and Ong (2003) found evidence to support Stein’s (1995) hypothesis, which suggests
that households’ decision to consume more housing goods is triggered by improved
affordability of households caused by changes in HDB house prices.
The questions of the persistence of hierarchical structure between different housing
types within the private housing market and between the private and public housing
market, however, have not been examined. We hypothesize that there is noncontinuous path of intra- and inter-market price discovery path in Singapore’s housing
markets. The hypothesis will be empirically tested in this study.
2.2.
Other Housing Studies in Singapore
Ownership of private residential property is well regarded as a social status, and a
dream of HDB dwellers, and those who have not owned a house. Despite the small
market share of the private residential property market in Singapore, research,
4
however, has been concentrated on this sector of the market. The free-market
operation of the private market also implies that the market is more responsive and
susceptible to shocks in economics, and price correction should be less “sticky” vis-àvis public housing market. This hypothesis was, however, rejected by Phang and
Wong (1997), who found that macro-economic factors like GDP, interest rate and
supply of housing, were not significant in explaining the price variations in private
housing prices in Singapore. They, instead, showed that government determined
public housing prices, and various policies public housing and CPF financing to have
significant impact on private housing prices. The linkage between the state-controlled
public housing market and the market-driven private housing market was again
affirmed by Lum (2002) using a structural housing price model corrected for nonstationary roots. Unlike Phang and Wong (1997), her model showed that demand and
supply macro-variables were significant determinant private housing prices over the
long run. The land sale program and the liberalization of public housing market were
proven to be effective short-run policy tools adopted by government in stabilizing the
private housing markets.
In an opposite direction of causality, economists are attracted to research into the
effects of housing wealth in the life cycle theory of consumption. Using Singapore
data on personal consumption expenditure and private housing prices from 19812000, Phang (2004) found no evidence to support the existence of wealth associated
with increases in price house price on the aggregate consumption. She also tested the
asymmetric response in the aggregate consumption function, and found that
households are bounded by liquidity constraints, which was evidenced by the negative
effects of private housing price increases on consumption. Ng (2001), in another
separate study using a shorter time-series data from 1990 to 2001, in contrary, found
positive wealth effects from private housing price increases to consumption in the
short run. In the long run, however, the impact of private housing price changes on
consumption was negative because of the increases in financing costs in owning
private houses. Edelstein and Lum (2003) tested the independent effects of housing
wealth in public housing and private housing markets on aggregate consumption over
two different periods: 1Q1990-2Q1997 and 3Q1997-4Q2004, and they found the
impact of increases in public households’ wealth to be far more significant than the
private households’ wealth on aggregate consumption. In the impulse response test,
they showed that the shocks on public housing wealth of households on consumption
were more persistent, particularly in the second sub-period.
Increases in public resale (HDB) housing prices created wealth effects not only on
household aggregate consumption, Bardhan, Datta, Edelstein and Lum (2003) also
found that the wealth effects were also extended to private housing sales. Positive
wealth amalgamated by HDB households mitigates their upward mobility constraint,
and increases the sales of private houses to this group of constrained HDB upgraders.
They also showed that stock equity wealth and real home rate were two significant
determinants of the volume of private housing sales in Singapore. Again, the results
were consistent with Stein’s hypothesis on the effects of housing price changes on
upgradability.
5
3.
Stratification of Singapore Housing Sub-Markets
Studies (Phang and Wong, 1997; Ong, 2000; Lum, 2002; Ong and Sing, 2002;
Bardhan, Datta, Edelstein and Lum, 2003) have found close interactions between the
public and private housing markets in Singapore. The public housing wealth is clearly
an important factor in not only stimulating private housing sale (Bardhan, Datta,
Edelstein and Lum, 2003), but also a key driver of aggregate consumption (Edelstein
and Lum, 2003). The inter-market mobility has also been proven to have driven the
housing price volatility (Ong, 2002, Lee and Ong, 2003). However, the previous
studies have omitted the impact of diversity of housing types in two sub-markets on
the price discovery and wealth creation process for different households. There are
clear differences in various housing classes and household groups in each housing
class. According to Stein’s (1995) hypothesis, the affordability levels for different
families: unconstrained mover, constrained mover, and constrained non-mover, will
dictate the housing choice that are available for them when mobility decision is made.
The heterogeneity in different housing sub-markets and sub-types would no doubt
have influence on household mobility and housing choice decision.
Lum (2002) and Bardhan, Datta, Edelstein and Lum (2003) have highlighted the
unique pyramid structure of public and private housing sub-markets in Singapore,
when describing the Singapore housing system in their papers. The prices of house in
the lower stratum in the pyramid support prices in the stratum immediately above it.
The housing stock as a proportion of total stock is smaller when we move up the
housing stratum. The hierarchical price structure and the different market size for the
two markets create a pyramid shape in the housing submarkets (Figure 3). There is
another hybrid housing class, known as executive condominium, which is developed
by private housing developers for sale to constrained HDB households. The eligible
households will entitled to government grants of S$30,000 to $40,000 through their
CPF account in the purchase of the executive condominiums. The buyers of executive
condominiums, on the other hand, are subject to some of the public housing
restrictions, such as a time-bar that prevent them from freely selling their units in less
than 5 years. This housing type is excluded in this study because its unique features of
this housing type that appeal to only a target group of households.5
[Insert Figure 3]
Public housing is a highly regulated submarket in Singapore, and its sheer market size
eclipses the private housing market. However, the public housing markets are more
homogenous and standardized in term of design and unit size, although quality of flat
have been improved over time by the HDB to meet rising inspiration and expectation
of new HDB dwellers. The prices of resale housing HDB flats are determined in the
open-market, and they are used to represent the public housing submarket in this
study. However, we do not further differentiate the housing types, such as executive
flat, 5-room and 4-room, within the public housing submarket in this study. Figure 3
shows the hierarchical structure of both the private and public housing submarkets.
5
Executive condominium (EC) is a hybrid housing class that is created in the mid 1996 to meet the
“sandwiched” class of young professionals, and also to stabilize the overheating private housing
prices. The EC sites are sold by the government at discounts to make ECs more affordable (Chua,
2000). The prices of ECs may be “distorted” and they are excluded in the study.
6
The private housing sub-market by the pricing structure6 into different hierarchical
strata, which follow in an ascending from the highest priced landed houses, such as
detached house, semi-detached house, and terrace, to non-landed houses like
condominium and apartments (Table 1).
Table 1 summarizes some key characteristics in both private and public housing
submarkets in Singapore. Based on the caveats lodged on 2,875 transactions of private
housing units in 4Q2003, the average prices for the five classes of private housing
were computed. There is a clear hierarchical order in the transaction prices, with
detached house with an average land area of 1,314.75 square meters (sqm) sold at
S$4,927,479 on average. Apartment units have smaller average floor area of 125.46
sqm, and the average selling price was S$743,830 in 4Q2003. In comparison, the
resale HDB price was relatively lower ranging from S$403,400 to S$159,300 for
executive flat to 3-room flat respectively. In term of the housing stocks, the
proportion of stock of public housing skews the scale with nearly 80% of the total
stock as in 4Q2003. The non-landed private housing consisting of condominium and
apartment was the second largest housing sector with 14% of the total housing stock.
Due to the scarcity of land, the landed sector commands market premiums, and they
are only owned by a small “unconstrained” group of households in the higher income
category (6.54%).
[Insert Table 1]
The hierarchical price structure in the hosing submarkets implies that there exists
segmentation between different sub-sectors of the housing markets. Empirical tests of
the segmentation hypothesis for the sub-sectors in both private and public housing
markets will be conducted in this study. With the price hierarchy in the housing
markets, price discovery and mobility are likely to occur in a more progressive and
incremental process from one sub-market to another. We hypothesize that upgrading
of households will more likely to occur from one stratum of housing submarket to the
one immediately above or below it. For example, HDB upgraders who faces financial
constraint will more likely to sell their public housing, and use the accrued equity to
purchase an apartment or condominium. Landed houses may be out-of-the-reach of
these constrained movers.
There are two hypotheses on price discovery and upward mobility that will be tested
in this study. Firstly, we will test whether segmentation exists in a hierarchical order
between the different sub-sectors of housing markets. We use the modified Engle and
Granger (1987) bivariate conintegration tests to test whether hierarchical stratification
of the hosing submarkets. The hierarchical strafication of housing market hypothesis
is not rejected, if we find only significant bivariate cointegration between two
intermediate stratums of the housing submarkets. There are no significant long-rum
contemporaneous relationships between two submarkets that are not in contiguous
order in the hierarchy. In other words, we expect that the public housing to have
significant cointegration with apartment submarket, rather than with detached housing
submarket. The second hypothesis involves testing the price discovery in different
housing submarkets using the vector autoregressive (VAR) analysis. The stratification
6
This price structure is based on the total price of typical type of house in each class. As shown in
Table 1, the unit prices of landed houses are smaller than non-landed because of the larger land
area taken by most of the landed houses.
7
and segmentation of the submarket structure will also means that price discovery
process is likely to take place between two contiguous strata in the hierarchical
market structure. Shocks in condominium market will likely to cause price changes in
terrace and apartment, rather than price variations in public housing market.
4.
Empirical Methodology
4.1.
Data Collection
Based on the hierarchical housing market structure proposed in Figure 3, prices of
different housing classes, transformed into logarithm form, are obtained for the tests.
Time series price data for the private submarkets: detached, semi-detached, terrace,
condominium and apartment, and the public resale were collected on a quarterly basis
for a 14-year sample period from 1Q1990 to 2Q2004. The private housing market
price indices were obtained mainly from the Real Estate Information System
(REALIS) of the URA, and the public resale price index was collected from the HDB.
We also obtained time series data for other exogenous macro-economic variables that
are included in the VAR model include GDP, mortgage interest rate.., from the
Singapore Time-Series System of the Department of Statistics (DOS), Singapore.
The housing submarkets are differentiated by a subscript i in the price variable, Pi,
where [i = (det, sdt, ter, cod, apt, hdb)], and the natural log-version of the price is
represented by the lower case of the variable, [pi = log(Pi)]. The return of the housing
prices is computed by taking the first order difference of the log-price for each of the
housing sector, [ri = dpi,t = (pi,t – pi,t-1)]. The notations used for the variable and their
respective sources are summarized in Table 2.
[Insert Table 2]
4.2.
Model Specifications and Modeling Strategies
1990s is a highly volatile period in the housing market, which witnessed sharp rise in
the prices in the 1994 to 1995 period, followed by price crashes associated mainly
with the government intervention and the regional financial crisis in the 1996 and
1997. Many housing studies have used a-priori defined regime shift dummy variable
to capture the permanent shocks to the housing price trends in their models (Phang
and Wong, 1997; Sing, 2001; Lum, 2002; Phang, 2004). This approach of modeling
structural break and regime shift, coupled with the Chow test, may not be accurate
when the break effects are more difficulty to ascertain when the number of break
points increases. When shocks is permanent, rather than transitory, cointegration
results based on the standard Engle-Granger (1987) tests will produce biased
conclusions. This paper one of the first works that applies the STOPBREAK model
developed by Engle and Smith (1999) to empirically test the stratification and
segmentation hypothesis in the housing market. The STOPBREAK model allows for
time-varying or stochastic shocks in the long-run relationships between two time
series. Next, we would test the inter- and intra-market price discovery hypotheses
using the vector autoregressive approach.
8
4.2.1. Cointegration and Stochastic permanent break (STOPBREAK) model
The Engle and Granger (1987) and Johansen (1988) cointegration methodologies have
been well established and widely applied in economics and finance literature.
According to Engle and Granger (1987), two series integrated in the order d, I(d), are
cointegrated, if the linear combination of the two series, [Yt = βXt + ut], results in a
residual, ut, that is stationary in less than order d. The results hold if there are no
short-term shocks that will destabilize the equilibrium in the system. When economic
shocks cause permanent and transitory shift to the equilibrium, the long-term impact
of the shocks is time-varying or stochastic. Engle and Smith (1999) propose a
stochastic break (STOPBREAK) approach to model a class of processes that incur
random structural shift at random intervals. They conjecture that a pair of variables
may move together for periods of time and jump apart occasionally. Engle and Smith
(1999) call this process a temporary cointegration.
Engle and Smith (1999) define the simplest form of STOPBREAK process for a time
series yt is given as follows:
y t = mt + ε t , t=0,1,...,T
(1)
where mt = E[ yt I t −1 ] is a time varying conditional mean, and ε t is error term.
t
mt = mt −1 + qt −1ε t −1 = m0 + ∑ qt −i ε t −i ,
t=1,2,...,T
(2)
i =1
where qt = q(ε t ) ∈ (0,1) s.t E[qt ε t I t −1 ] = 0
The above STOPBREAK process is a process where shock effects are permanent and
determined endogenously in the process. If q~t =1, the realized process at time t is a
random walk. If q~t = 0, the conditional mean will be a constant, the long-run forecast
for y will not be deviated from the mean value of q~ .
t
t
When a pair of time-series variables ( Yt , X t ) is involved, the general STOPBREAK
process can be specified as follows:
A( L) B( L)(Yt − X t δ ) = z t −1 A( L)ε t + (1 − z t −1 ) B ( L)ε t , t=1,2,...,T
(3)
where A( L) = 1 − α 1 L − α 2 L2 − ... − α p L p , B( L) = 1 − β 1 L − β 2 L2 − ... − β p L p , L is the
lag operator, z t denotes measurable function of information up to t, and ε t is an
innovation term.
If δ =0, B(L)=1-L, A(L)=1, the model comply with the simplest form of
STOPBREAK process. Alternatively, if δ ≠ 0, then we can say that the two series
establish only temporary cointegration effect, where the two series jump apart
occasionally and revert back to the equilibrium relationship in the long-run.
To test the persistence of STOPBREAK process, let’s assume that q t (γ ) =
ε t2
,
γ + ε t2
and the process in (1) and (2) can be written as follows:
9
∆yt =
− γε t −1
+ εt
γ + ε t2−1
(4)
Based on equation (4), the random walk null hypothesis can be tested as, [Ho: γ = 0],
against the alternative hypothesis, [H1:γ = γ ]. Engle & Smith (1999) found a locally
best test with sufficient to test the null hypothesis Ho: ϕ =0 against a negative
alternative using t-tests, where ϕ can be estimated using the following regression:
∆y t −1
∆y t = ϕ
+ µt
(5)
γ + ∆y t2−1
In this study, the STOPBREAK approach will be used to test the dynamic long-term
process of relative prices of different pairs of housing sub-markets over time, after
endogenously correcting economic shocks that are either transience or permanence.
4.2.2. Vector Autoregressive Error Correction Model (VECM)
After establishing whether there exist significant segmentation and hierarchical
stratification of the housing submarkets in Singapore, we would proceed with the tests
of price discovery across different submarkets using a dynamic Vector Autoregressive
(VAR) framework proposed by Sims (1980). In the earlier cointegration tests, we
found evidence of cointegration among the public housing market and the five private
housing sub-markets. Therefore, it would be useful to include cointegrating vectors in
the VAR process to adjust for the short-term variations between the two time series.
Vector autoregressive error-correction models (VECM) comprising the price variables
of different submarkets and other exogenous macro-economic variables are specified,
together with the cointegrating vectors that are used to explicitly deal with the issue of
stationarity in the proposed model.7 For a bivariate VECM system, the generalized
equations for both the residential property price and inflation variables with n-period
lags could be formally represented as follows,
n
n
p =1
q =1
∆y t = γ y µ t −1 + ∑ α p ∆y t − p + ∑ β q ∆xt − q + ε t
(6)
where yt are 6x1 vectors of endogenous log-price variables for public resale HDB,
apartment, condominium, terrace, semi-detached and detached houses; xt are k- vector
of exogenous variables, which include both demand and supply side factors like
building material price, all-share return, gdp growth rate, prime lending rate,
household formation as represented by increase in number of marriage, and
unexpected inflation rate in our study; A time dummy is also included to capture the
break that occur after the Asian financial crisis, and it is represented by dum1Q98,
which has a value 1 for periods after 1Q1998, and zero otherwise; αp and βp are
matrices of coefficients to be jointly estimated in the VAR process with appropriate p
7
The controversy is whether the variables included in a VAR should be stationary or not. According
to Engle and Granger (1987), if the variables are differenced and are cointegrated in the same
order, the correct method is to estimate the Vector ECM, which is a VAR with the addition of a
vector of cointegrating residual. Thus, this VAR system does not lose long-run information.
10
and q lags, and εt is a vector of innovation term. For the cointegrated series, the error
correction term (µt-1), which represents the speed of adjustment toward the long-run
values, is added in the VAR model. To differentiate VARs with cointegrated vectors
from the standard VAR in equation (6), γ with a binomial discrete value of 0 and 1 is
included, such that γ= 0 if the two variables are not cointegrated, and γ≠0 otherwise.
5.
Data Analysis and Empirical Tests
5.1.
Unit Root Tests
The standard Augmented Dickey-Fuller (1984) and Phillips-Perron (1988) tests are
conducted to test the order of integration of the log-price variables for different
housing sub-markets and the macro-economic variables. The results are summarized
in Table 3. The results showed that most of the housing market price variables are I(1)
stationary. The consumer price index is clearly a I(0) stationary variable as indicated
by both the ADF and PP test statistics. There was sufficient evidence, based on the
two tests, to suggest that all other macro-economic variables like building material
price, gdp growth, all-share return, prime lending rate and household formation are
first order stationary. In the subsequent EVCM tests, we would include the
unexpected inflation and prime lending rate, which are stock variables, in level term
in the VECM model, whereas other supply and demand side variables are included in
the first order difference terms.
[Insert Table 3]
5.2.
Cointegration and STOPBREAK Tests
We first conducted the pair-wise cointegration tests using firstly the standard
Johansen (1988) estimation, and then the time-varying stochastic shocks are allowed
in the Engle and Smith (1998) STOPBREAK model. The results of the Johansen’s
cointegration tests, which do not adjust for possible transitory and permanent shocks,
give weak evidence of cointegration between HDB resale price and the three landed
housing submarkets.8 We next move on to adjust for possible shocks that could be
transient or permanence in nature caused by economic events in the 1990s like the
Asian financial crisis in 1997. The STOPBREAK model proposed by Engle and
Smith (1999) provides a useful framework for testing the long-run relationships
between pairs of sub-housing market prices, which will not restrict temporary
deviation of the price series as a result of shocks.
The t-statistics of the STOPBREAK tests are summarized in Table 4. The results
showed that the number of significant pair-wise cointgration relationships between the
housing sub-sectors increase when permanent and transitory shocks are made
endogenous in the STOPBREAK models. We rejected the random walk null
hypothesis for the HDB resale price and the prices of all private housing sub-markets,
indicating that shocks may have established some permanent and transitory impacts
on the relative price processes in the public and all strata of the private housing
market. While we rejected that the public market and private market are segmented,
but we found no evidence to justify the hierarchical stratification in the two housing
8
The Trace test statistics at the asymptotic 5% critical values for the pair-wise cointegration tests
using Johansen’s (1988) estimation methodology are given in Table 4(b) in the Appendix
11
markets. However, based on the STOPBREAK test results in the private housing submarkets, we did observe cointegration on two pair of private housing sub-sectors:
apartment-condominium and terrace and semi-detached, which may not fully rule out
the stratification hypothesis in the private markets. The reactions of detached housing
price to economic shocks were significantly different from those experienced by other
private housing sub-markets, which thus explain that detached housing sector is rather
segmented from other private housing submarkets. In shorts, we rejected the
segmentation hypothesis between public housing and other private housing
submarkets. We also found stratification in selected strata of the private housing
submarkets, where cointegrations were only significant between a pair of non-landed
and also a pair of landed housing markets (terrace and semi-detached). Stochastic
price shocks were not observed between the detached housing market and other
private housing submarkets.
[Insert Table 4]
5.3.
Vector Autoregressive Error Correction Models
Other testing the pair-wise stochastic shocks and cointegration relationships across the
housing submarkets, we continue our price discovery tests by first testing the
multivariate cointegration in the housing submarkets using the Johansen and Juseliu’s
(1990) methodology. In the multivate tests, the exogenous variables like dbmp, dgdp,
dmar, PLR and unexp are included to control for demand and supply side effects, and
dum1Q98, the time dummy to correct for the impact of 1997 financial crisis is also
added. The unrestricted cointegration rank test results were summarized in Table 5.
The trace tests showed that there were six cointegrating vectors at 5% significant level
among the six housing submarkets, whereas, the Eigenvalue statistics showed that
there exist only four significant cointegrating vectors in the multivariate equations.
[Insert Table 5]
We incorporate four normalized cointegrating equations in the VECM models that
comprise six endogenous housing submarket prices, and other exogenous variables to
test the price formation processes for different housing submarkets. The results of the
VECM estimation with only one-period lag term for different housing price variables
were summarized in Table 6. The findings differ from the earlier results in Ong and
Sing (2002), who found significant bi-directional price discovery between public and
private housing markets. Our results indicate that price changes in various private
housing submarkets have not significant explanatory relationships on the price
variations in HDB resale houses. The price discovery process in the HDB resale
market is fully rejected, because there was still a price correction mechanism through
the cointegrating vector, which captures some of the private housing market price
dynamics. The price variations for HDB resale houses were also explained by the
building material price, prime lending rate and unexpected inflation.
[Insert Table 6]
All of the private housing price models have at least one significant cointegrating
vector reversing the price back to long-run equilibrium. We also observe that the lastquarter detached housing price have significant explanatory impact on other four
12
private housing submarkets. The coefficients of dpdet(-1) are significant and positive,
which may imply that the increase in housing wealth of detached households, who are
less financially constrained, will motivate them to allocate part of their accrued wealth
through investment in other private housing submarkets. The mobility behavior of this
group of unconstrained households may not fit into the unconstrained mover group
described by Stein (1995), who moves when price declines. In land scare Singapore,
housing can be regarded as a symbol of wealth, which can be included an investment
asset in a household’s portfolio, the wealthy or unconstrained households are likely to
increase their housing consumption by adding new housing into their portfolio, while
staying put at their existing detached houses that have appreciated in prices.
Therefore, the wealth accrued in detached housing submarket is translated into price
increases in other private housing sector.
Lagged-period condominium housing price changes were also found to convey
significant price information to the price generating processes in semi-detached and
detached housing submarkets. The results may fit well into the constrained mover
group of Stein (1995), who may find the wealth accumulated from the rising prices in
their private condominium increases their affordability to move up the housing
hierarchical “ladder” to landed houses. Negative price discovery effects were
observed from apartment submarkets to condominium and terrace submarkets. The
reverse negative price discovery process was also noted from terrace to apartment
submarkets. The close-substitutability of the types and relative pricing of the housing
options in the three housing submarkets could be one of the reasons explaining the
negative price effects. The same observation was also found between semi-detached
and detached housing submarkets.
Other exogenous macroeconomic variables that have significant explanatory effects
on housing prices include the building material price, prime lending rate, stock market
wealth, and unexpected inflations. The coefficients of these variables are of correct
signs. We also noted that the time dummy that represent that the post-1997 Asian
financial crisis structural adjustment was significant in the landed housing pricing
models: terrace, semi-detached and detached housing submarkets.
6.
Conclusion
Public housing is the largest housing submarket in Singapore, which constitutes a
nearly 80% of the total housing stocks as in 4Q2004, and public housing units are
normally sold at a subsidized rate by the government via its housing agency, the
Housing Development Board. The public housing price is regulated and less
susceptible to market volatility compared to the private housing prices. There is an
active resale public housing market, where public housing dwellers are allowed to
trade their houses after a time-bar of five years from the date of their purchase. This
segment of resale HDB market is liken the private housing submarkets, where
housing prices are more dependent on the market demand and supply conditions. The
prices are also more likely to fluctuate in accordance to the market and economic
cycles. This study examined whether there is clear stratification of the two housing
submarkets in some hierarchical structure. Price discovery processes between the
private and public housing sub-markets were also tested in this study using vector
error correction models (VECM).
13
Using the STOPBREAK tests, we rejected the random walk null hypothesis for the
HDB resale price and the prices of all private housing sub-markets, indicating that
shocks may have established some permanent or transitory impacts on the relative
price processes in the public and all strata of the private housing market. While we
rejected that the public market and private market are segmented, but we found no
evidence to justify the hierarchical stratification in the two housing markets. The
segmentation in the private housing sub-markets was less clear cut. We observe
STOPBREAK cointegration in the relatively prices of two pair of private housing
sub-sectors: apartment-condominium and terrace and semi-detached, which may not
fully rule out the stratification hypothesis in the private markets. In shorts, we rejected
the segmentation hypothesis between public housing and other private housing
submarkets. We also found stratification in selected strata of the private housing
submarkets, where cointegrations were only significant between a pair of non-landed
and also a pair of landed housing markets (terrace and semi-detached).
In the Johansen’s multivariate cointegration tests, we found at least four significant
cointegrating vectors in the six endogenous housing submarkets. At least one
cointegrating vector was found to be significant in explaining the short-term price
dynamics in the housing submarkets in our VECM models, which provide some
evidence of price discovery in the short-run price processes in the housing
submarkets. Our results indicate that after incorporating the error correction term,
price changes in the private housing submarkets have not significant explanatory
relationships on the price variations in HDB resale houses. In the private housing
submarkets, we observed significant and positive price effects from detached
submarket to other private housing submarkets, which may imply that the increase in
housing wealth of detached households, who are less financially constrained, will
motivate them to allocate part of their accrued wealth through investment in other
private housing submarkets. The wealth accrued in detached housing submarket is
translated into price increases in other private housing sector.
Lagged-period condominium housing price changes were also found to convey
significant price information to the price generating processes in semi-detached and
detached housing submarkets. However, negative price discovery effects were
observed from apartment submarkets to condominium and terrace submarkets, also
from semi-detached to detached submarkets. The close-substitutability of the types
and relative pricing of the housing options in the private housing submarkets could be
one of the reasons explaining the negative price effects.
14
Reference:
Ambrose, B.W., Chu, Y.Q., SaAadu, J. and Sing, T.F. (2003), “Default Risk in
Adjustable Rate Mortgages: Effects of Change to CPF Withdrawal Limits in
Singapore,” working paper, Department of Real Estate, National University of
Singapore.
Bardhan, A.D., Datta, R., Edelstein,R.H. and Lum, S.K. (2003), “A Tale of Two
Sectors: Upward Mobility And The Private Housing Market In Singapore,” Journal of
Housing Economics, 12, 83-105.
Barkhan, R. and Geltner, D. (1995), “Price Discovery in American and British
Property Markets,” Real Estate Economics, 23(1), 21-44.
Chua, B.H. (2000), “Public Housing Residents as Clients of the State,” Housing
Studies, 15(1), 45-60.
Edelstein, R.H. and Lum, S.K. (2003), “House Prices, Wealth Effects and The
Singapore Macroeconomy,” paper presented at the International Workshop on
“Housing Market and the Macro Economy: the Nexus,” jointly organized by the
Centre for Public Policy Studies at Lingnan University and the Economics
Department of the Chinese University of Hong Kong, 15-16 August 2003.
Engle, R.F. and Granger, C.W.J. (1987), “Cointegration and Error Correction
Representation, Estimation and Testing,” Econometrica, 25,1225-1228.
Engle, R.F. and Smith, A.D. (1999), “Stochastic Permanent Breaks,” The Review of
Economics and Statistics, 81(4), 553-574.
Gyourko, J. and Keim, D. (1992), “What does the Stock Market tell us about Real
Estate Returns?” Journal of the American Real Estate and Urban Economics
Association, 20, 457-485.
Johansen, S. (1988), “Statistical Analysis of Cointegration Vectors”, Journal of
Economic Dynamics and Control, Vol. 12, pp. 231-254
Johansen, S. and Juselius, K. (1990), “Maximum Likelikhood Estimation and
Inference on Cointegration – with Application to the Demand for Money,” Oxford
Bulletin Economics and Statistics, 52(2), 169-210.
Lamont, O. and Stein, J.C. (1999), “Leverage and House-Price Dynamics in U.S.
Cities,” RAND Journal of Economics, 30(3), 498-514.
Lee, N.J. and Ong, S.E. (2003), “Upward Mobility, House Price Volatility and
Prepayement Risk, working paper of Department of Real Estate, National Universityo
of Singapore.
Liow, K.H. (1998), “Singapore Commercial Real Estate and Property Equity Markets:
Close Relations?” Real Estate Finance, 41,603-616.
15
Liow K.H. (2001), “The Long-term Investment Performance of Singapore Real Estate
and Property Stocks,” Journal of Property Investment and Finance, 19(2), 156-174.
Liu, C.H., Hartzell, D.J., Greig, W. and Grissom, T.V. (1990), “Integration of the
Real Estate Market and the Stock Market: Some Preliminary Evidence,” Journal of
Real Estate Finance & Economics, 3, 261-282.
Lizieri, C. and Satchell, S. (1997), “Interactions Between Property and Equity
Markets: An Investigation of Linkages in the United Kingdom 1972-1992,” Journal
of Real Estate Finance & Economics, 15(1), 11-26.
Lum, S.K. (2002), “Market Fundamentals, Public Policy and Private Gain: House
Price Dynamics in Singapore,” Journal of Property Research, 19(2), 121-143.
Ng, H.M. (2001), “Private Residential Property Market and the Macroeconomy,”
Economic Survey of Singapore, First Quarter 2002, Ministry of Trade and Industry,
Singapore.
Okunev, J. and Wilson, P.J. (1997), “Using Nonlinear Tests to Examine Integration
Between Real Estate and Stock Markets,” Real Estate Economics, 25(3), 487-503.
Ong, S.E. (1994), “Structural and Vector Autoregressive Approaches to Modelling
Real Estate and Property Stock Prices in Singapore,” Journal of Property Finance,
5(4), 4-18.
Ong, S.E. (1995), “Singapore Real Estate & Property Stocks – A Cointegration Test,”
Journal of Property Research, 12, 29-39.
Ong, S.E. (2000), “Housing Affordability and Upward Mobility from Public to
Private Housing in Singapore,” International Real Estate Review, 3(1), 49-64.
Ong, S.E. and Sing, T.F. (2002), “Price Discovery between Private and Public
Housing Markets,” Urban Studies, 39(1), 57-67.
Phang, S.Y. (2001), “Housing Policy, Wealth Formation and the Singapore
Economy,” Housing Studies, 16(4), 443-459.
Phang, S.Y. (2004), “House Prices and Aggregate Consumption: do they Move
together? Evidence from Singapore,” Journal of Housing Economics, 13, 101-119.
Phang, S.Y. and Wong, W.K. (1997), “Government Policies and Private Housing
Prices in Singapore,” Urban Studies, 34(11), 1819-1829.
Schwann, G.M. and Chau, K.W. (2003), “New Effects and Structural Shifts in Price
Discovery in Hong Kong,” Journal of Real Estate Finance and Economics, 27(2),
257-271.
Sims, C. (1980). “Macroeconomics and Reality,” Econometrica. 48, 1-48.
Sing, T.F. (2001), “Dynamics of the Condominium Market in Singapore,”
International Real Estate Review, 4(1), 135-158.
16
Sing, T.F. (2004), “Common Risk Factors and Risk Premia in Direct And Securitized
Real Estate Markets,” working paper of the Department of Real Estate, National
University of Singapore.
Sing, T.F. and Sng, S.B.S. (2003), “Conditional Variance Tests of Integration
Between Direct and Indirect Real Estate Markets,” Journal of Property Investment &
Finance, 21(4), 366-382.
Stein, J.C. (1995), “Prices and Trading Volume in the Housing Market: A model with
Down-payment Effects,” The Quarterly Journal of Economics, 110, 379-406.
Wilson, P., Okunev, J. and Ta, G. (1996), “Are Real Estate and Securities Markets
Integrated? Some Australian Evidence,” Journal of Property Valuation & Investment,
14(5), 7-24.
17
Table 1: Characteristics of Private and Public Housing Markets in Singapore
Housing Type
Average
Floor/
Land Area
(sqm)#
A) Private Housing Market:
Detached
1314.75
House
Semi-Detached
340.10
House
terrace
208.18
Condominium
133.79
Apartment
125.46
Average
Transacted
Price (S$)#
Average
Unit
Price
(S$ psm)#
No of
Caveat
Lodged
(as at
4Q03)#
Housing
Stock (as
at 4Q03)@
% of
Total
Housing
Stock
4,927,479
4,062
104
9,915
0.97%
1,440,098
4,452
143
20,628
2.01%
1,052,364
803,168
5,344
5,867
314
1513
36,549
85,869
3.56%
8.36%
743,830
6,274
801
57,973
5.65%
Total*3
815,633
65,143
201,152
318,668
220,696
79.45%
7.99%
24.66%
39.07%
27.06%
B) Public Housing Market:
HDB data:
Executive Flat
5-Room
4-Room
3-Room
*1
*2
130
110
90
69
403,400
321,500
232,800
159,300
3,103
2,923
2,587
2,309
# The statistics are computed based on caveats lodged on all private residential properties transacted
from 1 September 2003 to 31 December 20003, as captured in Real Estate Information System
(REALIS) of the URA.
@ The cumulative housing stock information is obtained from the time-series data in REALIS, URA
*1 The size of different public housing types is taken from typical new housing flat type built by HDB.
The size for different HDB flats may have changed over time.
*2 The resale price was the 4Q average resale HDB flats that were published on the Business time,
“Prices of HDB resale flats rise 1.2% in Q2 from Q1,” by Andrea Tan, 24 July 2004.
*3 The total housing stock number was obtained from the HDB annual report 2002/2003, and the
number does not include rental flats (53,141)
Note: Condominium and apartment are two common non-landed housing types built by private
developers, they are quite homogenous in physical, but prices differs especially between the
high- and middle-end condominium, and apartment. The total stock size of apartment is also
smaller, but the hierarchy structure is determined based mainly on price structure in this study.
Source: URA, HDB
18
Table 2: List of Variables and Derivations
Notation
Variable Description
A) Public housing market:
Phdb
Resale HDB housing price index
B) Private housing market:
Papt
Apartment price index
Pcod
Condominium price index
Pter
Terrace price index
Psed
Semi-detached housing price index
Pdet
Detached housing price index
C) Macro-economic variable:
GDP
Gross domestic products
SGX
Singapore Exchange All-share index
PLR
Prime lending rate
CPI
Consumer price index
MAR
Total number of marriages
Derivation of Variable:
dphdb
ln-return of HDB price
dpapt
ln-return of apartment price
dpcod
ln-return of condominium price
dpter
ln-return of terrace price
dpsed
ln-return of semi-detached price
dpdet
ln-return of detached price
dgdp
Growth in GDP
dsgx
All-share return in natural log term
dmar
Change in number of marriage in natural
log term
uxcpi
Unexpected inflation rate
*
Source
HDB
URA
URA
URA
URA
URA
DOS
DOS
DOS
DOS
DOS
phdb,t – phdb,t-1
papt,t -papt,t-1
pcod,t – pcod,t-1
pter,t – pter,t-1
psed,t – psed,t-1
pdet,t – pdet,t-1
gdpt - gdpt-1
sgxt - sgxt-1
mart - mart-1
Derived using Fama
& Gibbons (1984)
(Appendix 1)
The natural logarithm form of the variables are represented in lower case of the respective
notations
19
Table 3: Results of Unit Root Tests
Augmented Dickey-Fuller
(ADF) Unit Root Test
ADF t-statistics
Variable
PP Adj. t-statistics
-1.957
1st order
difference
-3.266*
Order of
integration
I(1)
-1.784
1st order
difference
-3.241*
Order of
integration
I(1)
-2.570
-3.978*
I(1)
-2.174
-4.078*
I(1)
-2.138
-3.517*
I(1)
-1.997
-3.568*
I(1)
-2.253
-3.203*
I(1)
-2.052
-3.217*
I(1)
-2.471
-3.443*
I(1)
-2.031
-3.475*
I(1)
-2.111
-3.392*
I(1)
-1.899
-3.406*
I(1)
-2.127
-4.204*
I(1)
-1.546
-4.204*
I(1)
-3.110*
-4.023*
I(0)
-4.562*
-3.855*
I(0)
-2.819*
-5.304*
I(0)
-1.544
-5.157*
I(1)
-3.296*
-5.263*
I(0)
-2.479
-5.287*
I(1)
-2.157
-6.967*
I(1)
-3.330*
-6.300*
I(0)
2.131
-2.035
I(2)
-1.369
-3.276*
I(1)
Level
symbol
HDB housing
phdb
price
Apartment
papt
price
Condominium
pcod
Price
Terrace Price
pter
Semi-detached
psed
Price
Detached Price
pdet
Building
bmp
Material Price
Consumer
cpi
Price Index
Prime Lending
PLR
Rate
All-Share
sgx
Index
GDP
gdp
Total Number
mar
of Marriages
*significant at the 5% level
Phillips-Perron (PP) Unit
Root Test
Level
Table 4: t-Statistics of STOPBREAK Hypothesis Tests
Variable
HDB Resale
price, phdb
Apartment
price, papt
Condominium
price, pcod
Terrace perice,
pter
Semi-Detached
price, psed
Apartment
price, papt
Condominium
price, pcod
Terrace
perice, pter
Detached
price, pdet
3.79*
SemiDetached
price, psed
3.75*
3.29*
3.59*
-2.53*
-0.01
0.15
1.13
-1.37
1.15
1.75
-3.05*
0.23
3.38*
-1.23
Ho: the relative price follows a random walk process, i.e. there is no cointegration in the series.
* indicates significance at 5%
20
Table 5: Results Johansen and Juselius’s (1990) Cointegration Tests
Sample (adjusted): 1990Q4 2004Q1
Trend assumption: No deterministic trend (restricted constant)
Series: dphdp, dpapt, dpcod, dpter,dpsed, dpdet
Exogenous series: dbmp, dsgx, dgdp, dmar, PLR, uxcpi, dum1Q98
Lags interval (in first differences): 1 to 1
A) Unrestricted Cointegration Rank Test (Trace)
Hypothesized
Trace
0.05
No. of CE(s)
Eigenvalue Statistic
Critical Value
Prob.**
None *
0.6742
222.6559
103.8473
0.0000
At most 1 *
0.6269
162.0982
76.9728
0.0000
At most 2 *
0.6030
108.8610
54.0790
0.0000
At most 3 *
0.4714
58.9699
35.1928
0.0000
At most 4 *
0.2312
24.5437
20.2618
0.0121
At most 5 *
0.1744
10.3481
9.1645
0.0297
Trace test indicates 6 cointegrating eqn(s) at the 0.05 level
* denotes rejection of the hypothesis at the 0.05 level
**MacKinnon-Haug-Michelis (1999) p-values
B) Unrestricted Cointegration Rank Test (Maximum Eigenvalue)
Hypothesized
Max-Eigen
0.05
No. of CE(s)
Eigenvalue Statistic
Critical Value
Prob.**
None *
0.6742
60.5577
40.9568
0.0001
At most 1 *
0.6269
53.2372
34.8059
0.0001
At most 2 *
0.6030
49.8911
28.5881
0.0000
At most 3 *
0.4714
34.4262
22.2996
0.0006
At most 4
0.2312
14.1956
15.8921
0.0906
At most 5 *
0.1744
10.3481
9.1645
0.0297
Max-eigenvalue test indicates 4 cointegrating eqn(s) at the 0.05 level
* denotes rejection of the hypothesis at the 0.05 level
**MacKinnon-Haug-Michelis (1999) p-values
21
Table 6: Vector Error Correction Estimates
Dependent
Variables::
dphdb
dpapt
dpcod
dpter
Dpsed
dpdet
-0.3571**
[-2.6060]
0.1989
[ 0.6009]
-0.0945
[-0.2977]
0.5942
[ 1.3035]
-0.0770
[-0.4140]
-0.2291
[-1.1361]
0.0869
[ 0.3864]
0.0803
[ 0.2836]
0.3633
[ 1.5200]
-0.0978
[-0.5324]
1.4684**
[ 2.0573]
-0.0093
[-0.1358]
0.1254
[ 0.5050]
0.0039
[ 0.9016]
-1.3569**
[-2.0035]
0.0249*
[ 1.7086]
-0.0263
[-1.6589]
-0.0884
[-0.8810]
-0.9571***
[-3.9487]
0.5473**
[ 2.3548]
1.0251***
[ 3.0710]
-0.2004
[-1.4726]
-0.2576*
[-1.7442]
-0.0324
[-0.1970]
-0.5396**
[-2.6026]
0.0751
[ 0.4292]
0.5560***
[ 4.1331]
0.6902
[ 1.3204]
0.2122***
[ 4.2481]
-0.1107
[-0.6084]
0.0013
[ 0.4288]
0.1027
[ 0.2071]
0.0082
[ 0.7659]
-0.0061
[-0.5282]
-0.0641
[-0.4734]
0.5483*
[ 1.6761]
-0.8129
[-2.5913]
1.1597**
[ 2.5741]
-0.2309
[-1.2566]
-0.3831*
[-1.9222]
0.0793
[ 0.3566]
-0.4078
[-1.4574]
0.3297
[ 1.3956]
0.3673**
[ 2.0226]
-0.7683
[-1.0891]
0.1022
[ 1.5159]
-0.3013
[-1.2275]
0.0012
[ 0.2922]
-1.2825*
[-1.9159]
0.0106
[ 0.7354]
-0.0213
[-1.3594]
-0.5770***
[-5.0257]
0.3030
[ 1.0927]
0.4109
[ 1.5452]
-0.9809**
[-2.5686]
0.1578
[ 1.0133]
-0.3187*
[-1.8866]
0.1463
[ 0.7763]
-0.1391
[-0.5863]
-0.2587
[-1.2922]
0.3807**
[ 2.4737]
0.7888
[ 1.3191]
0.2189***
[ 3.8317]
-0.3042
[-1.4620]
0.0031
[ 0.8655]
-1.9882***
[-3.5040]
0.0226*
[ 1.8464]
-0.0396***
[-2.9756]
-0.5763***
[-4.8338]
0.3792
[ 1.3166]
-0.0489
[-0.1772]
0.3072
[ 0.7745]
0.3013*
[ 1.8631]
-0.2735
[-1.5588]
0.4291**
[ 2.1929]
-0.3641
[-1.4779]
-0.3997*
[-1.9219]
0.4863***
[ 3.0423]
1.0741*
[ 1.7295]
0.2508***
[ 4.2263]
-0.0571
[-0.2643]
0.0051
[ 1.3730]
-2.4431***
[-4.1458]
0.0022
[ 0.1720]
-0.0502***
[-3.6334]
-0.6717***
[-4.6849]
0.7346**
[ 2.1216]
-0.4538
[-1.3668]
0.4436
[ 0.9301]
0.2459
[ 1.2645]
-0.3466
[-1.6431]
0.6533***
[ 2.7768]
-0.1847
[-0.6237]
-0.6773***
[-2.7087]
0.6605***
[ 3.4366]
0.7299
[ 0.9774]
0.2298***
[ 3.2202]
-0.1944
[-0.7483]
0.0053
[ 1.1907]
-4.3526***
[-6.1428]
-0.0027
[-0.1768]
-0.0690***
[-4.1535]
Adj. R2
0.3216
0.6708
0.3138
0.5021
0.6217
0.6284
Cointegrating
Equations:
dphdb(-1)
dpapt(-1)
dpcod(-1)
dpter(-1)
dpsed(-1)
CointEq1
CointEq3
CointEq4
CointEq1
CointEq2
CointEq3
CointEq4
dphdp(-1)
dpapt(-1)
dpcod(-1)
dpter(-1)
dpsed(-1)
dpdet(-1)
dbmp
dsgx
dgdp
dmar
PLR
uxcpi
dum1Q98
CointEq2
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
-9.4201***
-12.7422*** -14.5032***
-5.1417***
[-6.4587]
[-6.1960]
[-6.1487]
[-6.6782]
8.4592***
10.4345***
11.9896***
3.6293***
dpdet(-1)
[ 6.9299]
[ 6.0624]
[ 6.0735]
[ 5.6324]
C
-0.6859**
-0.4903
-0.6437
-0.1737
[-2.4254]
[-1.2297]
[-1.4074]
[-1.1634]
t-statistics in brackets [ ]; C is the intercept term; and CointEq(k) is cointegrating vector.
*10% significance: 1.674;
**5 % sigificance: 2.005;
*** 1% significance: 2.670
22
200
35%
180
30%
160
25%
20%
140
15%
120
10%
100
5%
80
0%
60
-5%
Rate of Change in Price Index (%
Property Price Index
Figure 1: Historical Price and Return Trends of Private Residential Properties
and HDB Resale Flats
40
-10%
20
-15%
0
-20%
3
2
1
0
7
8
9
5
4
6
1
3
2
0
4
99 199 199 199 199 199 199 199 199 199 200 200 200 200 200
-1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
Q
Q
Q
Q
Q
Q
Q
Q
Q
Q
Q
Q
Q
Q
Q
Private Residential Property Price Index
Return of Private Residential Prperty Price
Qtr-year
HDB Resale Price Index
Return of HDB Resale Price
23
Figure 2: Distribution of Private Non-Landed Property Stock by Ownership
100%
Proportion of Homeownership in
Private Non-Landed Properties (%)
90%
80%
70%
60%
50%
40%
30%
20%
10%
0%
2
4
4
4
4
4
4
4
4
4Q
3Q
2Q
1Q
0Q
9Q
8Q
7Q
6Q
0
0
0
0
0
9
9
9
9
Year-Qtr
20
20
20
20
20
19
19
19
19
Foreigner
Permanent Resident
Singaporean
Company
24
Figure 3: Hierarchical Stratification of Public and Private Housing Types
Increase in Price (typical Unit)
Increase in Market Share (Stock)
Stein’s (1995) Mobility Classes
Detached
House
Unconstrained Mover
SemiSemi-Detached House
Terrace House
Constrained Mover
Condominium
Apartment*
Public Housing / HDB Flat
Constrained
Non-mover
*See Table 1. The market share of apartment is smaller than condominium. These two housing types are quite
homogeneous in design and appeal, and are always grouped as non-landed private residential housing. Besides
price, the two housing types are differentiated by the size of land parcel they are built thereon, and the facilities
provided in the development. Condominium will be equipped full-scaled facilities and services, and must be built
on land that are larger than 0.4 hectare. With the condominium status, there are no restrictions on foreign
ownership. Whereas for apartment, which is smaller in scale, only units in block more than 6-storey height could
be sold to foreigners.
25
Appendix 1
Table 4: t-Statistics of STOPBREAK Hypothesis Tests
Variable
Apartment
price, papt
Condominium
price, pcod
HDB Resale
14.40
14.34
price, phdb
Apartment
10.40
price, papt
Condominium
price, pcod
Terrace perice,
pter
Semi-Detached
price, psed
Ho: the number of cointegration equation is zero
* indicates significance at 5%
Terrace
perice, pter
Detached
price, pdet
16.43*
SemiDetached
price, psed
26.99*
14.77
13.45
14.44
10.64
14.42
14.13
12.59
9.05
19.87*
8.07
26