Journal of Financial Risk Management
2012. Vol.1, No.2, 7-14
Published Online June 2012 in SciRes (http://www.SciRP.org/journal/jfrm) http://dx.doi.org/10.4236/jfrm.2012.12002
Structural Change Modeling of Singapore Private Housing
Price in Simultaneous Equation Model
Weihong Huang1, Yang Zhang2
1Division of Economics, Nanyang Technological University, Singapore City, Singapore
2Faculty of Business Administration, University of Macau, Macau, China
Received March 2nd, 2012; revised April 15th, 2012; accepted May 10th, 2012
This paper investigates the structural change behavior of Singapore’s private housing market and in par-
ticular the impact of government policies on housing price determination. A structural model of price is
established and the “Regressive Segmentation (RS)” method is applied to detect the changing points
without prior knowledge of the structural changes. Our study shows that the changing points indicated by
the RS method are consistent with the timing of the policy changes.
Keywords: Private Housing Market; Structural Change; Simultaneous Equation Model
Introduction
Booms and slumps in housing prices have attracted the atten-
tion of both the general public and academic economists ever
since. From the academic point of view, the ready availability
of time-series data and the important policy implications of
high and volatile prices have meant that empirical modeling of
housing prices has been both a fertile and a challenging area.
In Singapore there are two segments in residential housing
market, the private housing market and the HDB1 resale hous-
ing market. The main difference between the two is that the
HDB resale housing market is, to some extent, regulated and
subsidized, while the private housing market receives limited
government intervention although the prices in both markets are
determined by the market forces.
Private housing market operates in a laissez-faire economic
system, where housing prices are mainly determined by a func-
tion of the demand and supply in the market. (Sing, Tsai, &
Chen, 2004) This segment of the market is dominated by few
major private developers. A variety of housing forms, with the
hierarchical structure from apartment, condominiums, terrace,
semi-detached house to detached housing, is made available by
private developers to meet different preference and aspiration
of potential buyers. The private housing units have much higher
housing prices with better designs, quality of finishes and fully-
equipped recreationally facilities. Getting into the private hous-
ing market is therefore viewed as the upper end of Singapore
owner-occupiers’ housing career. Ownership of private residen-
tial property is well regarded as a social status, and a dream of
HDB dweller, and those who have not owned a house.
Although being relatively small, the private housing market
has a significant impact on the Singapore economy. According
to the estimation given by Phang (2001), the ratio of gross
housing wealth in the private housing sector to GDP is 1.48,
while the same ratio in the public housing sector is 1.38. This
implies that the fluctuation of private housing prices could have
important implications for the national wealth holding. More-
over, becoming a private home-owner has become a national
phenomenon, attracting a significant proportion of public
home-owners to upgrade to private housing. The public housing
subsidies therefore leak out into the private housing sector
through such upward mobility and its social economic impacts
are significant.
Although Singapore has a relatively free economy, its hous-
ing market is far from being perfect. It is strongly dominated by
the public sector, in the forms of both direct provision and con-
trol of major housing stock, and regulating the eligibility crite-
ria, housing finance, prices, rentals and transaction costs. The
government’s intervention through the sale of leasehold private
residential lands program and the government linked property
companies also helps indirectly to cushion unnecessary price
inflation. The impacts of the public housing policies on the
private housing prices are profound, albeit indirect. As pointed
out by Phang et al. (1995), the effect of government interven-
tion on the public housing could filter into the private housing
market. Changes in the supply, expected price, finance and
eligibility criteria of public housing will influence the private
property market significantly. These policy distortions have
resulted in remarkable structural changes in the private property
market over time.
With the market more responsive and susceptible to external
shocks, price correction should be less sticky vis-à-vis public
housing market. In recent years, Singapore’s residential pro-
perty market, especially the private housing market has been
suffering from irregular price fluctuations. This has caused
much public concern about the affordability of private housing.
Thus the study of the structure of Singapore private housing
market and the behavior of the market is of great importance in
controlling real estate inflation. Interest in this sector also stems
from the fact that it is subject to the full rigor of market forces,
in sharp contrast to the established public housing market
where state-administered social pricing prevails mainly through
subsidies and loans to the HDB.
This paper investigates structural changes in Singapore’s
private housing market and in particular the impact of govern-
ment policies on housing price determination. A structural
1HDB, Housing Development Board, is a statutory board of the Ministry o
f
N
ational Development, considered to be the national housing agency.

W. H. HUANG, Y. ZHANG
model on price is established and the “Regressive Segmenta-
tion” (RS) method is applied to detect the changing points
without prior knowledge of the structural breaks. The rest of the
paper is arranged as follows. Literatures provides a review of
literatures and Method presents the method which is able to
detect, in simultaneous equations model, the changing points
with no prior information on the timing of the structural
changes. Empirical results are discussed in Empirical Result
and Discussion and Conclusion concludes.
Literatures
The literature on modeling of housing prices is very exten-
sive, especially in the developed housing markets in the UK
and North America. Many empirical housing models have been
developed based mainly on the stock-flow adjustment or the
classical Hendry’s neo-classical frameworks. In Hendry’s the-
ory of equilibrium demand and supply functions, the price of
existing houses was derived as a function of personal dispos-
able income, rental rate, interest rate, stock of mortgage, tax
rate, and number of families. Dicks (1990) extended Hendry’s
model for prices of new housing in the UK. Hsieh (1990) fur-
ther separated housing demand into service and investment
demand in a study of Taiwan’s housing market.
Following the traditional two-equation stock-flow model of
the residential market, the demand is typically stated as a func-
tion of the real price of housing, the user cost of financing that
price, the alternative cost of renting as well as demographic
characteristics and real permanent income. In supply side, con-
struction is always assumed to depend on housing prices, factor
costs and various interest rates (Di Pasquale & Wheaton, 1994).
Empirical practices show that the functional forms and lags
used tend to be largely data determined (Muellbauer & Murphy,
1997).
The stock-flow approach posits that the housing market will
clear through prices that equate demand with the existing stock
of housing. Supply is often taken to be exogenous as it is de-
termined by the decisions of housing producers in prior periods.
Such a specification fails to include supply-side features (Mue-
llauer & Murphy, 1997) and ignores the relationship between
housing stock and land market conditions (Di Pasquale &
Wheaton, 1994). Taking housing stock as fixed will lead to a
short run fluctuation in which price are completely demand-
driven. However, as shown in many studies (Peng & Wheaton,
1994; Rosen & Smith, 1983), the effect of a demand shock on
prices depends on the state of supply. This is particularly rele-
vant for the Singapore market where land sales program is po-
tentially useful mechanism for bringing the housing market into
steady-state equilibrium (Lum, 2002).
Despite the small market share of the private residential
property market in Singapore, research, however has been con-
centrated on this sector of the market. In the city-state of Sin-
gapore, the studies focusing on modeling private residential
housing market dynamics contain only limited theoretical stru-
cture. Empirical analysis includes the impacts of government
policies on private housing prices (Phang & Wong, 1997) and
the inflation-hedging characteristics of private housing prices
(Chen & Sing, 2000).
Ho and Cuervo (1999) and Tu (2001) incorporated an error
correction term in the cointegration models to adjust for the
short-term non-stationary variations. Ho and Tay (1993) deve-
loped a system of six simultaneous equations for the supply of
and demand for private residential properties in Singapore in a
two-stage least squares process. Other studies include Ong and
Sing (2002) on price discovery between private and public
housing market using a Granger causality error-correction mo-
del and Sing (2001) on the dynamics of the condominium mar-
ket in Singapore.
The free-market operation of the private market implies that
the market is more responsive and susceptible to shocks in
economics. But few have been seen to study the structural
change of long run behavior of private housing market in Sin-
gapore, especially in structural equation model. This provides
the basic rational for this empirical work.
Method
The basis of the method, for specialized cases, is documented
by Fisher (1958) and Guthery (1974). Thorough treatment and
description of the main idea in the context of simultaneous
equation model seems still sparse, with recent treatment in
Huang and Zhang (2004). Normally, structural change is said to
be present within the range of the index i, which in time series
data, corresponds to time or observation. With the index or par-
titioning variable identified, the inferential problem confronting
us involves three parts: 1) the specification of the number of
changes in the model, l; 2) the detection of the change point
{is}, or the boundaries of intervals over which each of the
model pieces applies; 3) the estimation of the model parame-
ters within each subdomain. If l and the {is} were specified,
step 3 would simply consist of applying the classical theory,
interval by interval. Summing the residual sums of squares for
the various intervals yields an overall index of the quality of fit
of the segmented model. With l fixed, the {is} may be estimated
by minimizing this index. Further minimization of the index to
estimate l will base on information criterion for model selection
problems.
In estimating the appropriate sample separation in simulta-
neous equation system, there are two approaches to analyze the
timing and form of structural changes, either to estimate equa-
tion by equation individually using a limited information esti-
mator, or globally consider joint estimation of the entire system.
First using limited information estimation, without loss of any
generality, we may consider the first equation in the system
with normal assumptions applied, and write it as
1111 11
γyYX u 

. The reduced form corresponding to this
is
I
II
YZ V

 , where


11
,
I
YyY,


12
,Z
X
X,


11
π,
I


and


11
,VvV
I.
Z
is the 
N
G matrix of
non-stochastic exogenous variables in the complete system,
1

is a Gm
1
(1)

 matrix of reduced form coefficients, and
I
V(Gm is a 11)

 matrix of reduced form disturbances
whose rows are assumed to be normally and independently
distributed with zero mean and covariance
I


β


. Comparing the
structural and reduced forms of the model, we have
where 1. Thus, one may es-
timate 1 u by utilizing appropriate estimators for VI and .
Then
0
1111 1
ββ
I
uvV V 
0
1
β1,
0
1
β
I
V
ˆˆ
may be estimated by applying OLS to yield
I
II
VYZ

, since
I
V
u
is reduced form coefficient and OLS
will give consistent estimation. Meanwhile, can be esti-
mated from structural form equation using 2SLS. Thus, the
appropriate estimator of 1 would then be . Since
we know that
0
1
β
0
ˆ
β
1
ˆI
uV
1
ˆ
I
ZI
VM , where Z Y1 ()
M
IZZZ
Z


 , it
follows that 1 u

may be obtained directly as the residual vector
of the unrestricted OLS regress of on
1
111
ˆ
βyY
Z
, that is,
8

W. H. HUANG, Y. ZHANG
regressing 0
1
ˆ
I
yY

 on
Z
. Denoting the coefficient
vector of said regression by and would be expressed
alternatively as .
1G
tt
yZ



2
,1
t



δ


1
2
l
t
1
u

2
ii
t

di




1
Applying recursive segmentation method, we define target
function, e, as the statistics that describe the overall goodness-
of-fit of the model using certain estimation criteria. The value
of the target function within a segment is called the diameter,
denoted as d. Obviously, e is a function of d. The use of ordi-
nary least square (OLS) gives specific form to the target func-
tion and diameters and simplifies the discussion. We therefore
have
ˆ
δ
Z
ti
()
min
ˆ
δ
s
tt
yZ

uy

1
,1
2, ,
ss
i
sl




11
(,
1, 2,
s
s
i
st i
epNl







min
)
,sl




11
11
2
ˆ
δδ
1,
ss
ss
tt t
ti
di yZ





where is the tth element of matrix. And e is defined
as:
t
yy
11
1
11
δ
s
s
i
tt
sti
ll
ss
s
yZ
i






As shown above, target function

(,
el)pN can be decom-
posed into the sum of individual diameters. Therefore the ulti-
mate goal is to obtain the optimal segmentation:


12
,, ,
l
ii i
 

(,)pNl 


, which minimizes the target function, i.e.,



(,)
min
ppNl p 


(, ) e pNl (N,) e l. let denote the resulting esti-
ˆ
δ
mates based on the given l partition 12 l. Substituting
these estimates in the objective function and denoting the re-
sulting sum of squared residuals as 12 l, the esti-
mated break points

,,
i i


,i

,, ,i
ii
SSE

12
,,ii
 ,l
i
 can be alternatively denoted
as




12
,,...,
arg m
,
lii
i

12
,i
12 ,
,,ii
 
in
l
i,l
iSSE i.
As an additive function of diameters, the target function


(,)
epNl

satisfies the separability condition in a multi-stage
decision-making problem in dynamic programming. Thus, by
using the technique of backward recursive optimization,

12 , or the optimal changing points can be identified
recursively without an exhaustive grid search. Details of this
algorithm are shown in Huang and Zhang (2004).
,, ,
l
ii i
 

If full information, or systems methods of estimation is used,
we may formulate the full system as YZ U

, where
and() 0EU  

E
δ
I
UU
3SLS
. In line with the principle of
system methods, the technique of three-stage least square is
used for joint estimation of the entire system of equations. Thus
the 3SLS estimator is ˆ

1
ˆˆ
1ˆ
1
Z
Y
ZZ I
I







where ˆ
Z
is the IV estimator for 2SLS. Again, the model is
assumed to have structural changes in the whole sample
period, i.e., subsamples. Following the definition of diame-
ter and target function stated previously and after a choice of a
1
l
l

normalization rule, we have ,

,1 ,1
ss
di ii

11
1
M
h
h
d



ss
i
where

1
,1
hss
dii
 is the diameter of the hth equation, for
the individual segment staring from
s
i to .
1ss is the summation of all the diameters throughout
the system. Given the structural changes in the form of
11 s
i
(,dii1)



12
,,,
l
ii i(,PN )l, we have

1
111
,1 , (,)
llM
sshss
ssh
ediidii pNl 


1
1


 

. Those corre-
sponding diameters can be calculated from 3SLS estimators.
Similarly, we have the optimum of target function as




(,)
min (,) (,)
ppNl
ee pNl pNl


. Again, the estimated break
points will be




12
12 12
, ,...,
,, ,argmin,, ,
l
ll
iii
ii iSSEiii. It is ap-
parent that the technique of backward recursive optimization
and dynamic programming procedure are applicable and again
RS procedure can be implemented to detect the structural
changes without grid search calculation.
By using recursive classification, we can obtain different re-
cursive segmentations simultaneously, given exact number of
segments l, on which in practice we may not have such infor-
mation. Another standard problem is that improvement in the
objective function is always possible by allowing more breaks.
That is to say, in determining optimal l0, it is expected intui-
tively that a more complicated model will provide a better ap-
proximation to reality. But, on the contrary, in most practical
situations a less complicated model is likely to be preferred if
we wish to pursue the accuracy of estimation. Information cri-
terion which derives from maximizing the posterior likelihood
in a model selection paradigm and enjoys widespread use in
model identification provides a natural baseline. Akaike (1973)
found a simple relationship between expected Kullback-Leibler
information and Fisher’s maximized log-likelihood function.
This relationship leads to a simple, effective, and very general
methodology for selecting a parsimonious model for the analy-
sis of empirical data.
The general form of Information Criterion (IC) is:




2ln ()
s
s
ICL MPm s , where


s
L
M is the value of
the maximum likelihood function of the model, while


s
Pm
is the penalty function. Thus, the RS method should choose be
the model with smallest IC value. By using computer simula-
tion, the investigation of the penalty function with different va-
lues of observations, variables and variance suggests that the
AIC function by Akaike, BIC of Schwarz and CAI of Sugiura
are all appropriate. Based on the results obtained in previous
section, for given number of l, we have found the optimal seg-
mentations and the corresponding estimation of the whole sam-
ple. Now the determination of l0 will be obtained according to
the IC criteria, i.e., the one which allows the greatest reduction
in the IC value:


0arg min
12
,,,...,
l
i i
s.
s
li lIC
Empirical Result and Discussion
Model Specification
As indicated in Ho and Cuervo (1999), “structural demand
and supply” model would have been more appropriate com-
pared with the VECM (Vector Error Correction Model) if the
objective of the study were to establish causal relationships for
structural analysis; to determine elasticities and multipliers for
policy analysis; and to make forecasts for planning purposes.
Because of these merits of system analysis, we will in this stu-
dy look at the demand and supply of private housing market
using simultaneous equation model. Our model extends the
analysis in previous literature by proposing a new approach to
structural modeling of the time series path of private housing
market. This allows us to disentangle supply-side factors from
demand-side influence, and in particular, the structural breaks

W. H. HUANG, Y. ZHANG
in housing market behaviors over time. Several important
macro-economic determinants of private housing prices are
identified and tabulated in Table 1.
The Demand Model
Private housing prices (RPPI)
In order to obtain an aggregate measurement of price level in
the private residential property market, the private Residential
Property Price Index (RPPI1) is used. The RPPI data from first
quarter of 1990 to the first quarter of 2004 is collected from
REALIS2—Real Estate Information System.
Public Housing Prices (HDB)
Prices of public housing units sever as the benchmark of the
price of private housing market. The Resale Price Index of
HDB Flat3 was used as a proxy4. This HDB variable is sup-
posed to capture the price level of public housing. This data is
obtained from the website of Housing Development Board,
where 1998Q4 is adopted as the base period with index at 100.
The pricing of HDB flats is largely determined by the statutory
board and is considered a policy decision, bearing in mind that
affordability is the main thrust of public housing here, although
it does take into account prevailing property market conditions.
The intermarket mobility between public and private market
occurs as the income of the population increases and prefer-
ences change. Appreciation in the values of public flats en-
hances the affordability of flat-owners to upgrade. Upgraders,
defined as those who upgrade from public to private housing,
typically reply on the capital appreciation of their flats to enable
them to purchase private properties (Ong, 1999).
On this account, the rising public resale price directly in-
creased the accessibility of public home-owners to upgrade to
private housing, which will transfer the public housing subsi-
dies to private housing. So public housing price is an important
determinant in demand for private housing. This upgrading
effect exceeds the effect of being substitute for private housing.
Therefore the HDB resale price is expected to be positively
related to the demand for private housing.
National income (GDP5)
An earlier Ministry of Trade and Industry’s article (2001) has
Table 1.
Private housing market determinants.
Demand Side Factors Supply Side Factors
Private housing prices Private housing stock
National income Private housing price
Mortgage rate Basic materials costs
Public housing prices Labor costs
Consumer price index Mortgage rate
shown that private residential property prices in Singapore are
fundamentally driven by economic growth, which captures both
the improvement in household purchasing power as well as
population growth. Phang et al. (1995) also suggests that the
fundamental of the private property market is determined by
factors of the macro-economic environment.
Singapore’s housing finance system allows the would-be
private home buyers to use their monthly Central Provident
Fund6 (CPF) contribution to pay off their mortgage debts. The
contribution rates are adjustable and are positively related to
medium to long term economic performance. This positive re-
lationship implies that macroeconomic performance may di-
rectly affect the would-be home-buyers’s housing affordability.
Ong and Sing (2002) provides evidence that real GDP is a
significant variable reflecting the impact of long-run economic
performance on the housing market. From the third quarter of
1986 until end of 1996, the growth of Singapore economy has
been strong. The growth in household income and their CPF
boosted the private housing market. Conversely, the poor eco-
nomic performance in 1996 and 1997 has resulted in a dramatic
fall in the prices of private properties. Therefore, GDP value is
chosen as one of the potential key factors determining private
housing prices, with a positive relationship expected.
Mortgage rate (PLR)
It has been suggested by economic theory that interest rates
and house prices be inversely related. Generally, lower interest
rates tend to increase housing demand, and therefore pushing
up housing prices. However, this effect is softened by a similar
increase in the supply of housing in response to higher house
prices and lower construction financing costs result from re-
duced interest rates. Thus, interest rates influence house prices
through the demand for, and supply of private housing. We use
PLR (Prime Lending Rate)7 in our model, which is the average
of nominal bank lending rate, serves as the measure of the cost
of housing finance or the cost of borrowing.
1The Residential Property Price Index is computed for all residential trans-
actions on a quarterly basis. It should be differentiated from the Property
Price Index that is an agglomeration of residential, commercial and indus-
trial property sales.
2This database is provided by Urban Redevelopment Authority (URA), the
national planning authority of Singapore which is entrusted with the re-
sponsibility of planning the physical development and optimizing the scarce
land resource in Singapore. The URA provides comprehensive and up-to-
date data and information of the real estate market to improve the market’s
efficiency and transparency. The private residential property price indices
p
ublished by the URA are transaction based indices compiled from caveats
lodged with the Land Registry.
3The HDB Resale Price Index is based on the transactions of public Hous-
ing Development Board flats on the resale market. In other words, resale
transactions are open-market transactions that occur subsequent to the ini-
tial sale, which is heavily subsidized by the government.
4Both RPPI and HDB resale price indexes are complied based on transac-
tions and do not suffer from the smoothing biases in appraisal price series.
5Rate of the GDP growth, used to estimate the changes in the income level,
obtained from TRENDS, the Time Series Retrieval and Dissemination
database maintained by the Department of Statistics in Singapore is used to
construct the time-series for the variables identified in the model. All the
variables are in their quarterly series. The TRENDS database is the national
repository of macroeconomic variables and sector-specific variables for the
Singapore economy. The reliability and integrity of this database, which is
maintained and updated by the Ministry’s DOS, are beyond any measure o
f
doubt.
Other variables
It is shown from housing economics literature that wage, as a
6CPF is the Singaporean’s social security system, mainly providing pension
schemes and medical care schemes. It is mandatory for both the employee
and the employer to contribute monthly a certain fraction of the employees’
salary to the fund to take care of the retirement, homeownership, and health-
care needs of the members. The CPF Board was set up to administer and
p
reserve the value of the savings of its members. The CPF enables easy
home-ownership through two popular schemes-the Public Housing Scheme
for HDB flats and the Residential Properties Scheme for all housing proper-
ties built on freehold land or with a lease of at least 60 years remaining.
7Prime leading rate, the average of nominal bank lending rate, obtained from
International Financial Statistics (IFS), the International Monetary Fund’s
p
rincipal statistical publication and is the standard source for all aspects o
f
international and domestic finance.
10

W. H. HUANG, Y. ZHANG
representative of the average real household income, could be
an important factor affecting housing prices. Yet, wage rate per
employee may not be a significant determinant in explaining
private housing prices in Singapore. Private housing market in
Singapore attracts either foreigners or local residents from mid-
dle or upper-middle income groups, whose incomes are not
available in time-series format. Measurement bias would exist
if simply using the average income for all employees. Therefore,
household income is not included in our model for private
housing demand.
Finally, demographic variable like household formation,
which is often used in housing study of UK and US, is not in-
cluded. The reason is that about 86 per cent of the population is
absorbed by the public housing sector in Singapore, while pri-
vate housing sector acts as the upper end of the home-owner’s
housing career. Therefore, new household formation is not
expected to be significant in explaining private housing prices
movements.
The Supply Model
In contrast to the demand side, housing supply is necessarily
specified in terms of the flow of new investment. In the market
for new construction, the supply of new housing units can be
expected to increase in response to positive production signals
provided by rising prices and/or declining costs.
Profit-maximizing firms will have a positive supply response
to selling prices for structures and a negative response to their
own costs of production (Basic material costs index base year
1985, and Labor cost index, collected from TRENDS). We use
index of supply of private residential units in the pipelines8 as
well as price and cost variables. Total housing stock9 is also
included in the supply function and a negative sign is expected
reflecting the responsiveness of new housing construction to
housing stock. Given other factors unchanged, available urban
land becomes scarce as the total housing stock increases. Higher
negative responsiveness of new housing construction to the
total housing stock would be an indication of a slow-down in
new housing construction with respect to the level of housing
stock, especially in a highly urbanized city state like Singapore.
Empirical Results
As discussed earlier, we have two endogenous variables—
price and quantity10—and two equations determining them in
the form of supply and demand equations. The error terms are
likely to be correlated across equations as well, given the tight
relationship between variables. Therefore we use three stage
least squares instrumental variables estimator to avoid statisti-
cal problems involved with using endogenous explanators. We
found all the series non-stationary in level. Rather than apply-
ing the commonly used error correction model, we use RS me-
thod to study the structure changes of private housing market.
The analysis of data using RS method is implemented by the
program written in SAS.
Using the whole sample data from 1991Q1 to 2004Q1, we
have the simultaneous equations model for private housing
market. All series are transformed to logarithmic form for the
usual statistical reasons, and hence the variable coefficients
estimate the percent change in quantity for a 1 percent change
in the variable. Regression results and parameters estimation
are shown in Table 2.
RS method then is applied to estimate the structural break
during the data time period. Figure 1 shows the corresponding
value for e and l. Here we apply the system methods of detect-
ing structural changes, i.e., we examine the structural instability
globally, using the technique of joint estimation of the entire
system of equations.
As can be seen from Figure 1, value of target function re-
duces dramatically, as the number of segments increases. Typi-
cally, its value starts to converge to 0 at point l = 2. Using
Schwarz’s Bayesian Criterion (SBC) to reconfirm our finding
given




ln2 ln
(,)
l
SBCNml N
eN pNl 
, we have the
following results as summarized in Table 3.
As can be seen the minimum value of SBC is reported at l =
2. Should there be one structural break during the sample pe-
riod, the program implemented by SAS indicates that the 31st
data point is the structural break point by using RS method. To
further clarify this point, various tests and sensitivity analysis
are conducted to justify the number of segments specified and
to examine the general robustness of the model specification.
The CUSUM and CUSUM of squares tests are applied to ex-
amine the stability of the coefficients. The test statistics were
beyond the pair of 5-percent critical values for both tests indi-
cating the instability of the coefficient and hence favor the sig-
nificance of the stated structural change occurred at the above-
mentioned date.
In view of this, we conclude that the optimal number of seg-
ments is 2, given the result from above tests. The corresponding
periods are the first quarter of 1991 and the second quarter of
1999. This indicates one significant structural change during
the whole sample period and suggests segmenting the data set
into two sub-samples for further investigation. This can be sim-
ply illustrated by Figure 2.
Now we look at two parts separately. We have individual
model whose estimation results are summarized in the Tables 4
and 5.
After taking into consideration of structural change, each in-
dividual segment achieves much better goodness-of-fit. More-
over, from the view of forecasting power, we find that the seg-
mented model outperforms the whole sample model in term of
prediction power. The model’s efficiency is tested by dynamic
simulation involving prediction and simulation under ‘PROC
SIMLIN’ of the SAS software11. The graphical plot of predicted
and actual values of the endogenous variable, RPPI, against
time is reproduced in the Figures 3 and 4. The figures show
simulation results, where the simulation using the second seg-
ment indicate a forecast much more closer to the real data than
8This comprises statistics on the supply of uncompleted private residential
units in the pipeline. This supply in the pipeline covers all developments
under construction as well those on which construction have not commenced
Developments on which construction have not commenced com
p
rised those
with written permission, provisional permission and those submitted to the
Competent Authority and are under consideration for planning approval, and
planned land sales by the government. The data are obtained from a combi-
nation of administrative records from the Development Control Division,
URA and the Building and Construction Authority and field surveys to
update the construction status.
9Stocks of completed private housing represented by available private resi-
dential units—from TRENDS.
10Private housing quantity (demanded and supplied) represented by the
index of supply of private residential units in the pipelines, data collected
from REALIS.
11The SIMLIN procedure reads the coefficients for a set of linear structural
difference equations (usually from a data set produced by PROC SYSLIN),
computes the reduced form, and uses the reduced form equations to generate
predicted and residual values for the endogenous variables.

W. H. HUANG, Y. ZHANG
Table 2.
Structural Model Estimation for Private Housing Market in Singapore
(using whole sample data).
Regressio n Model: Demand Model Supply Model
Variables: Regression Coefficients
Constant −0.077 (0.082) −0.003 (−0.008)
PLR −0.158 (0.501) −0.128 (0.148)
HDB 2.347 (2.609)
GDP (one period lag) 0.126 (0.314)
RPPI −3.797 (4.999) 0.749 (0.196)
CPI 22.839 (25.056)
BMC
−0.182 (0.966)
STOCK −0.017 (0.115)
Note: values in the parentheses are standard errors for the coefficients.
Table 3.
IC Test for value of l.
l 4 3 2 1
Target
Function 0.122129 0.14006 0.198682 1.409757
SBC −58.5252 −74.2742 −85.3134 −60.6964
Table 4.
Structural model estimation for the first segment (91Q1-99Q1).
Regression Model: Demand Model Supply Model
Variables: Regression Coefficients
Constant −0.026 (0.021) 0.008 (0.019)
PLR −0.570* (0.201) −0.081 (0.177)
HDB 0.322 (0.595)
HDB(one period lag) 0.156 (0.178)
GDP 0.283** (0.134)
GDP (one period lag) 0.291** (0.148)
RPPI −0.262 (0.353) 0.834* (0.315)
RPPI (one period lag) 0.679* (0.387)
CPI 4.047 (4.633) −1.250 (4.410)
BMC
−0.429 (1.378)
STOCK
−0.017 (0.137)
LC (two periods lag) −0.283* (0.113)
Note: values in the parentheses are standard errors for the coefficients; *(**)
Denotes coefficient is significant at 1% (10%) level.
the prediction from whole sample data. This is firstly due to the
occurrence of structural change during the sample period, re-
sulting in the poor prediction performance out of an unstable
series from the whole sample. Another reason behind is that the
most recent past contains more information about the immedi-
ate future than the distant past and on this account, most recent
regime may lead to better forecasts.
Discussion and Policy Implication
Singapore private residential property market is driven pri-
marily by market demand and supply, although it is subjected
Table 5.
Structural model estimation for the second segment (99Q2-04Q1).
Regression Model: Demand Model Supply Model
Variables: Regression Coefficients
Constant −0.024** (0.010) 0.025** (0.012)
PLR (one period lag) −0.108 (0.422) −0.128 (0.148)
HDB 1.030** (0.476)
GDP (one period lag) 0.255 (0.272)
GDP (two period lag) 0.055 (0.254)
RPPI −0.081 (0.642) 0.412** (0.161)
RPPI (one period lag) −0.126 (0.450)
RPPI (two period lag) 0.173 (0.129)
CPI (two period lag) 3.390** (2.124)
CPI 1.065 (1.962)
Quantity demanded
(two period lag) (−0.225) (0.217)
BMC −0.326 (1.040)
LC −0.051 (0.120)
LC (two period lag) −0.131 (0.112)
STOCK −3.565* (1.161)
Note: values in the parentheses are standard errors for the coefficients; *(**)
Denotes coefficient is significant at 1% (10%) level.
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
Target Function
0 1 2 3 4 5
Number of Segments
Figure 1.
e VS l.
91 Q104 Q1
99 Q2
99 Q1
Figure 2.
Segmentation of whole sample data.
*--real value --predicted value
Figure 3.
Simulation results using whole sample data.
12

W. H. HUANG, Y. ZHANG
*--real value --predicted value
Figure 4.
Simulation result using data from second segment.
to prudential government regulations and, to some extent, com-
petition from public housing. It is important to model economic
forces and market factors that drive the private housing market
in Singapore, from the perspective of policy makers, developers
as well as investors. That will help to improve the judgment of
the market dynamics and thus to ensure a more effective im-
plementation of housing policy.
Singapore private housing market has undergone cycles of
boom and bust over the last twenty years. In early to mid of
1990’s, the relaxation of the HDB rules and further liberaliza-
tion of Mortgage Loan Financing Scheme had expanded de-
mand and explained the sharp increase in the prices. In the fol-
lowing boom years of 1994-1996, prices in the residential mar-
kets more than doubled, driven by strong income growth, bull-
ish stock market performance, ease of obtaining financing
through banks and property speculation. The latest escalation in
price of private housing had sustained until 15 May 1996 when
some anti-speculative measures were imposed. The launch of
Executive Condominiums12 also set the benchmark of the pri-
vate housing prices at a relatively low level.
Moreover, Singapore economy was badly affected by the
global recession in the electronic sector in the fourth quarter of
1996, which resulted in several downward adjustments in the
growth projection in the year. The transaction volume and the
take-up rate of new private property fell dramatically. The RPPI
index fell 1.9% and 2.7% in the third and fourth quarter of 1996.
Subsequently, the Asian financial crisis and a recession in 1998
further weakened the property market, as prices bottomed out in
the fourth quarter of 1998.
As discovered by our model, the private housing market ex-
perienced a significant structural change in year 1999. Prices of
residential properties rose 11.4% in the 2nd Quarter 1999,
compared with 4.4% in the previous quarter. Prices of landed
properties rose 13.9% compared with 4.3% in the previous
quarter, among which prices of semi-detached 15.7%, detached
houses and terrace houses 13.4% and 13.1% respectively.
Prices of non-landed properties rose 9.4%, compared with 4.5%
in the previous quarter. Of this, prices of condominiums rose
9.0% while those of apartments increased by 10.5%. The num-
ber of private residential units under construction decreased by
6.6% to 30,455 units as at the end of 2nd Quarter 1999. The
number of uncompleted private residential units with sale li-
censes and building plan approvals declined 4.8%. A total of
1360 new private residential units were launched for sale in the
2nd Quarter 1999, 5.1% lower than the 1433 units launched in
the 1st quarter. During the 2nd quarter, 2723 new private resi-
dential units were sold by developers, 17.8% lower than the
3313 units sold in the 1st quarter 1999. Moreover, the occu-
pancy rate of completed private residential units as at end 2nd
Quarter 1999 is 0.1% percentage point higher than the occu-
pancy rate of the previous quarter.
From our segmented model we notice that, for demand side,
price of private housing is significant, and reversely related, to
housing demand in both two subsample periods. While the sign
for price with one time lag change from positive for the first
segment to negative for second segment. This could partly be
explained by the decreasing demand for speculation purpose.
GDP, together with its lag terms, remain to be significant and
positively associate with demand in two subdomain of data.
The coefficient of PLR is negative for both segments. The ne-
gative coefficient may be due to less demand for private hous-
ing as a result of a higher cost of borrowing money.
As shown from supply model, we find that, supply of private
housing is conversely related to current housing stock, basic
material cost and labor cost. Positive relationship is found be-
tween supply and price level. Especially for the 2nd segment,
price with two periods lag becomes significant in determining
housing supply. Another worth noting fact is the big jump of
coefficient of stock in supply model, indicating an increasing
responsiveness of new housing supply to the current stock.
As has been demonstrated by our model, the private housing
market is sensitive to changes in the public housing market
with high correlation coefficient. On this account, it should be
realized by policy makers that the measures directed at the pub-
lic housing sector may have increasingly significant implica-
tions for private housing price movements. This dynamics of
these two markets normally reinforces each other and this calls
for a more integrated approach to study the housing market as a
whole.
The private housing market is expected to turnaround in late
2004, yet caution continues to reign. From demand side, well-
located and reasonably priced projects continue to draw crowds
to the show flats. However, potential home buyers and upgra-
ders have been more prudent with their buys as the government
move to encourage a more flexible wage system and in the light
of CPF cuts. Uncertainty to the incomes of potential home
owners is thus introduced. From the supply side, investment
market is getting active with some developer restocking their
residential landbank. Another positive fact is the number of
unsold units in projects decreased. Some firmer signs of pick-
up of the price are shown from these sale activities. Currently
the mood in the private residential property market continues to
be cautious. Buyers remain concerned in the light of the CPF
cuts and ongoing restructuring of the economy.
Conclusion
In this paper, we have estimated structural models for hous-
ing supply and demand for Singapore private housing market
that fit the data reasonably well for the chosen time periods.
The RS regression model is established which is able to detect
the structural changes in the market, without any prior informa-
tion about the changing points or the timing of the external
12Executive 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.

W. H. HUANG, Y. ZHANG
14
shocks. This method provides a systematic and operational app-
roach that can accurately detect structural changing points
without any knowledge of the pattern and timing of possible
structural shifts. The method is based on the principle of dy-
namic programming and the use of recursive regression allows
global minimizers to be obtained using a number of sums of
squared residuals rather than an exhaustive grid search.
By applying structural change analysis, we are able to detect
the structural break point and segmented models show better
goodness-of-fit in estimation and improved accuracy in fore-
casting. The structural changes we detect are proved to be con-
sistent with policy change and external shocks to the model.
Our model reconfirms the findings by Lum (2002), that demand
and supply macro-variables are found to be significant deter-
minant for 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 market.
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