Upward Mobility, House Price Volatility and Housing
Equity
*Nai Jia Lee
National University of Singapore
Seow Eng Ong
National University of Singapore
July 14, 2004
*Corresponding
author.
Tel:
(65)-6874-6087;
fax:
(65)
6774-8684;
email:
rstlnj@nus.edu.sg.
1
Abstract
The failure of traditional price models to explain the large price swings observed
in housing market has motivated recent literature that attributes this
phenomenon to changes in housing demand of credit / equity constrained
households. We empirically test the equity constraint hypotheses by utilizing a
micro dataset from Singapore where a distinct demarcation between public and
private housing allows us to measure the ability of households to upgrade. Our
empirical results support the equity constraint hypotheses; younger and credit
constrained households are more likely to move when their ability to afford
better housing is enhanced, but there is no statistical evidence that mature and
financially unconstrained families move up the housing career when it is
favorable to do so.
2
1
Introduction
The volatility of housing prices is a well-known phenomenon and many studies
have sought to understand the large fluctuations in house prices. The standard theoretical
approach to the question treats the housing market much like any other asset market. In
this framework, house prices are forward looking and depend solely on current and
“future fundamentals” such as user costs of capital, rents and construction costs (Poterba,
1984; Dispaquale and Wheaton, 1996). However, this approach has encountered
empirical difficulties and many observers (e.g. Poterba, 1991) have concluded that house
prices are in part driven by non-fundamental speculative phenomenon such as fads or
speculative bubbles.
Stein (1995), however, departs from the standard approach by suggesting that the
large price swings and trading activity of the housing market can be explained by the
self-reinforcing-effects that run from house prices to down payments to housing demand
back to house prices. Stein also suggests that the down payment effects may cause house
prices to be more volatile than in an efficient markets setting where the constraint is not
binding. Furthermore, he hypothesizes that higher trading volume in a rising market is
largely attributed to the large down payment requirements. Down payment requirements
restrict the accessibility of would be movers to purchase a new flat, and this drop in
demand further depresses the prices further.
Ortalo-Magne and Rady (2001) further extend Stein’s theory by developing a lifecycle model, where households have different income and preferences, and assuming that
housing loans are limited by a down-payment requirement. They demonstrate that the
market interaction of young credit constrained households with richer unconstrained
households contribute to the large price swings and the positive correlation between
housing prices and the number of housing transactions.
Most past empirical tests on the equity constraint hypotheses relied on aggregate
housing data (Bardhan et. al, 2003). Other studies that utilized micro datasets focused on
verifying the equity constraint hypotheses in a property market downturn setting. Unlike
previous studies, we attempt to empirically test the equity constraint hypothesis by crossexamining the households’ characteristics and their ability to upgrade, using a micro
dataset from the Singapore residential market as a case study. Because Singapore has
3
distinct public and private housing markets, we are able to measure upgradability using
price changes from both public and private housing, mortgage rates and income.
We first test whether households move if they can afford to do so while
controlling for major house improvement. Stein’s hypothesis assumes that households
will move up their housing career or upgrade if they can afford to do so. Yet, households
may increase their consumption of housing by undertaking renovation of their homes
instead of moving to a larger house (Mandic, 2001). The purpose of the second test is to
verify the life-cycle model suggested by Ortalo-Magne and Rady (2001). Specifically, we
test whether younger, credit constrained households are more likely to move when their
levels of affordability of their desired homes are enhanced, and compare the results with
those of richer unconstrained households.
In order to test whether households move up their housing career or upgrade, we
have to first identify the desired housing needs of these would-be movers. Such needs of
the would-be movers are, nevertheless, found to vary in different countries, societies and
cultures. For instance, Bolt and Van Kempen (2002) found that Moroccan and Turkish
households in Holland view a move to a social rented dwelling as an upward move, in
contrast to the findings from other studies (Pickles and Davis, 1991). Furthermore, most
housing markets are not clearly segmented in terms of quality.
The housing market in Singapore, however, provides a good case study to test the
upgrading assumption in Stein’s model. The clear demarcation of the public housing
sector and the private housing monitor mobility between public and private housing. The
phenomenon is rooted in the Singapore housing system as well as its socioeconomic
system (Ong and Sing, 2002) and the rising trend for such mobility is mainly driven by
the desire for a new lifestyle or a higher social status rather than by the physical housing
needs.
The unique institutional setup and the clearly segmented residential market in
Singapore provide also an ideal setting for us to test Ortalo-Magne and Rady’s life cycle
model. In their model, Ortalo-Magne and Rady suggested the upward movement of the
constrained households living in the starter homes and downward movement of richer
households living in larger dwellings contributed to the large price swing. Public housing
in Singapore fits the description of starter homes very well. Many young credit
4
constrained households who are denied access to private housing purchase public flats
because of the grants and subsidies offered by the government. Additionally, the presence
of an active resale market for public flats facilitate the market interaction between the
credit constrained families and the richer households.
The study is organized as followed. We reviewed the related works in the section
2. Section 3 discusses the econometric model used to test the hypothesis. In Section 4, the
data and the variables are discussed. In Section 5, the results are presented and analyzed.
Section 6 concludes by summarizing the main points and offers some thoughts on policy
implications.
2
Literature Review
Stein (1995) proposes that large price swings are the consequences of self-
reinforcing effects from down payment to house prices. Stein attributes the large price
fluctuations to the mobility behavior of constrained households. The “constrained”
movers have an intermediate level of debt and they face binding financial constraints. In
equilibrium, each of the “constrained” movers chooses to sell their old house and buy a
new one, but the new house is smaller than they would like because they do not have
enough money for a larger down payment. However, this group of constrained movers
would be able to realize more from their sale of house upon an increase in price and
would use the extra money to make a down payment on a larger new house. Hence, the
housing demand for this group of “constrained” movers is an increasing function of price.
In other words, these “constrained” movers perform the crucial destabilizing role in the
model.
Ortalo-Magne and Rady (1998, 1999, 2001) further extend Stein’s static model by
developing a life-cycle model where agents face credit constraints and their housing
consumption is restricted to a discrete set of possibilities. There are two sets of agents;
one group consists of agents who are younger, credit constrained, and buy starter housing,
and the other group consists of agents who are older, and not credit constrained. In this
model, the agents can rent, stay with parents, move to a starter housing or a more
expensive housing. Generally, the prospective buyer prefers to own than rent. In addition,
5
they would like to live in more expensive housing rather than starter housing, which they
could first afford.
Assuming four periods, Ortalo-Magne and Rady further set parameters
determining the distribution income levels of the households. At each period, the
prospective buyer decides which type of accommodation to occupy in the following
period, execute the corresponding transactions on the housing and credit markets, and last,
consume the numeraire good. By specifying the age of the households, they further
identify the equilibrium price and demand, given a positive income shock. In their model,
they find that the income of households belonging to the credit-constrained group has a
greater influence on the housing demand, and fluctuation of prices. In addition, they find
that the property prices of the better housing are supported by the price of starter housing.
The price of the starter housing is further determined by the income of the credit
constrained households. In addition, the relative difference in user costs of both types of
housing to the utility premium of the better housing also determines the price, since
households of greater age tend to substitute for the flats.
Using the theoretical construct of Ortalo-Magne and Rady, Bardhan et. al (2003)
further examine the determinants of new private residential units sold in Singapore during
the 1990s. Their findings show that there is a statistically significant “wealth effect”
driving the sales of new private residential properties. Second, the real local interest rates
have a statistically significantly negative impact on these sales. Thirdly, they further
discover that an increase in the rate of change of public resale prices has an important and
significant effect on the sales of private residential units.
Lamont and Stein (1999) test Stein’s hypothesis by studying the borrowing
patterns at the city level from the American Housing Survey for 44 metropolitan areas
between 1984 and 1994. They find that house prices are more sensitive to city specific
shocks in cities where more homebuyers are highly leveraged. Their finding is consistent
with Stein’s hypothesis. In addition, Chan (2001) tests the above hypothesis by analyzing
the mobility of homeowners, using a sample of 5,094 residential single family 30-year
mortgages originated in New York, New Jersey and Connecticut. Chan (2001) finds that
there are severe constraints to mobility as a result of negative housing market shocks and
6
hence lower transactions, which is consistent with the volume-price correlation proposed
by Stein (1995).
Yet there are many counter hypotheses to Stein’s equity constraint hypothesis.
The relationship between price and moving decisions is first put forth by Hanushek and
Quigley (1979). They explain mobility decisions as precipitated by “mismatch” through
an unanticipated economic or demographic shock. They assert that adjustment is not
smooth or necessarily symmetric over price increases and decreases, but do not attribute
the friction to any particular characteristic of the market. Wheaton (1990) and DiPasquale
and Wheaton (1996) further formalize the household decision in a bargaining model.
They assert that household income, life cycle and demographic factors influence the
preferences of total household consumption. When an exogenous event initiate a series of
changes in the housing demand changes, the household will conduct a search and
contemplate the net gains or losses of moving as opposed to staying in the current
dwelling. Using the above framework, Dispaquale and Wheaton (1996) further
characterize the market dynamics of housing in different setups where households form
their expectations differently.
Similarly, Poterba (1984) and Topel and Rosen (1988) examine the impact of a
shock to the steady state, mapping out the adjustment process to a new steady state. A
shock such as an increase in income initially results an increase in real housing price
since the housing stock is fixed. The market thus adjusts with growth in the housing stock
and decline in property price to a new steady state. On the supply side, they assume that
the home-building industry composes of competitive firms and that the industry’s
aggregate supply depends on its output price, the real price of housing structure.
Assuming there are limits to supply of any factor of production, increases in demand for
construction will boost the equilibrium price of dwellings.
Numerous studies have lent support to the “mismatch” theories, and have
confirmed a positive correlation between housing prices and trading volume. Berkovec
and Goodman (1996) further formalize Wheaton’s search model (1990) and empirically
test the correlation between the changes in turnover rates and demand. Their findings
lend support to the search theories. Yet, such empirical evidence, which is based on
aggregate data, can only at most establish some causality between correlated series.
7
Other than the above, Genosove and Mayer (2001), Englehardt (2003), Leung et.
al (2003) and Seslen (2003) also test the equity constraint model. Genosove and Mayer
(2001), Englehardt (2003), and Seslen (2003) find that it is seller loss aversion rather than
the buyer equity constraint, that drives the phenomenon of low transactions during
property market downturn. Alternatively, Leung et. al (2003) establish evidence from
Hong Kong housing market that the equity constraints are supported in the short run and
the search hypothesis in the medium run. Hong Kong, like Singapore, also has public
housing and the households can sell their homes in the resale market. However, unlike
Singapore, a large proportion of households rent their housing under the public rental
housing program.
Recent events in Hong Kong housing market also provide some evidence in
support of Stein’s hypothesis. As documented by Ho (2002), the implementation of the
Tenant Purchase Scheme allow sitting tenants in selected blocks to buy the units in which
they were currently living at large discounts. The scheme made resale public flats look
extremely expensive and unattractive. As a result, the demand for resale flats plummeted
and the owners of the public flats were unable to “trade up”. The effects further spread to
other types of housing.
The empirical tests on Stein’s equity constraint hypothesis largely dealt with
aggregate data and households’ behavior during downturns. Yet, Stein’s model also
implicitly assumes that households’ decision to move is dominated by price movements.
Apart from socioeconomic factors that could trigger household mobility, households may
choose to stay in their houses and make adjustments to their housing consumption by
modifying or improving their dwellings (Struyk, 1987; Mandic, 2001). This is especially
true in developing countries where the households live in self-help housing (Mandic,
2001). Using Stein’s model (1995), we classify such households who prefer to make
adjustments to their housing consumption as non-movers. However, this assumes that
other groups of would-be movers always prefer to move than to make modifications to
their dwellings. This may not be true, since households may grow an attachment to the
area (Quigley, 1987) and prefer to make modifications to their dwellings instead.
In addition, if households change their housing consumption by making
modifications to their home rather than moving, the prices of housing may increase to
8
reflect the improvement in the housing quality. The increase in house prices may not lead
to an increase in demand, which means that the self-reinforcing loop from house prices to
down payments may break down. Hence, Stein’s model may not work if housing
modification is a major factor for the housing market in general, and for upgrading in
particular. Given that Singapore public housing is given a major facelift after 10 years,
the residential market in Singapore allows us to test whether upgrading still holds when
large scale renovations or improvements are made in the market. By including the binary
factors representing such major improvements in the model, the robustness of Stein’s
model is tested empirically by analyzing the relationship between household mobility and
the households’ ability to upgrade.
It is pertinent in our study to include a variable to capture the upgrading
phenomenon for households. Given the ability of the households to move up the housing
career is directly dependent on the households’ affordability of private housing, the
affordability measures could be a good starting part to derive such a variable. The
literature on housing affordability offers wide-ranging definitions of housing
affordability.
The more applicable measures for our study are the accessibility of homebuyers
defined by ANHS (1991) and the affordability index defined by Keare and Jimenez
(1983). The homebuyers’ accessibility to new housing (ANHS, 1991) is determined by
the households’ ability to afford the down payment. Given that the average homebuyers’
wealth is made up by the value of their current housing, the homebuyers’ affordability of
the house greatly depends on the capital gains obtained from the sale of their current
housing. On the other hand, the affordability index proposed by Keare and Jimenz (1983)
captures the buyers’ affordability in terms of mortgage payments.
Although the affordability measures above provide a good basis to analyze the
homebuyers’ upgrading behavior (Tu, 2003; Tu, et. al, 2004), these measures cannot
adequately explain the upgrading process as the interactions between them cannot be
observed and monitored. There are many households who may satisfy one of the
affordability measure but not the other. In addition, we cannot determine which factor is
dominant if we utilize both measures jointly.
9
Linneman and Wachter (1989) also use similar measures to estimate the extent by
which the desired purchase price exceed the maximum allowed under industry borrowing
standards. They propose size constraint measures: three each for income and wealth.
Hendershott, LaFayette, and Haurin (1997) further extend the study by allowing
households to select the loan-to-value ratio and mortgage product that minimize the
impact of the constraint. Haurin, Hendershott and Wachter (1997) further improve the
measures by having a fuller consideration of the endogeniety of wealth and income.
Ong and Sing (1999) propose another measure of affordability, which they termed
as the Threshold Upgradability Index (TUI). TUI incorporates both wealth and income
effects and is a measure of would-be mover’s ability to upgrade. Ong (2000) empirically
tests the model to evaluate the theoretical underpinning as well as the ability of the model
to predict private property price and found the model to be robust and a good predictor of
private property price.
The index is derived from the concept of the “threshold upgrader”. The threshold
upgrader is the owner of a HDB flat who is just able to upgrade to a private property prior
to a decline in values (Ong and Sing, 1999). The threshold upgrader relies entirely or
partially on cash proceeds from the sale of HDB flat to pay the required down payment of
the private property. The threshold upgrader, moreover, can just barely afford the
servicing of the mortgage. TUI is obtained by deriving the minimum of two prices; each
constrained by different conditions and is derived at the point of sale. Details are
provided in the next section.
3
Data
The data for this study was provided by a Housing Development Board (HDB)
Branch Office in Singapore. This HDB estate is one of the first HDB estates to be built.
Given that the majority of flats are more than ten years old, there is a high level of resale
activity. From a total stock of 37,000 units in the estate, a sample of 594 resale mortgages
spanning a period from 1982 to 2000 is observed. For each loan, we were provided the
borrower characteristics at the point of purchase of the flat, the characteristics of property
and the characteristics of loans at the point of purchase and sale of flat. Using the
information obtained from the mortgages, we model the motivation to move against four
10
categories
of
independent
variables,
borrower,
property,
mortgage
and
the
macroeconomic explanatory variables. Although the sample is small, the data reflects the
resale market well. We found that the 3-room and 4-room units represent the highest
percentage of the total number of resale transactions over the years, as shown in Exhibit 1.
5-room flats cover about 18% of the transactions. The different types of flats in the
sample have similar proportions respectively.
Our data do not offer information about where the sellers move to and
whether they upgraded or not. Furthermore, our measure of upgradeability, which is
described below, is derived from the price indices of private housing and public housing.
Nevertheless we are reasonably confident that the upgradeability measure is able to
capture the upgrading within the different types of HDB flats, and mobility decisions.
First, the Department of Statistics of Singapore shows that about 87,000 households
upgraded between 1991 and 1995, and that represents about 14 percent of the stock of
households in 1990. Second, as demonstrated by Ho (2002), the upgrading phenomenon
is intricately linked to other sub-sectors of the housing market.
From the data, we draw some cross-tabulations to observe the interactions between
household equity constraints and their mobility behavior. We first group households
according to the loan-to-value ratio at time of purchase and the estimated capital gains
/housing equity and tabulate the frequencies in Exhibit 2. An ANOVA test shows that
households with higher loan-to-value loans are more likely to move when capital gains
are high.
In addition, if the hypotheses were true, we would expect the households to build
sufficient equity before selling. We compute the difference in housing equity between
time of purchase and time of sale, and a simple t-test verifies that the difference is
positive and statistically significant from zero. In other words, the empirical evidence
supports our assumption on household equity build-up, which is consistent with the Stein
and Ortalo-Magne and Rady models.
The data also allows us to test the interaction between different housing segments.
The Ortalo-Magne and Rady model suggests that prices of better homes are supported by
the prices of starter housing. As such, we expect a positive correlation between capital
gains from public housing (starter homes) and prices of private properties in that
11
households are likely to build up more equity if the private house price increases. Exhibit
3 provides a cross-tabulation of the change in private price index and housing equity
accumulated by the time of sale. We find that large increases in private price indices
coincide with equity build up for HDB flats, providing anecdotal evidence in support of
the Ortalo-Magne and Rady model
Furthermore, household size could affect the required level of equity before a move
to private housing, assuming housing expenditure of families is positively related to
household size. We perform a simple linear regression test, with the housing equity at
time of sale as the dependent variable and the change in private price index and
household size as independent variables. The results (available on request) reveal that the
relationship between household size and level of housing equity is insignificant. The
insignificance may be due to the low standard deviation of household size; the average
household size 3.0997 members and its standard deviation is 1.34. So the required level
of equity does not depend on household size.
4
Research Design
The preliminary tests and cross tabulations provide support that equity constraints
affect household mobility decision. We further employ a probit analysis to evaluate the
effect of borrower-specific characteristics, property-specific characteristics, mortgagespecific and macroeconomic variables as briefly described in Exhibit on household
mobility. Descriptive statistics are presented in Exhibit 5.
Borrower-specific
characteristics include race, household size and age of buyer. Instead of gross household
income (GHHINC), we use the household income level (INCLEV) to account for inflation
and the relative changes in income over the study period:
INCLEV =
GHHINC n
AVEHHINC n
(3)
where GHHINCn is the real annual household income at year n and AVEHHINCn is the
average household income in year n, derived from the annual GDP at the point of
purchase.
12
Property-specific data includes the type of flat (differentiated by number of
rooms), the floor-level and the age of flat. Since the average age of flats in the estate is 24
years old, many flats have undergone Main Upgrading Programme (MUP) which is
designed for precincts which are 18 years and older. The MUP is essentially a program in
collective renovation, additions and maintenance where improvements are implemented
at three levels – precinct, block and within the flat. The improvements may involve
addition of utility room or balcony, lift lobbies, new facades, more landscaped areas and
multi-storey car parks. Generally, the government bears between 60% to 90% of the cost
of improvement works depending on the type of upgrading and the flat size. The
upgrading proceeds only if at least 75% of the flat owners in that precinct support the
exercise. Since the MUP can be viewed as an alternative way for households to increase
their housing consumption, it could influence the household’s motivation to sell (Mandic,
2001). Thus a dummy variable for MUP before sale is included. The date of
announcement is used as the benchmark because the announcement of MUP could
influence household motivations to move and hence, prices.
In addition, the market premium (PREMIUM) paid by the buyer is also
included in the model and is defined as the difference between price and valuation
(appraised value) of property divided by the valuation. The higher the premium paid
implies the greater the demand for the unit since any premium must be paid in cash.
Loan specific information includes the loan-value ratio (LV), loan outstanding
at prepayment date (OUTLOAN) and initial payment-to-income ratio (PAYINC). LV is
computed by dividing the loan amount by the appraised value or purchase price,
whichever is lower.1 The maximum loan-to-value ratio is 80% and the purchaser can at
most take a loan up to 80% of the purchase price or valuation whichever is the lower. The
date of origination (PDATE) is also included as an explanatory variable and coded in
terms of the year. Additionally, we measure the spread between the public interest rate
and the private housing loan rate for 15 years (INTDIFF), defined as the difference
between the 2 rates at the point of prepayment or at the censored date.
1
When no valuation is available, we assume the valuation is equal to the price transacted. Such cases occur
in the earlier years when valuation/appraisal is not required. The assumption is valid as flats of same
classification are resold at similar prices and the market is very stable during the earlier period.
13
Macroeconomic variables include the return on public residential market
(CHDBPR) obtained from the HDB Resale Price Index, the public mortgage rate at the
point of prepayment (SHDBINT) and the change in GDP per household (CGDP). The
change of HDB Resale Price Index is used to proxy capital gains over the holding period
between the date of purchase to the date of sale or June 2000, the censored date. The
change in GDP per household is a proxy for the change in income over the holding period.
From the literature reviewed earlier, these three variables are not only important in our
tests for mobility decisions (Ioannides, 1987; Ioannides & Kan, 1996), but also critical in
shaping Stein’s model (1995). From the prepayment literature, we also observe that
income changes have great influences on the borrowers’ decision to prepay (Zorn and
Lea, 1989).
The change in Stock Exchange of Singapore Index (CSES) is used to proxy
for market sentiments (Ong, 2000; Ong et al., 2002) as well as to capture borrower
expectations of the housing market, since property market tends to lag stock market.
Furthermore, this variable allows us to capture how changes in the return of other assets
affect the household mobility decisions (Zorn and Lea, 1989).
We also include the volatility of private mortgage rate (SMORTVOL) in our
analysis. Although the volatility of the mortgage rate is not tested in the empirical
analysis of mobility decisions, we expect that greater volatility of mortgage rates will
discourage buyers because the buyers are taking adjustable rate mortgages and will be
subject to greater interest rate risk. The volatility is measured by the standard deviation
over a 4-year rolling window.
Upgradeability variable
TUI is obtained by deriving the minimum of two prices; each constrained by
different conditions and is derived at the point of sale.2 The first price is constrained by
the price of HDB proxied by the HDB resale index. Suppose the HDB resale price moves
from H0 to H1 in period 1. In order for the threshold upgrader to upgrade, the private
property price must be P1R 4 such that
2
The TUI at the point of sale is chosen because we are trying to find out the level of TUI that will induce
sale.
14
P1R 4 =
(H 1 − H 0 )
0.245
+ P0 .
(4)
The 0.245 denominator is due to the minimum cash requirements of the purchase of the
unit3. The other price is constrained by the change in mortgage rate and income. If the
threshold buyer’s income is to increase to Y1 when the mortgage rate changes to i1, and
assuming that the loan-value ratio and the payment-income ratio remain constant after the
changes and all other factors unchanged, the new private property price P1 A that can be
afforded by the threshold buyer is
P1A =
Y1 MCi0 ,n ,12
Y0 MCi1 ,n ,12
P0 .
(5)
Hence, the threshold private property price that will allow households to upgrade,
generalizing from period 1 to t, is
[
]
TPPt = min Pt R 4 , Pt1A ,
(6)
since the threshold buyer is subject to both constraints. TUI is computed as a ratio of the
threshold private property price over the actual property price at time t. The year 1990 is
used as a base year as it is free of economic shocks. Hence TUIt is computed as follows:
TUI t = 100
TPPt
.
Pt
(7)
A higher TUI implies a higher affordability to upgrade. Exhibit 6 shows the changes in
TUI over time.
5
Results
Three tests were conducted to evaluate household mobility (Exhibit 7). In Model
A, the TUI variable is included to test the likelihood for a household to prepay. However,
several macroeconomic variables such as changes and volatility in HDB prices and
3
Before May 1996, the minimum down payment required for the purchase of private housing is 10% of
sale price. The minimum down payment required is, however, raised to 20% of sale price on May 1996 as a
measure to curb speculation. In this case, the TUI is adjusted accordingly to reflect the change in policies.
As at Sep 2002, buyers can use their Central Provident Fund to pay 10% of the sale price as down payment
in the latest changes.
15
private prices and difference between the public and private rates were omitted because
these variables are used to derive TUI and may lead to multi-collinearity.4
In Models B and C, we replace TUI with the variables omitted earlier. In addition,
we include another variable, the relative price difference between private housing and
public housing (RELPI) to analyze whether the HDB mortgagor is more likely to prepay
when the price differential has decreased. The relative price differential is obtained by
dividing the private property price index by the residential price index, with the base year
for both indices fixed at 1990. Hence, the larger the value of RELPI , the greater the price
differential between HDB and private residential properties. The difference between
Model B and C is that the households’ mobility and prepayment decisions are tested
against the public HDB rate in Model B whereas their decisions are tested against the
difference between the public and market rates in Model C. The likelihood ratio test
shows that at least one variable in all the three tests are significant and improved the
performance of the model.
The TUI variable is found to be positively related to the probability that the
household will move. In other words, households are induced to move when their level of
upgradability improves. Hence, Stein’s implicit assumption that the households will
move to consume more of the housing good when they able to do so is empirically
supported. The significance of TUI also reinforces the importance of the interaction
between starter homes and larger dwellings as postulated by Ortalo-Magne and Rady
(2001). In addition, the relationship between the main upgrading programme
(MUPB4SAL), which is used as proxy for alternative means of higher consumption of the
housing good, and household decision to move is negative but highly insignificant. Hence,
we cannot conclude that households use maintenance as an alternative means of
consuming more of the housing good (Mandic, 2001).
An interesting result from our tests is the relationship between change in GDP
(CGDP) and likelihood to move and prepay. The change in GDP, which also acts as a
proxy for income growth, is negatively related to the likelihood to move. One likely
4
Although TUI is computed using the change in income and mortgage rates, we further control for change
in GDP and mortgage rate volatility in model A as the treatment of these inputs in deriving the mortgage
volatility and change in income is different. Furthermore, as shown in (5), the movements of GDP and
mortgage rate may offset each other in the derivation of the overall TUI.
16
reason is that most households use the additional income for consumption of other goods
rather than housing. Given that the average sample household in this study is below the
national average, consuming housing requires an increase not only in income but also in
wealth. Thus increases in income may not be sufficient to induce them to move to better
housing. However, households that experience declines in income may be forced to
downgrade from their current housing consumption because they can no longer afford the
mortgage repayments.5
Changes in the Singapore Stock Exchange index (CSES) are positively related to
the borrower’s likelihood to move. This result provides an interesting contrast to the
findings of Ong, et. al (2002) and Zorn and Lea (1989).
A negative relationship
established by Zorn and Lea (1989) is attributable to better alternative investments than
paying down their mortgage. However, low to middle income households prevalent in
our sample are unlikely to have considerable investments in other assets. Hence, we
attribute the positive relationship to market sentiment reflected in the stock market that
helps to boost the demand and price in the general residential market.
We further establish that the smaller the relative price differential between private
and public housing (RELPI), the greater the likelihood to move and prepay. The
relationship is consistent with the TUI measure. Similarly, it is found that higher price
volatility is negatively related to household likelihood to move. This implies that buyers
are relatively risk adverse.
Most of the borrower-specific variables and property-specific variables are
insignificant in comparison to the macroeconomic variables. Among the property-specific
related variables, only the age of apartment and the date of purchase of unit are
significant. It is interesting to note that all borrower specific characteristics, except only
variables JOINT and MAL, are insignificant. These findings deviate from those of studies
on mobility decisions (for example, Davis and Pickles, 1991; Knapp, White and Clark,
2001), especially for variables representing household size, age of head of household and
income level of household.
5
Ong (2000) also discovers a similar relationship between mobility and change in GDP in his study on
prepayment of private mortgages using transaction data and provides a similar reasoning.
17
The mortgage specific variables have better explanatory power relative to
borrower and property specific variables. Interestingly, the loan to value ratio (LV) is
positively related to the household likelihood to move, although the relationship is
insignificant at 10 percent significance level. The relationship implies that mortgagors
who borrow a larger proportion of debt are more likely to move compared to one with
less debt, albeit the relationship is statistically insignificant.
Further analysis also shows that the private mortgage rate volatility (SMORTVOL)
is negatively and significantly related to the decision to move. This result implies that the
owners are relatively risk adverse and are unlikely to move and prepay when the market
is uncertain. In addition, it is also found that the higher the payment to income ratio
(PAYINC), the greater the likelihood the owners will move. However, as shown in later
analyses in Model B and Model C, the significance of the relationship is not stable when
we test with other variables.
Like Model A, the other two models provide a good fit with Log likelihood of –
39.78 and -41.46 respectively. Most of the variables exhibit similar relationship, except
payment-to-income ratio, which becomes insignificant. A likely reason is due to the
inclusion of the public mortgage rate as a test variable. Conversely, the property-specific
variables, which were omitted previously, exhibit similar relationship as that in the
preliminary test we did earlier in Model A.
Past empirical tests on mobility decisions show that buyers tend to be insensitive
to the prevailing mortgage rates (Davis and Pickles, 1991). The probit model shows that
mortgage interest rate is positively related to household mobility, which differs from the
results in Davis and Pickles (1991) and Ong (2000), that examines private adjustable rate
mortgages in Singapore. Nevertheless, the results are consistent with the findings of Zorn
and Lea (1989). As suggested by Zorn and Lea (1989), such a phenomenon may be a
response to the payment shock of rising mortgage payments. Interestingly, a separate
analysis shows that the spread between the private and public subsidized rate is
negatively related to prepayment risk, but not significant as shown in Model C6. The
6
We also carried out a semi-parametric duration test, and the results (available on request) are qualitatively
same as those of probit tests.
18
results imply that changes in the relative changes of private mortgage rate relative to the
subsidised rate do not significantly impact on the HDB households to move.
Consistent with the results in Model A, we found the relationship between
household likelihood to move and macroeconomic variables to be highly significant.
Changes in the HDB prices over the households’ occupation period, which are used to
proxy the property gains earned by households during the same period, are negatively
related to mobility. The results differed from the findings in the mobility studies on
European and US households, where capital gains are found not be the critical
determinants in households’ decision to move (Pickles and Davis, 1991; Ioannides, 1987).
When the change in the HDB prices variable is replaced by actual capital gains,
we find that the probability to move is positively and significantly related to actual capital
gains (results available on request). As buyers often pay a premium over the appraised
value7, the change in HDB prices may not be the best proxy for actual gains. Further tests
show that the correlation between the actual capital gains and the change in HDB price is
relatively low ( ρ =0.324).
It is noted that the price indexes generally reflect the changes in price in the
previous quarter, because of the process of compiling and collection of data. In other
words, CHDBPR should capture expected housing returns. According to the works of
Ortalo-Magne and Rady, housing market expectations do not affect much the moving
decision of credit constraint families. Yet, our results show that household expectations
of market returns have a negative and significant relationship with their likelihood to
move. He and Liu (1998) also discover that household expectations affect mobility
decisions. We suspect that not all households residing in HDB flats are credit-constrained;
some households hold HDB flats for investment purposes. We further conduct the
following tests to verify this issue.
We conduct three more tests to extend the above analyses. The equity constraint
model implies that households move when their equity constraints are reduced. In the
first test, we include the housing equity at the point of sale in the model and an interactive
variable that captures the household income level and the changes in income. The results
7
The average premium is 51% over the appraised value (Exhibit 5).
19
tabulated in Exhibit 8 show, however, that housing equity is negatively and significantly
related to household likelihood to move. We attribute the unexpected result to the
inadequacy of housing equity in capturing the changes in private residential prices. Given
that private residential prices are co-integrated with public residential prices (Ong and
Sing, 2003), a higher equity held by household resulting from increases in prices is
usually matched by a higher down payment required for their desired apartment. Hence,
the TUI better captures the equity constraint effect.
Further, we introduce an interactive variable (HINCCGDP) between change in
GDP over household’s length of stay, and their income level, HIINCOME, which took
the value 1 if their INCLEV was less than 1. The coefficient for HINCCGDP is positive
and significant, indicating that higher-income households are likely to move when
income increases, as compared to the lower-income households.
According to the models of Ortalo-Magne and Rady, households that are young
and credit constrained would be sensitive to changes in housing price, as compared to the
more mature and richer households. In our second test, we introduce YOUNGTUI in our
model. YOUNGTUI is an interactive variable derived by multiplying the change in TUI
over the household’s length of stay with YOUNG, a dummy variable that took the value 1
if the owners are more than 50 years old. Given that the mean age of marriage in
Singapore is about 25 years old8 , it is reasonable to assume that households with their
heads of households older than 50 years belong to ‘mature’ families. We find a positive
and significant coefficient for YOUNGTUI, suggesting that younger families are more
sensitive to changes in TUI, as compared to more mature families. The results support the
dynamic model of Ortalo-Magne and Rady. Additionally, the change in TUI is shown to
be insignificant for the more mature households.
We further introduce LOTUI in our third and last test, where LOTUI is derived by
multiplying the change in TUI over the household’s length of stay with income level,
LOW, a dummy variable that took the value 1 if its INCLEV was less than 1. We find that
financially constrained households are more sensitive to changes in their affordability
levels, as compared to the more well-off families, and this result further supports the
Ortalo-Magne and Rady model.
8
Singapore Census 2000
20
6
Conclusion
The distinct demarcation between pubic and private housing in Singapore allows
us to test Stein’s hypothesis (1995) by modeling household mobility and their ability to
upgrade. In addition, we also test the Ortalo-Magne and Rady life cycle model. Our
results provide empirical support for the Stein and Ortalo-Magne and Rady models. Our
paper also differs from those of Bardhan et. al (2003) and Leung et. al (2003); both use
aggregate data to discern the validity of the loss aversion and equity constraint
hypotheses.
Our analysis shows that households tend to move up the housing spectrum to
consume more housing good when they can afford to do so. In other words, this study
provides empirical support for Stein’s implicit assumption that would-be movers will
move to consume more housing. Interestingly, we find that major housing improvements
do not explain the decision to move. Hence, Stein’s model works well even if owners
have the choice to improve their current dwelling.
In addition, borrower- and property-specific variables play a less important role in
household mobility. Unlike households in Cardiff or New York, households in Singapore
appear to make mobility decisions based on capital gains and price movements. This,
however, does not mean that changes in the household demographic profile are not
important. Our tests only use the demographic profile of the households when they
purchase the flats. The data, unfortunately, does not capture household demographic
changes over time. It will be interesting to further evaluate the effect of demographic
changes in households on mobility and upgrading. Last but not least, future research on
the mobility behavior of households in different private housing segments would be to
further verify the equity constraint hypotheses would be insightful.
21
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25
Exhibit 1
Precentage of Transactions of each type of housing
100%
90%
80%
Percentage
70%
60%
50%
40%
30%
20%
10%
0%
1Q97
2Q97
3Q97
4Q97
1Q98
2Q98
3Q98
4Q98
1Q99
2Q99
3Q99
4Q99
1Q00
Time
3room
4room
5room
exec
26
Exhibit 2: Cross tabulation between capital gains and Loan-to-Value ratio and
ANOVA Test
Capital Gains
<0
0-30%
Total
30%-50%
>50%
Loan
<0.2
4
0
2
6
12
to
0.2-0.5
8
7
2
55
72
value
0.5-0.7
14
12
7
88
121
Ratio
>0.7
7
20
15
46
88
33
39
26
195
293
Total
Test
Sum of
Squares
Between Groups
df
Mean Square
F
7.588
3
2.529
Within Groups
330.767
289
1.145
Total
338.355
292
Sig.
2.210
.087
Exhibit 3: Housing Equity and Change in Private market housing price index
Housing Equity at time of sale relative to housing sale price (%)
<0
0-30
30-70
70-100
Total
>100
<0
0
0
25
32
13
70
Change
0-20%
0
0
1
6
2
9
in
21-50%
0
1
1
4
8
14
private
50%-
0
2
9
12
21
44
price
70%
index
70%-
0
0
3
6
15
24
1
0
0
3
126
130
1
3
39
63
185
291
100%
>100%
Total
27
Exhibit 4: Brief Description of Variables
Variable
Borrower-specific Characterisitics
BUYERAGE
Age of the older owner of the flat
MAL
Malay
IND
Indian
OTHERS
Other races excluding Chinese, Malay and Indian
HHOLD
Size of Household including owners
INCLEV
Household Income Level
Property-specific explanatory variables
R3
3 room
R4
4 room
BLDGAGE
Age of the building
PDATE
Date of purchase of flat. It is also the date of origination of
loan
MUP
Whether undergone Main Upgrading Programme before sale
Mortgage-specific explanatory variables
OUTSP
Ratio of outstanding loan to the selling price at time loan is
refinanced
PREMIUM
Market Premium
LV
Loan to value ratio at point of purchase
SPRICE
Selling Price
SVAL
Market valuation of property at sale
TERMDATE
Date where loan is refinanced or censored
PAYINC
Payment to income ratio
PREPAY
Prepayment
Macroeconomic explanatory variables
CSES
Change in the Stock Exchange of Singapore index
CGDP
Change in GDP
CHDBPR
Return from investing in HDB property market
28
SMORTVOL
Volatility in private mortgage rates
SHDBINT
HDB interest rate as at point of prepayment or censored date
HDBVOL
Volatility in HDB price index
INTDIFF
Difference in interest between HDB and private interest rate
CRPI
Return from investing in Private Residential market
RELPI
Index of relative price of private housing with
respect to HDB price
TUI
Threshold Upgradability Index
29
Exhibit 5: Descriptive Statistics
VARIABLE
MEAN
STD. DEV.
MINIMUM
MAXIMUM
FLOOR
8.65
5.48
1
25
R3
.539
.499
0
1
R4
.335
.472
0
1
BUYERAGE
38.48
10.98
21
79
MAL
.138
.345
0
1
IND
.488
.216
0
1
OTHERS
.505
.709
0
1
JOINT
.786
.41
0
1
HHOLD
3.133
1.45
1
7
INCLEV
.770
.522
0
3.93
PPRICE($)
115423
89735
20000
800000
SPRICE($)
97261
126100
0
750000
LOAN ($)
63401
56516.7
1800
328000
57.3
21.4
22.9
100
OUTSTAND($)
21525.29
37206.96
0
287346
PREMIUM (%)
51.3
10.11
-28.9
56
MUP
.318
.466
0
1
24.213
4.909
8.75
33
.556
.202
.19
1.55
HDBVOL
43.498
17.455
0
80.6
SHDBINT(%)
2.219
1.183
.43
4.51
CSES
.375
.549
-.554
2.289
CGDP
.721
.580
-.321
2.917
CHDBPR
1.071
1.009
-.2117
3.062
CHDBMR
2.926
2.409
-.561
9.488
LV (%)
BLDGAGE
SMORTVOL(%)
30
INTDIFF(%)
4.299
1.297
2.09
9.69
CAPGAIN
.728
1.407
-1
18.4805
99.3705
6.5294
69.9
114.1
TUI
Notes: The data for this study were provided from Housing Development Board (HDB) Branch Office of Singapore. A sample of
594 resale mortgages spanning a period from 1982 to 2000 is observed. The buyer characteristics are the age of the buyer
(BUYERAGE), the dummy variables for Malay (MAL), Indians (IND) and others (OTHERS). Other buyer characteristics
include size of household (HHOLD), and the household income level (INCLEV). The household income level is computed by
normalizing the reported household income with the overall household income adjusted to 1990 prices. The property related
variables include dummy variables of 3-room (R3) and 4-room (R4), age of unit (BLDGAGE) and dummy variable for Main
Upgrading Programme (MUP). The loan characteristics are loan- to- value ratio (LV), the outstanding balance (OUTSTAND)
and the payment- to- income ratio (PAYINC). Other variables include the purchase price (PPRICE), the selling price
(SPRICE), the premium which is the amount paid above valuation and the date of originations and prepayments.The
macroeconomic factors include the change in SES index (CSES), change in GDP (CGDP), change in HDB mortgage rate
(CHDBMR), change in HDB index (CHDBPR), the HDB public rate at point of sale (SHDBINT), the HDB price volatility
(HDBVOL), the private mortgage volatility rate at point of sale (SPMORTVOL) and the spread between the public and private
rates (INTDIFF). The households’ ability to upgrade is represented by the threshold upgradability index (TUI).
Exhibit 6: Threshold Upgradability Index
TUI as 1990 as base
140
120
100
80
TUI as 1990 as base
60
40
20
19
80
19 1Q
80
19 4Q
81
19 3Q
82
19 2Q
83
19 1Q
83
19 4Q
84
19 3Q
85
19 2Q
86
19 1Q
86
19 4Q
87
19 3Q
88
19 2Q
89
19 1Q
89
19 4Q
90
19 3Q
91
19 2Q
92
19 1Q
92
19 4Q
93
19 3Q
94
19 2Q
95
19 1Q
95
19 4Q
96
19 3Q
97
19 2Q
98
19 1Q
98
19 4Q
99
20 3Q
00
2Q
0
31
Exhibit 7 Probit Model of Mobilty
Coefficients
Variable
Model A
Model B
Model C
(Substitute SHDBINT
with INTDIFF)
CONSTANT
5529.2342
6180.0000
6306.4419
(.0000)
(.0000)
(.0000)
0.3340
0.5600
- 0.3678
(.9821)
(.9734)
(.9830)
Borrower-specific
variables
BUYERAGE
MAL
IND
JOINT
HHOLD
INCLEV
1.7205*
1.6840*
1.6191*
(.0010)
(.0035)
(.0039)
-0.3929
- 0.6061
- 0.5436
(.6279)
(0.5443)
(.5159)
0.7759
*
0.8097**
0.7411**
(.0828)
(.0753)
(.0950)
-0.6427
- 0.2147
- 0.1909
(.6234)
(.1811)
(.2165)
0.2337
0.9698
0.6062
(.5860)
(.8464)
(.9028)
-2.7741 *
- 3.077*
- 6.316*
(.0000)
(.0000)
(.0000)
Property-specific
variables
PDATE
PREMIUM
1.4310
(.3049)
BLDGAGE
FLOOR
R3
R4
MUPB4SAL
0. 1097**
1.5991
(.3043)
0.1365**
1.6022
(.2970)
0.1384*
(.0427)
(.0599)
(.0455)
-0.3567
- 0.1358
- 0.2121
(0.2701)
(.6868)
(.5261)
0.8382
- 0.1335
- 0.1811
(.9888)
(.8546)
(.7952)
-0.7245
- 0.5014
- 0.5488
(.2189)
(.4707)
(.4142)
-0.3398
- 0.2802
- 0.3085
(.3102)
(.5147)
(0.4647)
32
Mortgage-specific
variables
LV
INTDIFF
1.3501
1.5873
1.6596
(..4102)
(.1383)
(.1087)
NA
NA
- 0.2705
(0.7611)
SHDBINT
NA
2.295*
NA
(.0386)
PAYINC
SMORTVOL
0.7523 *
0.1699
0.2075
(.0033)
(0.6238)
(.5387)
-27.7439*
-38.8025*
-36.3303*
(.0000)
(.0000)
(.0000)
Macroeconomic variables
CSES
CGDP
CRPI
CHDBPR
HDBVOL
TUI
2.8233*
3.1348*
2.7925*
(.0038)
(.0053)
(.0151)
-19.7524*
-27.823*
-27.8606*
(.0000)
(.0000)
(.0000)
NA
5.8705*
NA
NA
0.2609
6.6037*
(.0005)
(.0003)
- 2.4190*
- 2.6393*
(.0015)
(.0005)
- 0.2808*
-0.1062
(.0152)
(.2656)
NA
NA
- 7.9365*
-8.1827*
(.0005)
(.0002)
-39.77867*
-41.45977*
(.0003)
RELPI
Log likelihood
NA
-45.79935*
Predicted
Model A
Model B
Model C
Actual
0
1
Total
0
1
Total
0
1
Total
0
299
2
301
299
2
301
299
2
301
1
9
284
293
9
284
293
9
284
293
Total
308
286
594
308
286
594
308
286
594
Notes: * Indicates significance at 5 per cent level and ** indicates 10 per cent level
33
The data for this study were provided from Housing Development Board (HDB) Branch Office of Singapore. A sample of 594 resale
mortgages spanning a period from 1982 to 2000 is observed. 3 tests have been carried out. In Model A, The threshold upgradability
index (TUI) is included. However, the HDB mortgage rate at the point of sale (SHDBINT), change in private residential price index
over the years of occupation (CRPI), price volatility of HDB housing (HDBVOL) and change in HDB price (CHDBPR) are omitted.
The buyer characteristics are the age of the buyer (BUYERAGE), the dummy variables for Malay (MAL), Indians (IND) and others
(OTHERS). Other buyer characteristics include size of household (HHOLD), and the household income level (INCLEV). The property
related variables include dummy variables of 3-room (R3) and 4-room (R4), age of unit (BLDGAGE) and dummy variable for Main
Upgrading Programme (MUP). Some of the property characteristics are omitted in Model A because they are highly insignificant. The
loan characteristics are loan- to- value ratio (LV) and the payment- to- income ratio (PAYINC). Other variables include the date of
originations (PDATE) and the amount paid over the valuation (PREMIUM). The macroeconomic factors include the change in SES
index (CSES), change in GDP (CGDP). In model B and C, the TUI is replaced by the omitted variables. In model B, the change in
HDB mortgage rate is used (SHDBINT) and the difference between private mortgage rate and public mortgage rate (INTDIFF) is used
in model C. Actual capital gains (CAPGAINS) is included in models B and C to test the appropriateness of CHDBPR as a proxy of
capital gains ,and is the difference between the selling and the purchase price and divided by the latter. The relative price of private
property to the price of HDB flats is represented by (RELPI). The Log likelihood ratio test shows that at least one variable is
significant in all 3 models at 5% level of significance. The restricted log-likelihood is -411.6756.
(Source: Author’s computation)
34
Exhibit 8: Housing Equity, and Interaction between Low Income and Equity
Constraints
Test 1:
Test 2:
Test 3:
Inclusion of equity, and
Interaction between TUI
Interaction between TUI
interaction between income
and Young Households
and Low Income Level
level and change in GDP
per capita.
Coefficient
P
Coefficient
P
Coefficient
P
CONSTANT
5394.8386
.0000
4817.4517
.0000
4930.7802
.0000
BUYERAGE
.1790**
.0115
-
-
-0.5358
.7008
MAL
7.971**
.0001
1.5061**
.0039
IND
-4.6234**
.0487
0.4499
.5920
0.3170
.7058
JOINT
0.2055*
.0904
0.9223**
.0498
0.9217 **
.0408
HHOLD
-0.8378
.1925
-0.1512
.2794
-0.1224
.3838
INCLEV
-
-
0.1575
.7093
-
-
PDATE
-11.7758**
.0000
-2.3958**
.0000
-2.4532 **
.0000
PREMIUM
1.7848
.8758
0.5349
.7032
0.70244
.6184
MUPB4SAL
0.1988
.8874
-0.1425
.7439
-0.1712
.6981
DUR
-0.6662**
.0004
-0.1595**
.0264
-0.1667**
.0190
BLDGAGE
0.1412 **
.0477
0.1092
.1092
0.1210
.0883
FLOOR
0.7596
.2801
-0.1320
.9687
0.7953
.8152
R3
-2.7133
.4128
0.4919
.5236
0.4141
.5634
R4
-0.6882
.8281
-0.7844
.9186
-0.1707
.8114
LV
-2.5229
.4550
1.0106
.2552
1.1083
.2226
INTDIFF
-2.2437
.7173
-4.9730
. 7012
-4.5260
.6752
PAYINC
2.8394*
.0611
0.4045
.1439
0.3727
.1641
CSES
1.9216**
.0363
3.9287**
.0000
4.2002 **
.0000
HIINCCGDP
7.9432*
.0571
-
-
-
-
CGDP
-73.4856**
.0199
-17.2773**
.0000
-17.8392 **
.0000
EQUI
-101.6782**
.0000
-
-
-
-
1.4330 **
.0061
35
SMORTVOL
-31.4476 **
.0000
-27.4843**
.0000
-27.8267 **
.0000
LOTUI
-
-
-
-
6.9003
.0992
YOUNGTUI
-
-
2.5245**
.0461
-
-
CTUI
-
-
-3.6222
.1903
-0.3055
.1921
Log likelihood
-39.3518
-42.07866
*
-41.83171
Notes: * Indicates significance at 5 per cent level and ** indicates 10 per cent level
EQUI represents the housing equity at the point of sale. CTUI represents the change in TUI over the households’ length of stay.
HIINCGDP is a interactive variable between change in TUI and HIINCOME, which takes the value 1 when INCLEV is greater than 1.
Similarly, LOTUI is the interactive variable between change in TUI and LOINCOME, which takes the value 1 when INCLEV is less
than 1. YOUNGTUI is the interactive variable between CTUI and YOUNG, which takes the value 1 if the head of household is
younger than 50 years old.
36