Estimating Hedonic Cost Functions: Case of Singapore’s private residential
property markets
Coulson, N. Edward1, Dong, Zhi2 and Sing, Tien Foo3
Date: May 1, 2015
1 Department of Economics and Lied Institute for Real Estate Studies, University of Nevada, Las Vegas. Email:
[email protected]
2 Department of Property, University of Auckland Business School. Email: [email protected]
3 Department of Real Estate, National University of Singapore. Email: [email protected]
1
Estimating Hedonic Cost Functions: Case of Singapore’s private residential
property market
Abstract
This paper aims to empirically test hedonic marginal cost function using characteristics of
condominiums and firms in Singapore’s private non-landed residential property market. We
propose a two-stage hedonic pricing model, where the first stage is the estimation of a hedonic
model for Singapore’s condominiums. Marginal characteristics prices are then calculated and
used as a dependent variable in the estimation of marginal offer/cost functions. We divide the
private non-landed residential property markets in Singapore into five sub-markets by planning
region, and merge three different databases including project level data, property transaction
information and developers’ characteristics for the period from January 1995 to March 2009.
Developers are differentiated by age since incorporation, initial size (i.e. paid-up capital) upon
incorporation, market share, listing status, and time varying cumulative development experience.
We also control for a set of quality attributes of the non-landed projects. We find that larger
firms tend to have significantly lower marginal costs for construction in respect to floor level for
buildings. We are able to provide useful insights on developers’ “learning-by-doing” strategies
in real estate development and their asymmetric marginal cost of construction.
Keywords: hedonic theory, cost function, developer heterogeneity, condominium price, new sale
price, competitive market
JEL Classification: D24, D41, R31
2
I. Introduction
This paper estimates hedonic marginal cost (or marginal offer) functions for private residential
property developers in Singapore. In the housing literature, there are many examples of the
estimation of hedonic bid functions by consumers. These estimates of marginal willingness-topay and consumer’s surplus for (continuously measured) housing characteristics are useful in the
cost-benefit analysis for environmental and other locational attributes. Zabel and Kiel (2000)
estimate the marginal willingness-to-pay for air quality; Coulson and Bond (1990) find that
significant difference in willingness-to-pay of households in high- and low-income brackets; and
Coulson, Hwang and Imai (2003) empirically estimate demand functions in neighborhoods with
mainly owner-occupation.
The opposite side of the demand function is the measurement of marginal offer (cost) functions.
Offer functions are usually thought to be non-estimable because housing supply is typically
assumed to be fixed: the net additions to supply are negligible compared to the incumbent stock
of housing. This assumption is not true in fast-growing housing markets, such as Singapore’s
private housing markets. Singapore’s total housing stock increased by about eighteen percent in
five years from 1995 to 2000, and by about thirty percent in fourteen years from 1995 to 2009
(Department of Statistics, Singapore). Singapore’s housing market can thus be used as a suitable
field laboratory for the estimation of marginal offer functions. We collected three different
sources of data on a large sample of transactions of new condominiums and apartments and the
corresponding firms’ (developers’) characteristics. We then consolidate three databases based on
the information of condominiums and apartments, development project details and firm
characteristics, and use the consolidated dataset to estimate the supply-side hedonic functions.
We can, to our knowledge for the first time, estimate marginal offer functions in private
residential markets. We estimate marginal offer functions for two important and easily measured
housing characteristics: the floor area and the floor level. Firms are differentiated in their
construction technology by their size, public listing status and past development experience (Ooi,
Sirmans and Turnbull, 2006; Dong and Sing, 2014; Dong and Sing, forthcoming). These
characteristics of firms are expected to shift cost curves in the new sale residential market. We
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conduct two-stage analyses for hedonic price functions and firms’ construction cost functions.
We identify the hedonic price functions for five distinct submarkets corresponding to the five
planning regions in Singapore. We then model firms’ cost function for construction with respect
to static and time-varying characteristics of condominiums and apartments.
Our empirical evidence shows that larger firms’ supply curves distinguish themselves from those
of smaller firms, and that larger firms sit on lower cost curves than smaller firms. Firms’
construction experience and market penetration significantly reduce marginal cost on floor level,
though the results on the marginal cost on square footage are relatively weaker compared to the
estimates for the floor level. Larger and more experienced firms enjoy significant reduction in
marginal cost when they build high-rise condominiums relative to smaller and less experienced
firms. There is an inverse U-shape relationship between developers’ time varying cumulative
construction experience and developers’ marginal costs on the floor level. The findings imply
that developers improve development efficiency by the floor level of buildings, based on their
experience. Developers’ initial paid-up capital signals their potential in achieving marginal cost
reduction in terms of floor area and floor level in a project.
This article contributes to the hedonic pricing literature by providing insights into the
understanding of firms’ construction cost functions. We develop a theoretical framework, and
estimate marginal cost functions on construction in a fast-growing market, where firms are
differentiated by technology advantage. This research presents new empirical evidence on
differential marginal cost functions for large and small firms when supplying a bundle of quality
characteristics for differentiated products. It also contributes to the understanding of land value.
The findings can lead to re-visiting the bid-rent function for land parcels when firms have
differentiated characteristics and varied cost-reduction benefits on developments. Firms are
found to be asymmetric in their construction costs and thus, they have asymmetric land value
functions and bidding strategies in land tenders (Dong and Sing, forthcoming).
The rest of the article is organized as follows. The next section provides the theoretical
development of the marginal offer function and its empirical estimable form. The third section
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describes data source and relevant statistics. The fourth section discusses the results on the cost
function. The last section concludes this research.
II. Theory and Empirical Model
Theory and empirical model
The theory of equilibrium in a market of differentiated commodities was developed by Rosen
(1974). We briefly review this theory, and the details can be referenced in Rosen (1974).
Construction firms are assumed to have cost functions that describe the cost of apartment
construction, C,
as a function of the unit’s location and structural characteristics, jointly
represented by the vector Z , characteristics of the firm, X, and an unobservable we label as
technology 1:
𝐶 = 𝐶( 𝑍, 𝑋; 𝑞)
(1)
C is convex in quantities, so that Cz , and Czz>0. Every unit has a unique set of characteristics
and the technology used to build a unit with that set of characteristics is unique and uncorrelated
with X, although we allow it to be correlated with Z. The market is assumed to be competitive in
the sense of Rosen (1974), so that prices are driven down to the point where each firm earns zero
profit. The cost functions become offer functions (so that we use these words interchangeably),
and each of the two firms becomes the lowest cost provider for some region of Z. The convexity
assumption means that the relationship between any two firm’s cost curves is shown in Figure 1,
where Zi represents the (continuously measured) amount of the ith condo attribute. The two
curves represent costs associated with two levels of firm characteristic X where for clarity we
assume that X is a scalar and X2>X1 and Cx>0. The schedule P(X) is the market price for units of
various sizes of Z. At level Z1, firm 1 is the lowest cost producer and the value of its cost
function determines the market price of the housing unit. At level Z3 firm 2 is the lowest cost
1
In a sense, we employ the notion that the construction of each given housing unit is by a different firm, in the
sense that the place and circumstances of that construction employsa unique technology shock. In the
estimation of the cost functions below, we treat the technology as correlated with the firm’s choice of Z, but not
with its characteristics X for reasons discussed below. The technology shock may nevertheless be correlated
across observations within the same firm, which we will account for by the usual clustering algorithm for the
standard errors of the coefficients.
5
producer. Note in particular that at the crossing point, Z2, the slope of the smaller firm’s cost
function is greater than that of the larger firm.
[Insert Figure 1 here]
The extension to a large number of firms, considered in e.g. Epple (1987), establishes that the
lower envelope of these large number of cost functions becomes the observed hedonic price
function that relates the price of the unit to its embodied characteristics. Firms sort themselves
along the spectrum of Z, so that (in this case) low X firms produce units with small Z. At each
offered level of Z there is a firm whose cost function is tangent to P(Z), that is, Pz = Cz(Z, Xj) for
some firm j.
One can then write down a function that maps X to Z as in Epple (1987) 2.
The function P(Z) is readily estimated from data on transactions and product characteristics.
However, it is usually of more interest to estimate the bid and offer functions that underlie P(Z).
A number of studies have attempted to estimate bid functions in the housing market, following
the advice of Epple (1987), Bartik (1987), Kahn and Lang (1988) and a number of subsequent
authors. Examples include Palmquist (1984), Coulson and Bond (1990), Kiel and Zabel (2000),
Coulson, Hwang and Imai (2003), etc.
However, we know of no examples where the
corresponding offer functions have been estimated. This would seem to be because it is often
hypothesized in studies of housing markets that the supply is fixed by the historical accumulation
of housing inventory and therefore exogenously given. However this assumption would seem to
have less force in a rapidly growing economy such as exists in Singapore. In such a case it
should be possible to estimate the cost function of producers, and as shown in Epple (1987), the
procedure should parallel that of bid functions. In the literature cited above, the demand (or bid)
function is specified as a regression of the hedonic price of the attribute on both the personal and
product characteristics attached to the individual transaction.
2
Similarly, consumers maximize utility subject to that hedonic function and their budget constraint. These
buyers exhibit concave bid functions that arise out of the maximization problem, which also exhibit a single
crossing property with respect to consumer characteristic Y, and a function that matches Y to Z (and thus to X),
all via the hedonic price function P(Z).
6
In a similar vein, in the present paper we want to regress the hedonic price of Z on both firm and
housing unit characteristics to obtain the marginal offer curve for Z. The first step is to estimate
the function P(Z) from market transaction data. For each observed transaction, the hedonic price
of attribute Z is calculated as the derivative of P(Z) with respect to attribute level Zi. Note that
this requires that P(Z) be nonlinear in Z. Linearity is unlikely to be the correct functional form
for P(Z) in any case (Rosen, 1974, Coulson, 1989, Ekeland, Heckman and Nesheim, 2002 and
2004, Ekeland, 2005) but nonlinearity is required for identification in these models. In the
second step these hedonic prices are regressed on Z and X.
In the hedonic bid literature, Epple (1987), Bartik (1987) and others have noted an identification
problem. Because the hedonic price function is nonlinear, consumers jointly choose price and
quantity. If there are any unobserved consumer attributes (“taste”), then shifts in that attribute
will be correlated with shifts in not only price but also quantity.
Therefore quantity is
endogenous in the bid function. Bartik’s particular example is instructive. He notes that suitable
instruments must be correlated with the consumer’s choice of quantity of Z, but not with taste,
and that variables that affect the budget constraint fulfill these conditions. If the parameters of
the bid function are constant across submarkets, but the hedonic function varies across
submarkets—typically regionally delineated submarkets—then indicator variables for these
submarkets, possibly interacted with agent characteristics, will be suitable. While Ekeland,
Heckman and Nesheim (2002 and 2004) and Ekeland (2005) note that with sufficient
nonlinearity estimation with a single market is possible, both Bartik (1987) and Epple (1987)
emphasize the practical importance of multi-market estimation in the estimation of bid functions.
We assume a similar phenomenon is at work in the supply function estimation. If there is an
unobserved supplier attribute (“technology”) then Z will be endogenous in the offer regression,
since shifts in the technology will cause the builder to change the vector Z. The cost function is
assumed constant across districts, but the hedonic function varies, due to differences in demand.
Then district binaries can serve as instruments in the estimate of the marginal offer function, as
well as interactions of these dummies with exogenous demand shifters Wi (to be discussed
below). We estimate the hedonic price index for five distinct markets in Singapore, using Chow
tests to justify our assumption of market segmentation, and use the variation in hedonic price
7
functions to model the (common) cost function for condo construction in Singapore, as a
function of firm characteristics.
Thus in stage 1 of this procedure we estimate a hedonic price function for condos in Singapore:
ln 𝑃𝑖𝑗 = 𝛽0 + 𝛽1𝑗 𝑍𝑖𝑗 + 𝛽2𝑗 𝐶𝑗 + 𝛽3𝑗 𝑇𝑗 + 𝑒𝑖𝑗
(2)
where i is the index for the individual condo unit and j = 1. . . .5 is the index for Singapore
districts (more detail about which in the next section) 3. Also
Pij = sales price of condo i in region j
Zij = vector of condo characteristics
Cj = vector of binary variables for postal codes within j.
Tj = vector of year-of-sale dummies in each district
We then calculate for each i the hedonic price of that unit’s kth characteristics Zijk as
𝐻𝑖𝑗𝑘 = 𝜕𝑃𝑖𝑗 ⁄𝜕𝑍𝑖𝑗𝑘
(3)
The second stage is the estimation of the marginal offer function:
𝐻𝑖𝑗𝑘 = 𝛾1 𝑍𝑖𝑗𝑘 + 𝛾2 𝑋𝑖𝑗 + 𝑣𝑖𝑗𝑘
(4)
where X is a vector of firm characteristics, and as noted above the unit characteristics, Z, are
endogenous because it is correlated with the technology ν. In the usual logic of two state least
squares estimation we can replace Z with the fitted values from the regression
𝑍𝑖𝑗𝑘 = 𝛿1 𝐷𝑗 + 𝛿2 𝐷𝑗 𝑊𝑖𝑗 + 𝜀𝑖𝑗𝑘
(5)
and the parameters of interest in the marginal offer function can be consistently estimated. .
3
In the results section we limit the estimation of the marginal offer functions to two characteristics, the
floorspace of the unit and its floor. We induce additional variation in the marginal price of the unit by
interacting those two characteristics in the hedonic regression. For notational simplicity we omit that
consideration here.
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The expectation is that, given the normalization that X is an indicator of firm size, γ2 should be
negative, given the smaller slope for the larger firm at the crossing point Z2 (i.e where Z is held
constant)
III. Data
Private Residential Market in Singapore
Singapore’s housing market is made up of two distinct segments of market. It consists of a
subsidized public housing market 4, and a fully laisse-faire private housing market. Figure 2
shows the compositions of housing stocks in the two markets for the last 30 years from 1980 to
2009. The total housing stock has expanded by more than two-fold from 472,700 units in 1980 to
about 1,119,600 in 2009. The intensive public housing program in the 1980s has contributed to
the rapid expansion in the public housing stocks, which saw the ratio of public housing stocks
reaching the peak of 88.07% in 1995. The housing needs of most of the residents have been
fulfilled by 1990s, and the focus has been shifted to providing a variety of housing choices. The
government has allocated and sold more residential lands via its sales of sites program for private
developers to build for private housing units. From 1995 to 2009, the private housing stocks have
increased gradually from 11.93% in 1995 to 16.48% in 2009 (Figure 2). More than two-third of
the private housing stocks in 2009 are made up of non-landed housing units, which include
condominiums and apartments. Many private developers have become active in non-landed
developments, which consist mainly of strata-titled units with shared facilities, to meet the rising
housing aspiration of more affluent residents.
[Insert Figure 2 here]
We use empirical data on non-landed housing transactions and housing developers in the primary
(new sale) market to analyze how developers’ characteristics affect new sale prices of nonlanded housing in the subsequent section.
4
The government via its housing agency, Housing and Development Board (HDB), plans, builds, and sells public
housing flats at concessionary prices to eligible Singapore citizens, whose gross monthly household income
does not exceed S$10,000.
9
Data Source
We collected non-landed housing transaction data from Real Estate Information System
(REALIS), a public database on property transactions currently managed by Urban
Redevelopment Authority (URA), for the sample period from January 1995 to March 2009. The
transaction data include price, property attributes (floor area, floor level, property type 5), postal
address (including 6-digit postal code), planning district. We measure various spatial
characteristics, such as distances to Central Business District (CBD), Mass Rapid Train (MRT)
stations, bus stations, and other amenities such schools and seas. We find project details, such as
development size (total units in a development), date of completion and land tenure (leasehold or
freehold), and name of developer from Real Estate Developers’ Association (REDAS) online
resources and developers’ corporate websites. We also obtain developers’ directory - “Who’s
Who in Real Estate”, published REDAS various information of developers, which include
incorporate date, country of incorporation, paid-up capital, year of joining REDAS and status of
listing on the local exchange. We merge the transaction database with project details and
developers’ profiles for our empirical tests. Our final samples include 44,256 transactions that
are captured in the caveats.
Private Non-Landed Residential Property Projects and Developers
The total non-landed housing stocks for the full sample of 393 development projects are
estimated at 102,318 units. By development size, Reflections at Keppel Bay developed by
Keppel Land was the largest condominium project with a total number of 1,160 units. Whereas,
The Bayshore developed by Far East Organization is the second largest condominium
development with a total of 1,038 units.
We sort development projects by different developers and estimate the market share by dividing
cumulative new launched units over total housing stocks taking into account joint-venture
arrangements by two or more developers. Based on identities of developers and their related
parties, such as subsidiaries/parent companies, private and public vehicles and also merged
5
The non-landed properties are categorized into two types - condominiums and apartments. Condominiums are
projects built on lands with a minimum size of 0.4hectare; and they come with full facilities and no restriction
on foreign ownership. However, apartments are small projects with limited facilities. Foreigners are only
allowed to purchase apartments that are 6-storey or higher under the Residential Properties Act.
10
entities, we compute the housing market share using new total housing stocks of the
developments. Table 1 summarizes the top ten developers by shares of total non-landed housing
units developed. We found that the private residential market in Singapore is highly concentrated
with the top ten developers covering 76.04% of the total supply in the private non-landed
residential market, as shown by Table 1. By aggregate new housing units for the period from
1995-2009, City Developments and its parent firm, Hong Leong Holdings is the largest
developer with a market share of 18.22% and a total of 18,638 units. Far East Organization (with
its listed vehicle Orchard Parade Holdings) was the second largest developer with completed
units amounting to 16,691 units (16.31%). The merged entity CapitaLand (formed after the
merger of DBS Land and the Pidemco Land) takes the third position with a market share of
8.82%.
[Insert Table 1 here]
Descriptive Statistics - Overall Sample
Based the caveats lodged, the transaction data consisting of 63,315 observations capturing about
61.88% of the total non-landed residential property stocks for the sample period. The list of key
variable (with symbols) and their descriptive statistics are summarized in Table 2. The average
transaction price of the samples is S$1,069,798, and the average size of the transacted units is
126.20 square meter (sqm). The average transaction price for per square meter is S$7,978.35. We
measure various spatial variables, and the average distance to the Central Business District
(CBD) was estimated at 9.25 kilo-meter (km), and the average distance to MRT stations was
estimated at 1.14 km. We then use a dummy variable as our proximity measure, if the amenities
are within 0.3km radius; and for school 1km, which is the priority distance for primary school
allocation was used. Around 26% observations in the sample are within 1km distance from a
popular school, and 21% of condominium units are close to water body. The freehold tenure
dummy is used to indicate property that has 999 years or freehold land tenure, against 99 years
land tenure. 46% of units are on either 999 years or freehold land tenure. Around 51% of
purchasers in the sample have already owned one or more privately developed condominiums.
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Developers vary substantially from each other in relation to their age, paid up capital, developed
units and market share. The average age of developers is around 34 years from the date of
incorporation to the transaction date. The youngest developer is less than 4 months old, 0.32
year, and the oldest developer had been established around 119 years ago before the transaction
date. Lippo Group was set up as a “shell” company with S$2 paid up capital for their real estate
development operation in Singapore 6. 70% of developers are publicly traded companies. A
developer’s market share ranges from 0.02% to 16%. The largest developer’s market share is as
high as 800 times of a smallest developer’s market share. On average, a developer has completed
developing 3,697 condominium units by the time of new sale transactions.
[Insert Table 2 here]
Descriptive Statistics by Region
There are five urban regions in Singapore. Condominiums and developers exhibit a variation of
characteristics across five regions. We view regions as sub-markets in the hedonic estimation,
and thus we are able to identify the marginal price on a bundle of quality characteristics through
variations across these regions. Table 3 shows the statistics of the characteristics of
condominiums and developers, separated by five regions (Central, East, North-east, North,
West). Interestingly, Central region attracts a wide range of developments in terms of price
spectrum. The most expensive unit, sold at S$31,400,000, is located in this region. The region
boasts the largest condominium in the sample with a living area of 1,023 square meters. Small
units sold at less than 330,312 also sit in the region. The region has the closest proximity to
Raffles Place, the CBD and financial center, with an average of 5.21km distance. It also hosts the
highest-level condominium, on 53-floor, in the sample. Around 41% to 57% condominium units
in East, West and Central regions are on 999 years or freehold land tenure. North and North-East
regions have less proportion of units that are on 999 or freehold land tenure, from 19% to 22%.
Interestingly, the region with the highest land-rent—Central region—has the largest percentage
of 999 years or freehold. Central region attracts luxurious condominiums, as shown by the high
demand of 999 years or freehold land tenure (that requires a price premium), the large standard
deviation of price and the most expensive condominiums in the region.
6
This company is under family business owned by an Indonesia tycoon.
12
West region has major industrial buildings and manufacturers. The industrial sector may impose
negative impact on condominium price. This region has the cheapest unit in the sample, sold at
S$107,000. North region is less developed in relation to high quality condominiums, with the
highest new sale price of S$1,180,000. This price is around 45%, 40% and 35% of the highest
new sale price in East, West and North-East regions respectively. It is only about 4% of the
highest new sale price in Central region. North region has the lowest percent of units, only 2%,
which are close to water body. This region is relatively isolated from CBD area with the largest
average distance to CBD, around 17km. These facts may result in that the region is unattractive
to developers in regard to the development of high-quality condominiums.
Changi Airport is located in East region. It is a five-star international airport with high turnover
all year round. The largest condominium in this region is ranked the second among the largest
condominium across all regions, with a living area of 445 square meters. However, the
maximum new sale price in this region is the second lowest among the maximum new sale price
across all regions. The pollution and potential hazard from the airport prevent developers from
developing high-end condominiums in this region and the land-rent is substantially lower than
CBD area because the average distance to CBD is about 12km. In respect to North-East region,
the most expensive new sale condominium is sold at the second highest price, S$3,419,680,
among the maximum transaction price of condominiums across all regions. The largest
condominium unit in this region is the second smallest among the largest living area of units
across all regions. This region has become popular within the past decade in respect to new
developments of public and private condominiums and a variety of amenities in neighborhood.
These facts imply that this region may be the second to Central region in regard to its popularity
among developers.
Developers have different strength of experience in development across regions. Especially for
North region, developers’ age ranges from 14 to 44 with an average of 34. However, much
younger developers develops and sells condominiums in the other four regions than in North
region, with the minimum developers’ age ranging from 0.32 to 4.35 in the other four regions.
The other four regions have also witnessed developments by developers who have been more
13
than 112 years old. The oldest developer, 119 years old, has developed projects in Central
region. Developers’ paid up capital upon their incorporation varies across region. The average
paid up capital is highest in West region, followed by Central, East, North-East and North
regions (from high to low). The average paid up capital in North region is significantly lower
than other regions, with only around 6% of that of North-East region. Only 10% of
condominiums in North region are developed by a publicly traded (listed) developer. This
percentage is substantially lower than the proportion in the other regions, above 69%. The above
shows that well-established developers do not participate in the condominium development
market in North region, though the average market-share of developers is similar across all
regions, ranging from 5.43% to 8.94%.
The average number of units developed by a developer till transaction date ranges from 2,904 to
4,288 across five regions. Condominiums in North-East region are developed by less
experienced developers, on average, than the other regions. Interestingly, condominiums sold in
North region are developed by more experienced developers than the other regions, as shown by
the average number of units developed by a developer till transaction date. The value of this
variable seems to be contradictory to what we have observed on developers’ age and whether a
developer is publicly traded or not in this region. It has two possible reasons. The smaller and
younger developers in North region have developed a large number of condominium projects
during a short period of time. The other reason is that the time on market of new sale
condominiums in North region is longer than in the other regions. The latter is consistent with
the characteristic of North region.
Purchasers of condominiums in Central region are more likely to upgrade their life quality or
invest into another privately developed unit; around 68% of purchasers in Central region have
already owned at least one condominium when they purchase another one. In contrast, most
purchasers of condominiums in North region are first-time condominium buyers, with only 21%
of them have already owned one or more condominiums. Around 36% to 39% purchasers in
East, North-East and West regions stay in a privately developed condominiums when they
purchase another one.
14
[Insert Table 3 here]
IV. Results
The first stage results are presented in Table 4. This first stage, recall, is a hedonic regression in
which the log of the individual unit’s transaction price is regressed on a vector of its
characteristics. The regression is performed separately for each of the five regions of Singapore.
The fit is strong; across the five submarkets the R2 measures range from 80% to 90%. This is
perhaps not unexpected given that there is somewhat less in the way of unobservable
characteristics (compared to, say, a sample of US single family homes) in this collection of
transactions. The hedonic variables generally have the expected sign and are for the most part
statistically significant, although they are not always large in magnitude. The interesting outlier
among the regions is region 4 (North). This region has the largest R2 but omits several of the
binary variables because of lack of sample variation. Even then, the coefficients for the variables
that are included do not always exhibit the same sign or level of precision as observed in the
other four markets. This is seemingly due to collinearity and the relative sameness of the units in
this sector (as most exemplified by the aforementioned exclusions.)
[Insert Table 4 here]
The fact that the observable variables are not always substantive determinants of transaction
price is exemplified by the unit count of the building (totalunit). This variable is only statistically
significant in three of the five submarkets, and even then indicates that an increase of 100 units
moves prices by as little as -.04% to .09%.
More substantive is the finding that units farther
from the CBD are lower in price, in accordance with the standard urban model (e.g. Henderson,
1986). The gradient ranges from a low of a 0.2% decline to a high of 8% decline per kilometer
of distance.
The coefficients for water proximity (dumsea) are similarly positive across all five markets, with
the estimates ranging from roughly .06 through .19. Note that this coefficient is one of those not
estimated for the North region.
15
The coefficients on the binaries representing proximity to school (dumsch) and proximity to bus
interchange (dumbus) are a little more varied across the regions. The former is measured
precisely in only two of the three available regions (it is not estimable for both the North and
Northeast), and these two are of opposite sign. 7 The latter is also statistically significant only in
two regions as well. However the binary for tenure status (dumten) is uniformly positive and the
order of magnitude is the same across markets.
Finally, we turn to the variables which are the focus of our demand estimation in the next step.
The coefficient of apartment size (in square meters) is always positive, very precisely estimated,
and with a very narrow range across the submarkets. A 100 square meter increase raises sale
price by 0.5-0.7% increase in each of the five. The coefficient for the number of floors (flr) is
also well-estimated with coefficients ranging from .009 through .014, with high levels of
precision. The exception (again) is the North region, where the coefficient is much smaller
(.0004) and a t-ratio of about slightly less than 2. Nevertheless, our general conclusion is that
these coefficients are precisely estimated enough that we can have some confidence in the
estimation of the related hedonic prices.
We turn now to the estimation of those hedonic offer functions. Recall from above that these are
the regressions of the implicit price of the two attributes on the physical characteristics flr and
areasqm (we omit the remaining characteristics, as in e.g. Ohsfeldt and Smith (1985) etc.).
These characteristics are endogenous; we use instruments that include region dummies and the
interaction of region dummies with a dummy that describes demander characteristic
(dumpreaddress). This variable indicates whether a purchaser previously stays in a privately
developed unit or government subsidized unit when he buys the present condominium in the
sample 8.
7
8
There are two opposite forces for the proximity to schools. The neighbourhood of a highly demanded school is
attractive to buyers. However, the potential air and noise pollution impose negative effect on the proximity to
school. It appears that the benefits of living near a school offset the potential problem of air pollution in Central
region; but the neigbourhood close to school area is weakly dominated by the effect of pollution in East region.
The Sargan test indicates overwhelmingly that the two characteristics are endogenous. More importantly the
first stage does seem to provide a good fit.
16
There are several results of note as shown in Table 5. The first is that the coefficients on own
characteristics are positive, which is congruent with the fact that these estimates are in effect
supply curves. Recall that the main prediction of the model is that larger firms are the builders
of larger units, which is equivalent, surrounding the analysis of Figure 1, to the fact that the
coefficient of the relevant firm characteristic is negative. This is the case for several of the
coefficients. The strongest results are those for the firm characteristic paidupcapital. A one
standard deviation increase in this variable lowers the marginal cost of a square foot of
floorspace by approximately 3.5% and the marginal cost of a floor by about 14%. These seem
like substantive drops, and are indicative of the cost advantages of a larger firm, on a more
substantial financial footing. The coefficient of the variable developerage, however, while
having the expected negative sign (indicative of older firms having cost advantages) has a very
small magnitude and is statistically insignificant. A decade more experience confers a cost
advantage of only .08% for floorspace and .3% for floor.
[Insert Table 5 here]
Totbuilt, a measure of actual construction experience, is entered as a quadratic. As can be seen
in the table, the functional form related to this characteristic have different convexity properties.
The marginal cost function with respect to this variable is U-shaped for square feet and inverse
U-shaped for floor level. A one standard deviation increase in totbuilt yields a .5% increase in
the marginal cost of square feet and 1.7% decrease in the marginal cost of floor level. The firm’s
market penetration (pctotal) also has stronger negative results for floor than for square footage.
The coefficient is almost ten times the magnitude in the former than the latter. This set of results
makes some sense; large firms have a particular cost advantage over small firms when it comes
to setting the height of a building, relative to the floor area. The addition of a floor is more likely
to involve the kind of scale economies that a larger firm can bring to bear on a project, certainly
relative to the size of a single condo unit.
Finally, the one variable that is not directly related to size is whether the firm is publicly traded
or not. This is negative in the square feet regression but positive in the floor regression. Publicly
listed firms are able to tap on equity markets for cheaper capital, and they are usually the market
17
leaders in the new technology adoption, which allows them to operate more efficiently. They are
able to reduce marginal costs in square footage of development projects relative to non-listed
family firms, which are slow adopter in new technology. However, projects with higher floors
are more expensive to build, because of the more sophistical structure and also mechanical and
electrical services that come with tall buildings. The marginal costs increases exponentially with
increases in the floor level. Public firms do not have cost advantage over private firms in
building high-rise condominium projects, though the marginal effect is insignificant.
V. Conclusions
We have, for the first time, used the methodology for estimating hedonic marginal bid functions
to estimate the analogous functions from the supply side: the hedonic marginal offer, or cost,
functions. We find that larger firms have lower marginal cost functions indicating an advantage
in producing structures with increased quantities of floor area and floor level. The findings can
be extended towards the understanding of the formation of urban land value and spatial structure
when firms sit on different supply curves in a competitive market.
References:
Bartik, T. J. (1987). The estimation of demand parameters in hedonic price models. The Journal
of Political Economy, 95(1), 81-88.
Coulson, N. E. (1989). The empirical content of the linearity-as-repackaging hypothesis. Journal
of Urban Economics, 25(3), 295-309.
Coulson, N. E., & Bond, E. W. (1990). A hedonic approach to residential succession. The Review
of Economics and Statistics, 72(3), 433-444.
Coulson, N. E., Hwang, S. J., & Imai, S. (2002). The value of owner occupation in
neighborhoods. Journal of Housing Research, 13(2), 153-174.
Dong, Z., & Sing, T. (2014). Developer heterogeneity and competitive land bidding. Journal of
Real Estate Finance and Economics, 48(3), 441-466.
Dong, Z., & Sing, T. (forthcoming). How do land auction formats influence the market structure
and aggregate surplus of real estate development? Real Estate Economics, forthcoming.
18
URL at AREUEA: http://www.areuea.org/publications/ree/view_article.phtml?id=18526
URL at SSRN: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2545999.
Ekeland, I., Heckman, J. J., & Nesheim, L. (2002). Identifying hedonic models. American
Economic Review, 92(2), 304-309.
Ekeland, I., Heckman, J. J. and Nesheim, L. (2004). Identification and Estimation of Hedonic
Models. Journal of Political Economy, 112(S1), pp. S60-S109.
Ekeland, I. (2005). An optimal matching problem. ESAIM: Control, Optimisation and Calculus
of Variations, 11(01), 57-71.
Epple, D. (1987). Hedonic prices and implicit markets: estimating demand and supply functions
for differentiated products. The Journal of Political Economy, 95(1), 59-80.
Henderson, J. V. (1986). Efficiency of resource usage and city size. Journal of Urban economics,
19(1), 47-70.
Kahn, S., & Lang, K. (1988). Efficient estimation of structural hedonic systems. International
Economic Review, 29(1), 157-166.
Ohsfeldt, R. L., & Smith, B. A. (1985). Estimating the demand for heterogeneous goods. The
Review of Economics and Statistics, 67(1), 165-171.
Ooi, Joseph T. L., Sirmans, C. F. and Turnbull, Geoffrey K. (2006). Price formation under small
numbers competition: Evidence from land auctions in Singapore. Real Estate Economics, 34(1),
pp. 51–76.
Palmquist, R. B. (1984). Estimating the Demand for the Characteristics of Housing. The Review
of Economics and Statistics, 66(3), 394-404.
Rosen, S. (1974). Hedonic prices and implicit markets: Product differentiation in pure
competition. Journal of Political Economy, 82(1), pp. 34-55.
Zabel, J. E., & Kiel, K. A. (2000). Estimating the demand for air quality in four US cities. Land
Economics, 76(2), 174-194.
19
Table 1: The Top 10 Developers in Singapore by Market Share
Name
1
2
3
4
5
6
7
8
9
10
Total Unit
City Development Ltd + Hong Leong Group
Far East Organisation
CapitaLand
Frasers Centrepoint Ltd
Keppel Land Ltd
GuocoLand Ltd
Wing Tai Holdings Ltd Singapore
MCL Land Ltd
Allgreen Properties Ltd
Ho Bee Group
18638
16691
9021
8930
5219
4983
4491
3931
3534
2371
Market
share
18.22%
16.31%
8.82%
8.73%
5.10%
4.87%
4.39%
3.84%
3.45%
2.32%
Cumulative
Market Share
18.22%
34.53%
43.34%
52.07%
57.17%
62.04%
66.43%
70.27%
73.73%
76.04%
Note: The table compute the market share based on the number non-landed residential property developed by the
developers for the period from 1995 to 2009. Based on the identities of developers and their related entities, such as
parents/subsidiaries, merged entities, private/public entities, we compute the total units of residential projects
developed by the developers and divide the project units by total housing units launched in the market as the
indicator of the market share of the respective developer. The cumulative market share is the sum of the developers’
market share followed the ranking of the developers, in the descending order.
20
Table 2: Descriptive Statistics
Variable
Symbol
Mean
Std. Dev.
Min
Max
A) Condominium Characteristics
Transaction price ($)
transactedprice
1,069,798
1,112,341
107,000
31,400,000
Log of transaction price
lnp
13.69
0.52
11.58
17.26
Area (square meter)
areasqm
126.20
45.19
39.00
1,023.00
Total floor levels
flr
8.72
7.11
1.00
53.00
Distance to CBD (km)
distcbdkm
9.25
4.51
0.61
17.87
Distance to MRT (km)
distmrtkm
1.13
0.82
0.05
4.60
Proximity to bus interchange
dumbus
0.07
0.25
0.00
1.00
Proximity to popular school
dumsch
0.26
0.44
0.00
1.00
Proximity to water body
dumsea
0.21
0.41
0.00
1.00
Freehold in tenure
dumten
0.46
0.50
0.00
1.00
B) Developer Characteristics
Age of a developer
developerage
33.88
0.32
119.27
2.00
1.66 x1011
Paid up capital upon incorporation ($)
paidupcapital
Listed on Stock Exchange
public
Total number of units developed by a developer
totalunit
Market share of developed units for a developer (%)
Number of units developed by a developer till
transaction date
C) Purchaser Characteristic
Previous Address (Private Apartment)
2.13 x10
24.54
10
10
5.38 x10
0.70
0.46
0.00
1.00
7,519.24
5,104.72
16.00
16,691
pctotal
7.35
4.99
0.02
16.31
totbuilt
3,696.74
3,219.43
0.00
15,750
0.51
0.50
0.00
1.00
dumpreaddress
Note: The table summarizes the descriptive statistics (including means, standard deviations, minimum and maximum) that are computed from a total number of
63,315 observations for the sample period from 1995 to 2009. The symbols used for the respective variables are also included in the table for easy reference in
subsequent empirical results. Purchasers’ previous address indicates whether a purchaser has already owned a privately developed condominium(s) or not.
21
Table 3: Descriptive Statistics of Condominiums and Developers by Five Regions in Singapore
Variable
a)
Condominium Characteristics
Transaction price ($)
Symbol
Log of transaction price
lnp
Area (square meter)
areasqm
Total floor levels
flr
Distance to CBD (km)
distcbdkm
Distance to MRT (km)
distmrtkm
Proximity to bus interchange
dumbus
Proximity to popular school
dumsch
Proximity to water body
dumsea
Freehold tenure
dumten
b)
Developer Characteristics
Age of a developer
developerage
transactedprice
Paid up capital upon incorporation ($)
(x1010)
Listed on Stock Exchange
paidupcapital
Total number of units developed by a
developer
Market share of developed units for a
developer (%)
Number of units developed by a
developer till transaction date
totalunit
c)
Purchaser Characteristic
Previous Address (Private Apartment)
public
pctotal
totbuilt
dumpreaddress
1) Central
2) East
1,462,721.00
(1,548,791.000)
13.950
(0.620)
133.560
(57.670)
10.700
(8.430)
5.210
(2.520)
1.170
(0.910)
0.050
(0.220)
0.360
(0.480)
0.210
(0.410)
0.570
(0.490)
761,078.50
(231,243.900)
13.500
(0.270)
121.440
(35.050)
5.860
(4.360)
12.250
(2.420)
1.300
(0.670)
0.330
(0.180)
0.110
(0.310)
0.250
(0.430)
0.410
(0.490)
3) North-East
724,963.30
(194,743.500)
13.460
(0.230)
121.310
(27.110)
7.510
(5.080)
9.780
(1.720)
0.600
(0.470)
0.100
(0.300)
0.010
(0.130)
0.200
(0.400)
0.220
(0.410)
4) North
632,015.40
(153,734.000)
13.330
(0.230)
120.530
(28.360)
5.670
(4.560)
17.150
(1.010)
1.070
(0.380)
0.000
(0.000)
0.000
(0.000)
0.020
(0.140)
0.190
(0.390)
5) West
763,914.30
(254,322.900)
13.500
(0.300)
118.630
(27.030)
8.150
(5.840)
13.190
(2.180)
1.150
(0.830)
0.120
(0.320)
0.330
(0.470)
0.210
(0.410)
0.420
(0.490)
35.150
(27.510)
2.040
(5.250)
0.730
(0.440)
6947.830
(5130.600)
6.790
(5.010)
3528.450
(3029.060)
29.360
(13.990)
1.280
(4.260)
0.730
(0.440)
7618.960
(5020.840)
7.440
(4.910)
3852.820
(2902.040)
28.010
(18.800)
1.150
(4.030)
0.760
(0.430)
5559.670
(3914.850)
5.430
(3.830)
2904.040
(2478.930)
34.210
(7.310)
0.067
(0.051)
0.100
(0.290)
8813.860
(4899.030)
8.610
(4.790)
4287.660
(4130.030)
37.140
(27.610)
3.660
(6.750)
0.690
(0.460)
9144.680
(5080.060)
8.940
(4.960)
4113.930
(3755.370)
0.680
(0.470)
0.370
(0.480)
0.360
(0.480)
0.210
(0.410)
0.390
(0.490)
22
Note: The above table summarizes the descriptive statistics of condominium and developer characteristics including means in first row of each variable and
standard deviations in parentheses, for five planning regions in Singapore (Central, East, North-East, North and West). The statistics are computed from a total
number of 63,315 observations for the sample period from 1995 to 2009. The symbols used for the respective variables are also included in the table for easy
reference in subsequent empirical results.
23
Table 4: Hedonic Regression Results
Variable
Symbol
1) Central
2) East
3) North-East
4) North
5) West
Total number of units
developed by a developer
totalunit
Distance to CBD (km)
distcbdkm
Area (square meter)
areasqm
Total floor levels
flr
Distance to MRT (km)
distmrtkm
dumbus
9.10e-06***
(0.000)
-.0796603***
(0.008)
.0055367***
(0.000)
.0102776***
(0.001)
.3504983***
(0.018)
.1669243***
(0.011)
Proximity to popular school
dumsch
Proximity to water body
dumsea
Freehold tenure
dumten
Constant
_cons
Observation
R2
N
-4.78e-06***
(0.000)
-.0057475**
(0.002)
.005003***
(0.000)
.0131946***
(0.001)
.0224653***
(0.005)
0.013809
(0.011)
-.0213751*
(0.008)
.0139067*
(0.006)
.1300695***
(0.005)
12.91004***
(0.021)
11285
0.799958
1.25E-06
(0.000)
-0.00221
(0.013)
.0053594***
(0.000)
0.000393
(0.002)
-.4386668***
(0.062)
Proximity to bus interchange
7.36e-06***
(0.000)
-.0141088***
(0.002)
.0063976***
(0.000)
.013971***
(0.000)
.0678434***
(0.003)
.1082459***
(0.010)
.048353***
(0.005)
.0819404***
(0.007)
.1864156***
(0.004)
12.81815***
(0.017)
25712
0.895568
5.66E-07
(0.000)
-.0190319***
(0.003)
.0064864***
(0.000)
.009077***
(0.001)
.0567633***
(0.005)
-0.00463
(0.004)
-0.00642
(0.005)
.0599167***
(0.004)
.2635342***
(0.004)
12.69553***
(0.031)
12852
0.87266
.1953856***
(0.020)
.1878739***
(0.007)
13.11377***
(0.065)
5215
0.880473
.2457829***
(0.018)
12.95934***
(0.215)
2328
0.904805
Note: The table entries are estimates and standard errors of coefficients of the indicated variables in the hedonic model of condo sale price (equation (2). Also
included are year dummies, postal code dummies and nonparametric interactions between floor and floor area. * for p<.05, ** for p<.01, and *** for p<.001.
24
Table 5: Estimation of Marginal Price on Building and Firm Characteristics
Variable
Symbol
Square feet
Floor
Area (square meter)
areasqm
Floor level
flr
Total built-up area
totbuilt
Quadratic term on total built-up area
quadtotbuilt
Age of a developer
developerage
Market share of developed units for a
developer (%)
pctotal
.0160745***
(0.001)
.1340026***
(0.003)
-1.26E-06
(0.000)
9.59e-10*
(0.000)
-0.0000876
(0.000)
-0.0045
(0.003)
.0233738***
(0.001)
.1125839***
(0.003)
.0001732***
(0.000)
-7.31e-09***
(0.000)
-0.0003684
(0.000)
-.0391***
(0.003)
Paid up capital upon incorporation ($)
paidupcapital
Listed on Stock Exchange
public
Constant term
_cons
-6.43e-13***
(0.000)
-.0359679*
(0.014)
6.00247***
(0.069)
-2.66e-12***
(0.000)
0.0288293
(0.017)
5.692975***
(0.097)
Note: The table entries are coefficients and standard errors from a regression of the marginal price of the indicated
column’s characteristic on the vector of building and firm characteristics. Year dummies are also included in both
specifications. The two building characteristics are treated as endogenous, with region binaries and their
interaction with demand characteristics serving as instruments. * for p<.05, ** for p<.01, and *** for p<.001.
25
Figure 1: Hedonic Price Function and Firms’ Cost Curves
$
P(Z)
C(Z, X2)
C(Z, X1)
Z1
Z2
26
Z3
Figure 2: Total Housing Stocks and Private Housing Stock Ratios
1,500
18%
16%
14%
12%
13.71%
14.37%
15.52%
16.26%
15.61%
17.10% 16.89% 17.27%
16.48%
1,400
1,300
1,200
11.93% 12.29%
1,100
10%
1,000
8%
900
6%
800
4%
700
2%
600
Total Housing Stock ('000)
% of household by dwelling type
20%
500
0%
1995
2000
2001
2002
Total housing stocks (in unit)
2003
2004
2005
2006
2007
2008
2009
Ratio of Private Housing Stock to Total Housing Stock (%)
Note: The figure shows the total housing stocks in the vertical bars for the period from 1995 to 2009. The statistics
are obtained from the Department of Statistics, Singapore. The ratios of private housing stocks (including both
landed and non-landed units) to the total housing stocks are represented by the darken line in the figure.
27