# RECORD ebefda640bee5302366b339dc1624f32b129581a
# TITLE: Property price gradients: the vertical dimension
# YEAR: 2011.0  VENUE: nan  DOI: 10.1007/s10901-010-9203-8
# AUTHORS: S. Wong; Wing-Chau Kwong; Y. Yau; A. Cheung
# PAGES: 13  CANDIDATE TABLE PAGES (1-based): [7, 9]
# ABSTRACT: This is an empirical study on the pricing of two vertical property attributes: floor level and building height. Floor level is the vertical location of a unit in a multi-storey building; the extra price paid for a higher floor level is labelled a floor-level premium. Previous hedonic price studies unequivocally showed that the floor-level premium is positive, but they were silent on whether its magnitude varies with floor levels and with buildings of different heights. Indeed, building height is a feature of a building, not its constituent units, so it is not clear whether building height alone should affect the units’ prices. Based on a sample of highly homogeneous housing units in buildings of varying heights, we found that (1) the floor-level premium was not constant, but diminished as floor level increases; (2) there was no significant difference in the pattern of the floor-level premium between high-rise and low-rise buildings; and (3) there was a positive and significant premium for units in low-rise buildings over those in high-rise ones. These findings can help developers determine the optimal height and shape of their development.


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ARTICLE
Property price gradients: the vertical dimension
S. K. Wong • K. W. Chau • Y. Yau • A. K. C. Cheung
Received: 17 December 2008 / Accepted: 15 November 2010 / Published online: 4 December 2010
 The Author(s) 2010. This article is published with open access at Springerlink.com
Abstract
This is an empirical study on the pricing of two vertical property attributes:
floor level and building height. Floor level is the vertical location of a unit in a multi-storey
building; the extra price paid for a higher floor level is labelled a floor-level premium.
Previous hedonic price studies unequivocally showed that the floor-level premium is
positive, but they were silent on whether its magnitude varies with floor levels and with
buildings of different heights. Indeed, building height is a feature of a building, not its
constituent units, so it is not clear whether building height alone should affect the units’
prices. Based on a sample of highly homogeneous housing units in buildings of varying
heights, we found that (1) the floor-level premium was not constant, but diminished as floor
level increases; (2) there was no significant difference in the pattern of the floor-level
premium between high-rise and low-rise buildings; and (3) there was a positive and sig-
nificant premium for units in low-rise buildings over those in high-rise ones. These findings
can help developers determine the optimal height and shape of their development.
Keywords
Housing price  Hedonic model  Floor level  Building height  Price gradient
1 Introduction
‘‘Location, location, location’’ is a famous old saying that teaches us the importance of
location in choosing and pricing property. Taken literally, location refers to the geographic
position of a building. It has become a major focus in urban economics since Alonso’s
(1964) famous work on land rents and location in a monocentric city came out. Nowadays,
thanks to advances in technology (e.g., GIS), the concept of location not only refers to the
S. K. Wong (&)  K. W. Chau  A. K. C. Cheung
Department of Real Estate and Construction, The University of Hong Kong,
Pokfulam Road, Pokfulam, Hong Kong
e-mail: skwongb@hku.hk
Y. Yau
Department of Public and Social Administration, City University of Hong Kong,
Tat Chee Avenue, Kowloon, Hong Kong
123
J Hous and the Built Environ (2011) 26:33–45
DOI 10.1007/s10901-010-9203-8


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Pit ¼ b1LRi þ c1FLi þ c2FL2
i þ a0 þ a1AGEi þ a2SIZEi þ a3RDVi
þ a4GDVi þ a5DPVi þ a6MTRDi þ a7INDEXi þ eit
ð4aÞ
The variables used in Eq. 4a are defined in Table 3. Variables like building age, flat
size, views, distance to the MTR station, and time factors are control factors.6 Our first
focus was on b1, which measures the relative price of a low-rise building to a high-rise
building (i.e., a test of Hypothesis 3). We expected its sign to be positive because, as
discussed before, living in a dense environment may lead to overcrowding and higher
mental and physical health risks. Our second interest lay in the coefficients of floor levels
c1 and c2. We added a square term for floor level to cater for any non-linear effect (i.e., a
test of Hypothesis 1).7 We expected c1 to be positive and c2 to be negative. We also
estimated a more flexible specification for the price—floor relationship by replacing the
continuous floor variable with floor dummies FL(j) (see Table 3 for its definition) as the
independent variables in the hedonic price model specification:
Pit ¼ b1LRi þ
X
10
j¼2
cjFL jð Þi þ a0 þ a1AGEi þ a2SIZEi þ a3RDVi
þ a4GDVi þ a5DPVi þ a6MTRDi þ a6INDEXi þ eit
ð4bÞ
The first floor is taken as the base floor level. As such, the coefficients of the floor dummies
should be positive and increasing with floor level.
To test Hypothesis 2, we relaxed the assumption in Eq. 4a and 4b that the patterns of the
floor-level premium are the same for both low-rise and high-rise buildings. We added an
interaction term for the low-rise dummy (LR) and floor levels (FL and FL(j)) to Eq. 4a and
4b. The resulting equations were:
Table 2 Descriptive statistics of the property transaction data
Mean
Std. dev.
Min
Max
Telford Gardens (No. of transactions = 807)
Property price (HK$mil)
1.66
0.34
0.95
2.69
Age (year)
22.08
1.96
18.00
26.08
Flat size (ft2)
601.42
30.98
392.00
681.00
Floor level
5.33
2.84
1.00
10.00
MTR distance (m)
155.45
55.87
64.35
231.23
Street view (%)
0.17
–
–
–
Podium garden view (%)
0.27
–
–
–
MTR depot view (%)
0.13
–
–
–
Low-rise building (%)
0.75
–
–
–
6 The base period for the time dummies was January 2000. The base view type for the view dummies is a
building view.
7 We tried to add the square terms of AGE and SIZE to the equation, but they were insignificant.
Property price gradients
39
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Pit ¼ b1LRi þ b2LRi  FLi þ b3LRi  FL2
i þ c1FLi þ c2FL2
i
þ a0 þ a1AGEi þ a2SIZEi þ a3RDVi þ a4GDVi
þ a5DPVi þ a6MTRDi þ a7INDEXi þ eit
ð5aÞ
Pit ¼ b1LRi þ
X
10
j¼2
bjLRi  FL jð Þi þ
X
10
j¼2
cjFL jð Þi þ a0 þ a1AGEi
þ a2SIZEi þ a3RDVi þ a4GDVi þ a5DPVi
þ a6MTRDi þ a7INDEXi þ eit:
ð5bÞ
If the coefficients of these interactive terms are significant, then that would imply
different patterns of the floor-level premium. We shall present and discuss the results in the
next section. The statistical software employed is EViews 6.
4 Results
The results of the two hedonic price models without interaction terms (i.e., Eq. 4a and 4b)
are shown in Columns 1 and 2 of Table 4. The R-squared values of these models were over
85%, indicating that our models explained a great deal of variability in the data. The two
models were similarly structured except that Eq. 4a assumed a quadratic floor function and
Eq. 4b a flexible step function. For both models, the coefficients of the control variables
(except AGE and MTRD) were highly significant with expected signs and comparable
Table 3 Definition of the variables
Variable
Definition
Pit
The transaction price (in HK$million) of property i at time t
LRi
A building height dummy that equals 1 when property i is a low-rise and zero when it
is a high-rise
FLi
The floor level of property i
FL(j)i
A floor dummy that equals 1 when property i is on the jth floor and zero if otherwise (base
floor = 1/F)
AGEi
The building age of property i in months
SIZEi
The gross floor area of property i in square feet
RDVi
A view dummy that equals 1 when property i possesses a view facing the road and zero if
otherwise
GDVi
A view dummy that equals 1 when property i possesses a view facing the podium garden and
zero if otherwise
DPVi
A view dummy that equals 1 when property i possesses a view facing the MTR depot and zero
if otherwise
MTRDi
The distance between property i and the MTR station in metres
INDEXi
A monthly property price index for residential developments published by the Rating and
Valuation Department, HKSAR Government (Index = 100 in year 1999)
a, b, c and
v
Coefficients to be estimated
eit
The error term capturing all unmeasured effects
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S. K. Wong et al.
123


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magnitudes.8 Most importantly, we found the following results regarding floor-level and
low-rise premiums:
Table 4 Estimation results
Eq. 4a
Eq. 4b
Eq. 5a
Eq. 5b
Variable
Coefficient
Coefficient
Coefficient
Coefficient
LR
0.0486b
0.0391b
0.1092a
0.1060b
FL
0.1181b
–
0.1280b
–
FL2
-0.0082b
–
-0.0084b
–
FL(2)
–
0.2460b
–
0.2888b
FL(3)
–
0.2966b
–
0.3455b
FL(4)
–
0.3214b
–
0.4023b
FL(5)
–
0.3345b
–
0.3566b
FL(6)
–
0.3490b
–
0.4168b
FL(7)
–
0.3739b
–
0.3993b
FL(8)
–
0.3691b
–
0.4365b
FL(9)
–
0.3662b
–
0.4075b
FL(10)
–
0.3611b
–
0.4680b
LR*FL
–
–
-0.0143
–
LR*FL2
–
–
0.0004
–
LR*FL(2)
–
–
–
-0.0605
LR*FL(3)
–
–
–
-0.0684
LR*FL(4)
–
–
–
-0.1117a
LR*FL(5)
–
–
–
-0.0336
LR*FL(6)
–
–
–
-0.0983a
LR*FL(7)
–
–
–
-0.0326
LR*FL(8)
–
–
–
-0.0903
LR*FL(9)
–
–
–
-0.0592
LR*FL(10)
–
–
–
-0.1452b
CONSTANT
-2.4929b
-2.3789b
-2.520b
-2.3945b
AGE
0.0022
0.0017
0.0023
-0.0017
SIZE
0.0034b
0.0033b
0.0034b
0.0033b
RDV
-0.0935b
-0.0997b
-0.0966b
-0.1059b
GDV
0.0420b
0.0470b
0.0415b
0.0436b
DPV
-0.0817b
-0.0839b
-0.0816b
-0.0810b
MTRD
-2.68 9 10-5
-9.96 9 10-5
-2.13 9 10-5
-8.35 9 10-5
INDEX
0.0198b
0.0199b
0.0198b
0.0199b
R-squared
0.8520
0.8671
0.8532
0.8698
Adj. R-squared
0.8501
0.8642
0.8510
0.8655
We employed White’s standard errors to adjust for heteroskedasticity
a Significant at the 5% level
b Significant at the 1% level
8 The insignificance of AGE and MTRD was probably due to low data variations. All buildings in the
residential estate were built between 1980 and 1982 and were within 250 m of the subway station.
Property price gradients
41
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Hypothesis 1 maintains that floor-level premiums are constant across different floor
levels. However, in Eq. 4a, both c1 and c2 were significant at the 1% level with opposite
signs. This suggested that the floor-level premium diminishes as floor level increases,
hence rejecting Hypothesis 1. Since the quadratic floor function is rather restrictive, Eq. 4b
provided a flexible step function for estimating floor-level premiums. Both the results of
the step and quadratic functions are plotted in Fig. 2. For the step function, we found a
drastic jump in property prices from the 1st to the 2nd floor (about 15% of a property’s
price), which implied a great difference in perceived environmental quality (e.g., noise,
security issues) between the first two floors. The premiums of the other floors appeared
more or less the same, but a re-estimation of Eq. 4a without the first floor still showed a
slightly diminishing pattern (with c1 = 0.0505 and c2 = -0.0031, both significant at the
1% level). Therefore, the hypothesis that the floor price gradient is linear was rejected as
far as the low floor zone was concerned. A non-linear gradient likely resulted from vari-
ations in environmental quality along the vertical dimension.
Hypothesis 3 maintains that low-rise buildings do not command a premium or discount
over high-rise buildings. However, in both Eq. 4a and 4b, the low-rise premium (b1) was
consistently positive and significant at the 1% level, suggesting that units in taller (and
thus, denser) buildings were sold at a discount to units in shorter buildings, ceteris paribus.
The estimated low-rise premiums were HK$48,584 in Eq. 4a and HK$39,076 in Eq. 4b,
representing about 2–3% of the mean transaction price in the sample. These results rejected
the constant density hypothesis and confirmed that there was a greater premium for shorter
buildings than for taller ones. The premium can be attributed to a lower population density
in the common areas of shorter buildings, as elaborated on in Sect. 2.
Next, we estimated Eq. 5a and 5b to test if the pattern of the floor-level premiums was
constant across buildings of different heights, as maintained by Hypothesis 2. The
regression results of Eq. 5a and 5b are shown in Columns 3 and 4 of Table 4. Central to
these equations are the interaction of terms LR with the floor levels. Both interaction terms
in Eq. 5a and most of the interaction terms in Eq. 5b, however, were insignificant. There
was no evidence to support the ‘‘relative’’ logic that floor-level premiums varied with
buildings of different heights. Hence, Hypothesis 2 was not rejected.
1.5
1.6
1.7
1.8
1.9
2.0
2.1
1
2
3
4
5
6
7
8
9
10
Floor level
Price of a notional property (HK$mil)
Quadratic function
Step function
Fig. 2 The relationship between floor levels and property prices
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S. K. Wong et al.
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