1# RECORD ebefda640bee5302366b339dc1624f32b129581a2# TITLE: Property price gradients: the vertical dimension3# YEAR: 2011.0 VENUE: nan DOI: 10.1007/s10901-010-9203-84# AUTHORS: S. Wong; Wing-Chau Kwong; Y. Yau; A. Cheung5# PAGES: 13 CANDIDATE TABLE PAGES (1-based): [7, 9]6# 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.789===== PAGE 1 (score 6, numeric-paren 0, table-words 0, var-words 6) =====1011ARTICLE12Property price gradients: the vertical dimension13S. K. Wong • K. W. Chau • Y. Yau • A. K. C. Cheung14Received: 17 December 2008 / Accepted: 15 November 2010 / Published online: 4 December 201015 The Author(s) 2010. This article is published with open access at Springerlink.com16Abstract17This is an empirical study on the pricing of two vertical property attributes:18floor level and building height. Floor level is the vertical location of a unit in a multi-storey19building; the extra price paid for a higher floor level is labelled a floor-level premium.20Previous hedonic price studies unequivocally showed that the floor-level premium is21positive, but they were silent on whether its magnitude varies with floor levels and with22buildings of different heights. Indeed, building height is a feature of a building, not its23constituent units, so it is not clear whether building height alone should affect the units’24prices. Based on a sample of highly homogeneous housing units in buildings of varying25heights, we found that (1) the floor-level premium was not constant, but diminished as floor26level increases; (2) there was no significant difference in the pattern of the floor-level27premium between high-rise and low-rise buildings; and (3) there was a positive and sig-28nificant premium for units in low-rise buildings over those in high-rise ones. These findings29can help developers determine the optimal height and shape of their development.30Keywords31Housing price Hedonic model Floor level Building height Price gradient321 Introduction33‘‘Location, location, location’’ is a famous old saying that teaches us the importance of34location in choosing and pricing property. Taken literally, location refers to the geographic35position of a building. It has become a major focus in urban economics since Alonso’s36(1964) famous work on land rents and location in a monocentric city came out. Nowadays,37thanks to advances in technology (e.g., GIS), the concept of location not only refers to the38S. K. Wong (&) K. W. Chau A. K. C. Cheung39Department of Real Estate and Construction, The University of Hong Kong,40Pokfulam Road, Pokfulam, Hong Kong41e-mail: skwongb@hku.hk42Y. Yau43Department of Public and Social Administration, City University of Hong Kong,44Tat Chee Avenue, Kowloon, Hong Kong4512346J Hous and the Built Environ (2011) 26:33–4547DOI 10.1007/s10901-010-9203-8484950===== PAGE 7 (score 15, numeric-paren 0, table-words 3, var-words 7) =====5152Pit ¼ b1LRi þ c1FLi þ c2FL253i þ a0 þ a1AGEi þ a2SIZEi þ a3RDVi54þ a4GDVi þ a5DPVi þ a6MTRDi þ a7INDEXi þ eit55ð4aÞ56The variables used in Eq. 4a are defined in Table 3. Variables like building age, flat57size, views, distance to the MTR station, and time factors are control factors.6 Our first58focus was on b1, which measures the relative price of a low-rise building to a high-rise59building (i.e., a test of Hypothesis 3). We expected its sign to be positive because, as60discussed before, living in a dense environment may lead to overcrowding and higher61mental and physical health risks. Our second interest lay in the coefficients of floor levels62c1 and c2. We added a square term for floor level to cater for any non-linear effect (i.e., a63test of Hypothesis 1).7 We expected c1 to be positive and c2 to be negative. We also64estimated a more flexible specification for the price—floor relationship by replacing the65continuous floor variable with floor dummies FL(j) (see Table 3 for its definition) as the66independent variables in the hedonic price model specification:67Pit ¼ b1LRi þ68X691070j¼271cjFL jð Þi þ a0 þ a1AGEi þ a2SIZEi þ a3RDVi72þ a4GDVi þ a5DPVi þ a6MTRDi þ a6INDEXi þ eit73ð4bÞ74The first floor is taken as the base floor level. As such, the coefficients of the floor dummies75should be positive and increasing with floor level.76To test Hypothesis 2, we relaxed the assumption in Eq. 4a and 4b that the patterns of the77floor-level premium are the same for both low-rise and high-rise buildings. We added an78interaction term for the low-rise dummy (LR) and floor levels (FL and FL(j)) to Eq. 4a and794b. The resulting equations were:80Table 2 Descriptive statistics of the property transaction data81Mean82Std. dev.83Min84Max85Telford Gardens (No. of transactions = 807)86Property price (HK$mil)871.66880.34890.95902.6991Age (year)9222.08931.969418.009526.0896Flat size (ft2)97601.429830.9899392.00100681.00101Floor level1025.331032.841041.0010510.00106MTR distance (m)107155.4510855.8710964.35110231.23111Street view (%)1120.17113–114–115–116Podium garden view (%)1170.27118–119–120–121MTR depot view (%)1220.13123–124–125–126Low-rise building (%)1270.75128–129–130–1316 The base period for the time dummies was January 2000. The base view type for the view dummies is a132building view.1337 We tried to add the square terms of AGE and SIZE to the equation, but they were insignificant.134Property price gradients13539136123137138139===== PAGE 8 (score 12, numeric-paren 0, table-words 3, var-words 6) =====140141Pit ¼ b1LRi þ b2LRi FLi þ b3LRi FL2142i þ c1FLi þ c2FL2143i144þ a0 þ a1AGEi þ a2SIZEi þ a3RDVi þ a4GDVi145þ a5DPVi þ a6MTRDi þ a7INDEXi þ eit146ð5aÞ147Pit ¼ b1LRi þ148X14910150j¼2151bjLRi FL jð Þi þ152X15310154j¼2155cjFL jð Þi þ a0 þ a1AGEi156þ a2SIZEi þ a3RDVi þ a4GDVi þ a5DPVi157þ a6MTRDi þ a7INDEXi þ eit:158ð5bÞ159If the coefficients of these interactive terms are significant, then that would imply160different patterns of the floor-level premium. We shall present and discuss the results in the161next section. The statistical software employed is EViews 6.1624 Results163The results of the two hedonic price models without interaction terms (i.e., Eq. 4a and 4b)164are shown in Columns 1 and 2 of Table 4. The R-squared values of these models were over16585%, indicating that our models explained a great deal of variability in the data. The two166models were similarly structured except that Eq. 4a assumed a quadratic floor function and167Eq. 4b a flexible step function. For both models, the coefficients of the control variables168(except AGE and MTRD) were highly significant with expected signs and comparable169Table 3 Definition of the variables170Variable171Definition172Pit173The transaction price (in HK$million) of property i at time t174LRi175A building height dummy that equals 1 when property i is a low-rise and zero when it176is a high-rise177FLi178The floor level of property i179FL(j)i180A floor dummy that equals 1 when property i is on the jth floor and zero if otherwise (base181floor = 1/F)182AGEi183The building age of property i in months184SIZEi185The gross floor area of property i in square feet186RDVi187A view dummy that equals 1 when property i possesses a view facing the road and zero if188otherwise189GDVi190A view dummy that equals 1 when property i possesses a view facing the podium garden and191zero if otherwise192DPVi193A view dummy that equals 1 when property i possesses a view facing the MTR depot and zero194if otherwise195MTRDi196The distance between property i and the MTR station in metres197INDEXi198A monthly property price index for residential developments published by the Rating and199Valuation Department, HKSAR Government (Index = 100 in year 1999)200a, b, c and201v202Coefficients to be estimated203eit204The error term capturing all unmeasured effects20540206S. K. Wong et al.207123208209210===== PAGE 9 (score 17, numeric-paren 0, table-words 4, var-words 2) =====211212magnitudes.8 Most importantly, we found the following results regarding floor-level and213low-rise premiums:214Table 4 Estimation results215Eq. 4a216Eq. 4b217Eq. 5a218Eq. 5b219Variable220Coefficient221Coefficient222Coefficient223Coefficient224LR2250.0486b2260.0391b2270.1092a2280.1060b229FL2300.1181b231–2320.1280b233–234FL2235-0.0082b236–237-0.0084b238–239FL(2)240–2410.2460b242–2430.2888b244FL(3)245–2460.2966b247–2480.3455b249FL(4)250–2510.3214b252–2530.4023b254FL(5)255–2560.3345b257–2580.3566b259FL(6)260–2610.3490b262–2630.4168b264FL(7)265–2660.3739b267–2680.3993b269FL(8)270–2710.3691b272–2730.4365b274FL(9)275–2760.3662b277–2780.4075b279FL(10)280–2810.3611b282–2830.4680b284LR*FL285–286–287-0.0143288–289LR*FL2290–291–2920.0004293–294LR*FL(2)295–296–297–298-0.0605299LR*FL(3)300–301–302–303-0.0684304LR*FL(4)305–306–307–308-0.1117a309LR*FL(5)310–311–312–313-0.0336314LR*FL(6)315–316–317–318-0.0983a319LR*FL(7)320–321–322–323-0.0326324LR*FL(8)325–326–327–328-0.0903329LR*FL(9)330–331–332–333-0.0592334LR*FL(10)335–336–337–338-0.1452b339CONSTANT340-2.4929b341-2.3789b342-2.520b343-2.3945b344AGE3450.00223460.00173470.0023348-0.0017349SIZE3500.0034b3510.0033b3520.0034b3530.0033b354RDV355-0.0935b356-0.0997b357-0.0966b358-0.1059b359GDV3600.0420b3610.0470b3620.0415b3630.0436b364DPV365-0.0817b366-0.0839b367-0.0816b368-0.0810b369MTRD370-2.68 9 10-5371-9.96 9 10-5372-2.13 9 10-5373-8.35 9 10-5374INDEX3750.0198b3760.0199b3770.0198b3780.0199b379R-squared3800.85203810.86713820.85323830.8698384Adj. R-squared3850.85013860.86423870.85103880.8655389We employed White’s standard errors to adjust for heteroskedasticity390a Significant at the 5% level391b Significant at the 1% level3928 The insignificance of AGE and MTRD was probably due to low data variations. All buildings in the393residential estate were built between 1980 and 1982 and were within 250 m of the subway station.394Property price gradients39541396123397398399===== PAGE 10 (score 8, numeric-paren 0, table-words 1, var-words 6) =====400401Hypothesis 1 maintains that floor-level premiums are constant across different floor402levels. However, in Eq. 4a, both c1 and c2 were significant at the 1% level with opposite403signs. This suggested that the floor-level premium diminishes as floor level increases,404hence rejecting Hypothesis 1. Since the quadratic floor function is rather restrictive, Eq. 4b405provided a flexible step function for estimating floor-level premiums. Both the results of406the step and quadratic functions are plotted in Fig. 2. For the step function, we found a407drastic jump in property prices from the 1st to the 2nd floor (about 15% of a property’s408price), which implied a great difference in perceived environmental quality (e.g., noise,409security issues) between the first two floors. The premiums of the other floors appeared410more or less the same, but a re-estimation of Eq. 4a without the first floor still showed a411slightly diminishing pattern (with c1 = 0.0505 and c2 = -0.0031, both significant at the4121% level). Therefore, the hypothesis that the floor price gradient is linear was rejected as413far as the low floor zone was concerned. A non-linear gradient likely resulted from vari-414ations in environmental quality along the vertical dimension.415Hypothesis 3 maintains that low-rise buildings do not command a premium or discount416over high-rise buildings. However, in both Eq. 4a and 4b, the low-rise premium (b1) was417consistently positive and significant at the 1% level, suggesting that units in taller (and418thus, denser) buildings were sold at a discount to units in shorter buildings, ceteris paribus.419The estimated low-rise premiums were HK$48,584 in Eq. 4a and HK$39,076 in Eq. 4b,420representing about 2–3% of the mean transaction price in the sample. These results rejected421the constant density hypothesis and confirmed that there was a greater premium for shorter422buildings than for taller ones. The premium can be attributed to a lower population density423in the common areas of shorter buildings, as elaborated on in Sect. 2.424Next, we estimated Eq. 5a and 5b to test if the pattern of the floor-level premiums was425constant across buildings of different heights, as maintained by Hypothesis 2. The426regression results of Eq. 5a and 5b are shown in Columns 3 and 4 of Table 4. Central to427these equations are the interaction of terms LR with the floor levels. Both interaction terms428in Eq. 5a and most of the interaction terms in Eq. 5b, however, were insignificant. There429was no evidence to support the ‘‘relative’’ logic that floor-level premiums varied with430buildings of different heights. Hence, Hypothesis 2 was not rejected.4311.54321.64331.74341.84351.94362.04372.143814392440344144425443644474458446944710448Floor level449Price of a notional property (HK$mil)450Quadratic function451Step function452Fig. 2 The relationship between floor levels and property prices45342454S. K. Wong et al.455123456