Centre for Urban Economics and Real Estate. Working Paper Spatial Autocorrelations and Urban Housing Market Segmentation

Transcription

1 Centre for Urban Economics and Real Estate Working Paper Spatial Autocorrelations and Urban Housing Market Segmentation Yong Tu University of Singapore Shi Ming Yu National University of Singaproe Hua Sun University of British Columbia October 28, 2005 Centre for Urban Economics and Real Estate Sauder School of Business University of British Columbia 2053 Main Mall Vancouver, BC V6T 1Z2 Tel : or cuer@sauder.ubc.ca Web:

2 Spatial Autocorrelations and Urban Housing Market Segmentation Yong Tu National University of Singapore, Singapore Hua Sun University of British Columbia, Canada Shi-Ming Yu National University of Singapore, Singapore Please forward correspondence to the first author by at or by mail to The Department of Real Estate, National University of Singapore, 4 Architecture Drive, Singapore All comments are welcome.

3 Abstract This paper seeks to let data define urban housing market segments, replacing the conventional administrative or any pre-defined boundaries used in the previous housing submarket literature. We model housing transaction data using a conventional hedonic function. The hedonic residuals are used to estimate an isotropic semi-variogram, from which residual variance-covariance matrix is constructed. The correlations between hedonic residuals are used as identifier to assign housing units into clusters. Standard submarket identification tests are applied to each cluster to examine the segmentation of housing market. The results are compared with the prevailing structure of market segments. Weighted mean square test shows that the defined submarket structure can improve the precision of price prediction by 17.5%. This paper is experimental in the sense that it represents one of the first attempts at investigating market segmentation through house price spatial autocorrelations. Key words: housing submarket, isotropic semi-variogram, price spatial autocorrelation 2

4 I Introduction For nearly five decades, one important contribution of housing economics has been its recognition that urban housing market should be depicted as a set of distinct but interrelated housing submarkets, across which the hedonic housing prices are significantly different. Submarket concepts have widespread applications in property valuation and price prediction (Adair et al, 1996), local housing market analysis (Tu and Goldfinch, 1996, Maclennan and Tu 1995), urban planning (Jones, 2002) as well as submarket based mortgage default risk analyses (Capone and Goldberg, 2001). However as Palm (1978) points out that submarket models should be used in housing analysis, only if the submarkets are carefully defined, reflecting true hedonic price differences. Watkins (2001) also concludes that there is considerable imprecision surrounding the conceptualization of housing submarkets, caused by demarcation criteria or definitions, statistical methods as well as the selection of the smallest units of analysis (or product group). The imprecision may essentially limit the applications of submarket concept. This paper focuses on the identification of topographically based housing submarkets, for which researchers may typically take the assumed (for example, political jurisdiction boundaries used in Strazheim, 1975) or modeled (using statistical methods to form geographically units, Bourassa et. al 1999) geographical boundaries as the smallest units of analysis, which are then aggregated up to submarket level based on the significance of hedonic price differences across the units. Both Goodman and Thibodeau (1998) and Bourassa et al (1999) argue that if the smallest units of analysis are imposed rather than modeled, one cannot be confident that the resulting submarkets are identified in an 3

5 optimal way. Bourassa et al (2003) further points out that defining submarkets depends on the purpose that the submarkets are constructed. For the purpose of mass appraisal, established neighborhood or urban boundaries rather than modeled geographic units are perhaps more suitable. The focus of modeled geographical boundaries is to let data determine the structure of submarkets. In the previous literature, some grouping techniques, for example, cluster analysis are used to assign housing units to clusters based on the principle of minimizing the dwelling dissimilarities within a cluster and maximize the dwelling heterogeneities between the clusters (Dale-Johnson, 1982; Bourassa et al., 1999; Dunse et al., 2002). The boundaries formed by these methods may be imprecise due to the unobservable or immeasurable neighborhood-specific factors. Recently, Clapp and Wang (2004) attempt to use residual spatial autocorrelation information to define neighborhood boundaries (the smallest geographic units), which are not only independent of any prior definition but also are not necessarily engaged in any measurements on neighborhood factors. Their pioneering work adopts a non-parametric spatial statistical method to actually identify neighborhood boundaries (CART neighborhood), and they recommend that the CART neighborhood should be used as the smallest units of analysis in submarket identification. This paper also adopts spatial correlation information inherent in the hedonic residuals to define property clusters which are used as the smallest units of analysis to define market 4

6 segments (submarkets). Being different from the previous literature, we first focus on using an estimated spatial autocorrelation structure to assign geo-coded housing transactions into property clusters. These clusters are then used to further identify the inherent housing market segments. We then test if the property clusters formed by spatial autocorrelation structure reflect market segments. It is widely accepted that spatial autocorrelations stem from the neighborhood characteristics shared by the properties (Basu and Thibodeau, 1998), and hence, spatial autocorrelation structure should reflect neighborhood structure. Second, previous housing submarket definitions typically have an implied common assumption that any urban housing unit must belong to some submarket. In other words, the resulting submarket structures from those previous research papers typically cover the whole urban area. This may not be true in the sense that some housing developments or residential areas may not belong to any submarket. For example, they may be geographically isolated and too small to form any submarket by themselves, like some new housing developments at the edge of a city. However, previous housing submarket definitions cannot identify these isolated cases. And hence, simply classifying these units into any submarket may cause the imprecision of submarket identification. The method proposed in this paper is able to identify these units. The paper will hopefully provide a new angle to look into housing market segmentation. The next section reviews the literature with an emphasis on the definitions of urban housing submarkets. Section III presents the research design and methodology. Section IV reports the empirical results and compares market segments defined in this paper with 5

7 the a priori submarket structure used in Singapore. Section V summarizes the main findings and conclusions. II Neighborhood, submarket and spatial autocorrelations Galster (2003) points out that housing submarket and neighbourhood are not synonymous, but have a straightforward relationship. A neighborhood is defined as a bundle of spatially based attributes associated with clusters of residences, sometimes in conjunction with other land uses. The bundle of attributes includes physical dwelling structural characteristics, infrastructure, environmental features, proximity as well as sociodemographic and political features, which contributes to the neighborhood value of a housing unit. Housing units in one neighborhood are likely to have similar neighborhood values, and hence the hedonic prices for dwelling related hedonic factors are unlikely to have any significant differences, implying that housing units in one neighborhood tend to be in the same topographically based submarket. However, a submarket is more than a neighbourhood: it is a collection of neighbourhoods. It may be comprised of several neighbourhoods, across which hedonic prices have no significant differences, regardless of their location or propinquity, because, it is possible that two different neighborhoods may generate the same level of neighborhood value to a housing unit. The reasons for spatial variations of housing prices can be further elaborated as below. In the short run, with the restrictions on the freedom of buyers and sellers to enter the market in certain urban geographical area, hedonic housing price differentials across neighborhoods may be accentuated or reduced. But in the long run, with capital and 6

8 labor mobile within an urban area (on the supply side) and with buyers also mobile within the urban area (on the demand side), the only factor that would systematically influence the price of housing services would be the differential price of land (Goodman and Thibodeau, 1998, page 123). The long run differential land prices across urban areas are due to the unique neighborhood spatial features attached to the land. Galster (2003) points out that spatially-based attributes does not mean that they are intrinsically coupled with the geography. Some are physical environment (for example, sea view, physical outlook of neighborhood, good spatial amenities), whereas others are associated with individuals who lend their collective attributes to the space purely through aggregation (for example, income, race). These attributes are not easily duplicable, resulting in the formation of housing submarkets. Clapp et al (2002) argue that long run house price spatial variation is attributable to three reasons. First, Housing prices change relatively slowly over long distances due to accessibility to major urban facilities or main locations of interests, for example, CBD. Second, employment sub-centres or a nicer water view require closer proximity to have an influence on housing prices. And hence, they may cause spatial patterns of housing price over shorter distance than the first type of factors. Third, neighbourhood amenities, for example, school quality, physical neighbourhood image, and neighbourhood income level. Since in any urban city, spatial features vary across neighborhoods, submarkets are likely to exist in any urban cities. This is despite that spatial features that divide neighborhoods or submarkets may be different in different cities. 7

9 In other words, for dwelling related hedonic factors, hedonic housing price differentials across space are caused by both short run market forces and long run neighborhood spatial feature differences. In the short run, housing market segmentation may be attributable to both market forces and spatial features, but in the long run, submarket structure is mainly determined by the spatial differences in neighborhood structural characteristics and amenities (also see Goodman and Thibodeau, 1998). In a conclusion, neighborhood features contribute to house price spatial autocorrelations. Hedonic residuals derived from a market-wide hedonic function are spatially correlated. The residual correlation pattern is consistent with the city s neighborhood spatial pattern. In a widely cited book written by Cliff and Ord (1981), the reasons for residual spatial autocorrelations are identified. Applied to the analysis of submarket, the reasons for spatial autocorrelations among the hedonic residuals are, first, the uncaptured non-linear relationships between the dependent and independent variables. On the one hand, although some methods are available in choosing the parametric hedonic function form (Halvorsen and Pollakowski, 1981), the true hedonic function form is typically unknown. On the other hand, housing price variation across neighborhoods implies that neighborhood level hedonic function form can be varied across neighborhoods too. A market-wide hedonic mean function therefore cannot represent neighborhood level hedonic mean function. Since a neighborhood is likely to be in one submarket, hedonic function forms within a neighborhood should be similar. The errors caused by the 8

10 uncaptured non-linear relationship are therefore expected to be correlated for the units in one neighborhood. Second, some related independent variables may be omitted from a hedonic function. In a traditional hedonic house price regression, the important determinants of property value include a property s structural characteristics, and a bundle of neighborhood spatial attributes. Across neighborhoods, these spatial attributes are not only different, but also difficult to be identified or quantified (also see Dubin 1992). In a hedonic analysis, some proxies are typically used in the mean function to measure the impacts of these factors on housing prices. For example, linear distance to the CBD is typically used in a market wide hedonic mean function, but a shorter linear distance to the CBD does not necessarily mean that the actual road distance is shorter. Even if the road distances are similar, roads with better condition (for example, highway) may generate better accessibility to the CBD. Those uncaptured spatial impacts are classified into hedonic residuals, forming residual spatial autocorrelations. If the properties share similar accessibility to the CBD, both their prices and residuals are likely to be correlated, given that other factors are the same. Following the above argument, we believe that housing units associated with those spatially correlated residuals are likely to be in one neighborhood and hence in one submarket. Housing units associated with spatially uncorrelated residuals should be in different submarkets. 9

11 III Research Design and Methodology The research design follows three steps: estimating market wide hedonic residual spatial autocorrelation structure; clustering housing units into groups according to their spatial autocorrelations (finding the neighbourhoods; and applying standard submarket tests to aggregate the clusters to submarket level and to test submarket segmentation. Empirically identifying true house price spatial correlation structure is a challenge. This is because we can not be sure that the estimated spatial autocorrelation structure is the true spatial autocorrelation structure. Bearing this in mind, this paper will empirically estimate residual spatial autocorrelations against a selected Geo-statistical method. The estimated correlation structure is used as a proxy to indicate housing price spatial autocorrelation structure. Geo-statistics offer different ways to estimate residual variance-covariance matrix (reflecting residual correlations). They are differentiated by the assumptions on correlation structure. Most research on spatial autocorrelation in house prices has assumed that the correlation structure is isotropic, meaning that the correlation is a function of distance only. Spatial data can be anisotropic when spatial autocorrelation is a function of both distance and direction separating points in space. Gillen, et al (2001) find evidence that in some submarkets (referring to the investigated urban housing market), the spatial autocorrelation in the hedonic residuals is anisotropic, where residents typically commute to a regional or local CBD. In the paper, they examine directional autocorrelations along two directions: north-south and east-west with the 10

12 tolerance region of ±45 degrees. Clapp and Wang (2004) also find anisotropic spatial autocorrelation among hedonic residuals. Although these empirical evidences show that housing price correlations may be a function of both distance and direction, anisotropic assumptions cannot be used in this analysis to construct variance-covariance matrix. This is because, technically, constructing variance-covariance matrix under anisotropic assumption demands prior knowledge on the directions along which housing prices may be correlated. Such information is usually not available, which makes the method less popular. Therefore, in this paper, we adopt the isotropic assumption. We first model the relationship between housing price and housing characteristics using a semi-logarithmic hedonic function (equation 1). Log ( P) = f ( X ) + ε (1) Where P is a vector of dwelling transaction prices, X is a vector of (possibly transformed) housing characteristics.ε is a vector of residuals. When the residuals are spatially autocorrelated, E {ε ε }= σ 2 K = Ω, a variance-covariance matrix, will have non-zero offdiagonal elements. Geo-statistics offers a few tools that can directly model the matrix Ω (Pace et al, 1998; Dubin et al, 1999). In this paper, we choose a Spherical Semivariogram functional form (Basu and Thibodeau, 1998) to estimate the variance and covariance matrix (Ω). 11

13 Let l denote the location of property i, and ε l ) i ( i denote the hedonic price equation residual for the property located at l i. Assuming that the spatial process is second-order stationary and isotropic, meaning that the mean and variance of each residual distribution are constant at all locations and the correlation between the residuals is a function of the distance separating the properties only. The co-variogram ( C ( l i l j ) ) for the distribution of the residuals is C ( l i l j ) = Cov { ε ( l i ), ε ( l j )}, for any two properties located at locations l i, l j. l i l j denotes the (Euclidean) distance between locations l and l and Cov ε ( l i ), ε ( l )} i j { j is the covariance between the two residuals. Note that C ( 0 ) is the constant variance for the residual distribution. The semi-variogram ( γ l l ) ) of the spatial process is defined by equation 2. ( i j γ l l ) = 0.5Var { ε ( l ) ε ( l )} = C ( 0 ) C ( l l ) (2) ( i j i j i j The semi-variogram defined in equation (2) is an increasing function of the distance between any two properties. Other features in relation to the semi-variogram are as below. First, assuming that h = l i l, clearly, γ ( h) = γ ( h) and mathematically γ ( 0) = 0. j Second, γ (h) is discontinuous near the origin, which is γ ( h ) θ 0 > 0, as h 0. Matheron (1963) labeled the discontinuity θ 0 as the nugget. Third, observations may eventually become spatially uncorrelated as the distance between them increases. Therefore, the semi-variogram will stop increasing beyond some threshold and will become a constant. That is, γ ( h) C *, as h. The threshold C * is called the sill of semi-variogram. The range of semi-variogram is the value h 0, which makesγ ( h 0 ) C *. So the range of semi-variogram is essentially a distance between two 12

14 observations beyond which observations become spatially uncorrelated. According to equation (2), the Sill is also the variance of the residual. To estimate the semi-variogram, Spherical function specification is used as it provides a finite Range which can assist us to identify the submarket. The range indicates that dwellings within the range must be spatially correlated. The Spherical semi-variograms specification is as below. h h 3 θ 0+ θ 1[1.5( ) 0.5( ) ] θ2 θ 2 γ ( h; θ) = 0 θ1 + θ2 if if if 0 < h θ2 h = 0 h > θ 2 (3) The nugget for the spherical semi-vriogram is θ 0, the sill is θ 0+ θ 1, and the range is θ 2. The method of moments estimator (Matheron, 1963) is used to estimate the three parameters (θ 0, θ 1, θ 2 ) in equation (3). To estimate the standard errors of these estimates, it is assumed that the semi-variogram residuals are independently and identically distributed with zero mean and constant variance. With the estimated parameters (the nugget θ 0, the sill θ 0+ θ 1, and the range θ 2 ) and the distance matrix which gives distance relationship between two properties and is calculated using the X-Y coordinates, the estimates of elements of variance-covariance matrix, Ω are derived (equation 4). 13

15 C( l i l h h 3 θ1{1 [1.5( ) 0.5( ) ] θ 2 θ 2 ) = C( h) = θ 0 + θ1 0 j if if if 0 < h θ 2 h = 0 h > θ 2 (4) Non-zero entries in this empirical variance-covariance matrix indicate the existence of spatial correlation between two properties. As the range estimated above equivalently reflects the spatial autocorrelation, it is used as the criterion to group dwellings into clusters. In other words, all the housing units are categorized into clusters according to the rule of range. Clustering housing units into groups according to their spatial autocorrelation structure Starting from any housing unit, say unit-1, if the distance from unit-2 to unit-1 is less than the estimated range, they are classified into one cluster. If the distance from another unit, say unit-3, to unit-2 is less than the range, but the distance from unit-3 to unit-1 is greater than the range, unit-3 is also grouped into the same cluster as unit- 1 and unit-2. The cluster chain should continue in this manner until there is no more units joining this cluster. The cluster formed in this way ensures that each housing unit in the cluster is at least spatially correlated with another unit in the same cluster (to a certain degree, sharing similar spatial features), or in other words, housing units in the different clusters will not share any common spatial features. 14

16 By grouping in this way, it is possible that all housing units in a market are grouped into one cluster if the market is continuous. However, an urban housing market is typically discontinuous. Physically, it means that the market may be divided by rivers, main roads, green parks or non-residential buildings etc. Socially, it means that the market may be divided by income groups or ethnic groups. Therefore, it is unlikely that all units are absorbed into one cluster. Market segmentation For the property clusters identified above, standard submarket tests are applied to each cluster. First, Chow-test (Allen et al 1995) is applied to any two clusters under the null hypothesis that the two hedonic mean functions for the two clusters are equivalent. The results aggregate the clusters to submarket level. Second, Tiao-Goldberger test (Michaels and Smith, 1990; Allen et al 1995) is applied to all submarkets under the null hypothesis that across submarkets, all coefficients for a hedonic variable are equal. The results further confirm the identified submarket structure. Third, the resulting submarket structure is compared with the prevailing submarket structure. Weighted mean square test (Bourassa et al 1999; Watkins 2001; Schnare and Struyk 1976) is used to determine the best submarket classification under the null hypothesis that the defined submarket structure improves the predictability of the model better. IV Empirical Results The above procedure is applied to Singapore condominium market. The condominium transaction data with hedonic characteristics are obtained from an online real estate 15

17 transaction database (Realink). The system obtains its information from official sources on property caveats and transactions and is subscribed by the real estate services industry, including appraisal and agency. It is maintained by the Singapore Institute of Surveyors and Valuers, the national professional body representing the real estate professions. Realink has been established since 1990 and is a comprehensive database that is used by the industry. The dataset used in this study includes 4,192 condominium units transacted between January 2000 and December They are located in 480 different condominium projects, which account for nearly 72% of the total number of condominium projects in Singapore. In the dataset, the size of condominium projects ranges from 8 dwelling units to 1,232 units. Each condominium project may have more than one building block with the height of the block ranging from 2 to 37 stories. Each transaction record is associated with the variables indicating the full address, hedonic characters, condominium project characters. All transactions are geo-coded and some standard neighborhood variables are measured and added to the dataset. The statistics of some key variables are given in the first column of Table 4 below. In Singapore each building block corresponds to one postcode. The geo-statistical information in our dataset is then recorded at the building level, with each building corresponding to one X-Y coordinate. The distance matrix is constructed as follows: for the dwellings located in the same building block, the distance between them is zero; for dwellings located in different building blocks, the distance is measured as the distance 16

18 between the respective buildings. In the dataset, the average distance between the buildings is km with a standard error of 5.375km. The shortest distance is km, while the longest distance is km. Estimating empirical semi-variogram A conventional hedonic function is estimated against all transaction data. The functional form is carefully selected against the criterion of R 2. All significant independent variables are retained in the function. The hedonic modeling results are reported in Table A2 of the appendix. The residuals are used to estimate the empirical Spherical Semi-Variogram (Table 1). The variance-covariance matrix is constructed. Table 1 Empirical Spherical Semi-Variogram [1] Estimators Std θ θ ** θ 2 (Kilometre) ** Note: 1. the empirical OLS hedonic function associated with the estimation of Semi-variogram is in Table A2 of the appendix. The semi-variogram is estimated using the method of moments estimator (Matheron, 1963). The software is MatLab. 2. ** indicates the significance of 1%. The empirical Spherical Semi-Variogram shows that, although nugget is insignificant, both sill and range are significant at the 1% significance level. The nugget is and the sill is The range is km, meaning that the spatial correlation between housing prices exists significantly within a range of km. 17

19 Identifying property Clusters The estimated coefficients in Table 2 are brought into equation (4). An empirical variance-covariance matrix is obtained. Based on it, all dwellings are grouped into the clusters by following the rules illustrated in Section III. In Singapore condominium market, the estimated variance-co-variance matrix can be simplified. In this market, each dwelling unit is located in a building block and each building block is within a condominium project. Therefore, it is intuitive that if a dwelling belongs to a cluster, all the dwellings in the same condominium will belong to the same cluster. For this reason, the estimated variance and co-variance matrix are simplified at the building block level. For each condominium project, we randomly select one building block, and the covariance between any two buildings is then estimated. Based on this simplified variance co-variance matrix, the dwellings as well as the condominiums where the dwellings belong, are grouped into clusters. Empirically, 21 clusters are obtained. Out of the 480 condominiums, there are 44 that do not belong to any clusters. In other words, their hedonic residuals are not correlated with any other condominiums. These condominiums are either geographically isolated or they are older developments which are priced differently from the relatively newer condominiums. The spatial information related to these 21 clusters is presented in Table 2. Their locations are indicated on Map A1 in the Appendix. 18

20 Table 2 Spatial Information of Property Clusters Clusters Numbers of Condo Projects Distance between the condos in the clusters Min (Meter) Max (Meter) Mean (Meter) Std (Meter) ,688 2, , , , , , , , , , , , , , , , In order to aggregate these clusters to submarket level, Chow-test (Allen et al 1995) is adopted. Initial analysis shows that clusters 16 to 21 are too small to form any independent submarkets. They are also independent of any other larger submarkets. Therefore, at this stage, we only consider the clusters that consist of at least five condominiums. In total there are 15 such clusters. Chow-test is applied to these 15 clusters, resulting in 8 submarkets (See Table 3). 19

21 Table 3 Define Submarkets Submarkets Clusters Numbers of Condo Projects ,7,9,11,13, , ,15 10 All 416 Note: Chow-test results are available at request. The above submarkets are illustrated by Map 1 below. It should be noted that out of the 480 condominium projects in the dataset, 13% are not grouped into any submarket. Comparing these clusters with others, we find that they are either older condominiums (their quality and facilities are typically inferior to newer condominiums) or are geographically isolated condominiums. These non-submarket projects are indicated in Map 1 using dots. For the 8 submarkets, their selected characteristics are presented in Table 4 below. The selected characteristics of condominiums that not belong to any submarkets are given in Table A4 in the appendix. 20

22 Table 4 Selected Characteristics of Submarkets in Singapore Condominium Market Variables Submarkets Whole Mean (Std) 1 Mean (Std) 2 Mean (Std) 3 Mean (Std) 4 Mean (Std) 5 Mean (Std) Price (S$) 1,024,723 1,452,52 949, ,155 1,303, ,548 (580,485) (916,609) (450,745) (297,707) (573,899) (210,161) Size(sqm) ,87 (56.925) (79.995) (52.403) (36.278) (75.006) (34.951) Level (5.831) (6.601) (6.423) (4.706) (3.12) (6.884) Age (year) (6.308) (6.211) (5.83) (3.891) (5.924) (5.105) Total_units (279.92) ( ) ( ) ( ) ( ) (87.541) Dist_MRT (km) (0.9086) (0.3477) (0.7243) (0.7386) (0.9227) (0.7844) Dist_CBD (km) (4.3642) (1.5403) (3.3217) (2.4463) (0.5928) (0.7803) Dist_Secon Mean (Std) 1,273,108 (342,891) (57.957) 6.18 (4.88) (4.765) ( ) (0.1412) (0.3821) Mean (Std) 671,051 (164,279) (32.969) 8.25 (5.315) 8.22 (5.28) ( ) (0.3183) (0.4982) dary(km) (1.7793) (0.7041) (1.0728) (1.4674) (0.4418) (0.629) (0.3321) (0.5612) Dist_Junior (km) (2.6239) (0.9421) (1.8593) (2.2363) (0.6391) (0.5082) (1.1657) (0.1456) Frequency (%) Freehold BBQ CarPark GYM Jacuzzi Fitness Minimart Mph Playgrou Sauna Mean (Std) 721,504 (155,033) (37.77) 5.38 (3.758) 6.83 (5.526) ( ) (0.4735) (0.6732) (0.5617) (1.3601)

23 Squash Swimming Tennis Wading Security Others Primary Note: Definition of all variables are given in Table A1 in the Appendix. 22

24 In order to justify if the above formed housing submarket structure reflects true market segmentation, Tiao-Goldberger test and weighted mean square test are performed (Michaels and Simith, 1990; Allen et al 1995; Bourassa et al 1999; Schnare and Struyk 1976). To conduct these tests, a hedonic function for each submarket must be estimated. To resolve the problem of residual spatial autocorrelation at submarket level, an empirical spherical semi-variogram is estimated at each submarket level (Table 5). The results show that the range for submarkets 5, 6, and 7 is statistically insignificant, indicating that the hedonic residuals derived from the submarket level hedonic function are in fact spatially uncorrelated. Table 3 shows that these three submarkets are relatively small submarkets, each occupying a smaller size of geographical area (also see Map-1). Such results imply that for housing units located within a smaller geographical area where the degree of homogeneity is generally high, their prices can be well explained by the conventional hedonic function resulting in the correlated residuals. Based on these results, a GLS estimation (generalized least square) is applied to submarkets 1, 2, 3, 4 and 8, while an OLS estimation is applied to submarkets 5, 6 and 7 to derive a hedonic function (See Tables A3-1 to A3-8 in the appendix). Tiao-Goldberger test is carried out to determine whether the hedonic prices of a hedonic factor are significantly different across housing submarkets. Across all submarket hedonic functions, dwelling size is the only hedonic factor appearing to be statistically significant. And hence, Tiao-Goldberger test is applied to dwelling size only. The results show that the hedonic prices of size are significantly different across all submarkets. To compare this submarket structure (see Map 1) with the prevailing submarket structure (see Map A2), a weighted mean square test is applied. It is shown that, overall, our defined submarket structure can significantly reduce the price prediction error by 32.23%. To compare the defined submarket structure with the prevailing submarket structure, prime districts (Submarket 1 in Map A2) are selected. We find that nearly 50% of the condominium units located in the prime district (submarket 1 in Map A2) are in fact re-

25 grouped into other submarkets in our newly defined submarket structure. A weighted mean square test applied to the transactions located in the prime district, shows that price prediction based on newly defined submarket structure can improve the precision by 17.5%. Table 5 Empirical Spherical Semi-Variogram at Submarket Level Submarkets Sill (Std) Nugget (Std) Range (Std) (0.0027) (0.002) (0.357) (0.002) (0.0012) (0.0087) (0.0011) (0.0006) 1.58 (0.009) (0.0028) (0.0021) (0.0210) (0.0070) e-011 (0.0272) (1.8489) (0.0029) e-008 (0.0038) (2.4030) (0.0013) e-008 (0.1135) ( ) (0.0006) (0.0005) (0.0167) Note: Tiao-Goldberger and weighted mean square testing results are available at request. 24

26 Map 1 Singapore Condominium Submarket Structure On the whole, the study has revealed significantly more submarkets than previously thought of. The delineation between the submarkets is also more defined than the broad geographical sectors that are usually used to identify the locations of condominiums. Nevertheless, most of the 8 newly defined submarkets could be juxtaposed with existing acknowledged submarkets. In Map 1, submarkets 1 and 4, for instance, reflect what has been commonly referred to as the prime residential districts. Submarket 6 corresponds to an established private residential area just outside the prime district. Similarly, submarkets 2 and 3 could be juxtaposed with existing residential estates. This new empirical evidence seems to confirm that the existing submarket delineation is well established in terms of neighborhood and price characteristics. 25

27 The second important revelation of this study is that submarkets need not be clustered together geographically. While submarkets 2 and 3 do correspond with existing submarkets, our study shows that new clusters exhibiting similar characteristics to these geographical submarkets have been established over time. More interestingly, these clusters are located quite far apart from the established geographical sector. This underlines the fact that with improved transport infrastructure, location is no longer the sole key determinant for the pricing of condominium housing in Singapore. This is especially so if the differences in the other neighborhood characteristics such as amenities and public infrastructure could offset the advantages of location. This finding adds a new perspective to prospective house buyers as geographical location is not the only criterion in identifying submarkets with similar pricing mechanism. The third significant finding is the recent emergence of new submarkets in private condominium housing in Singapore. Submarkets 5, 7 and 8, are relatively new in that they are the result of decentralization which saw many condominium projects developed on suburban vacant sites sold by the government through the Urban Redevelopment Authority (the Planning Authority of Singapore as well as the principal agent for the sale of state land for private developments) and the Housing and Development Board (the public housing authority in Singapore). These sites are typically located near to public housing estates, which enjoy the convenience of nearby amenities and facilities. 26

28 Fourth, the defined submarket structure can significantly improve the precision of price prediction by 32.23% if it is compared with the prediction against whole market, or by 17.5% if it is compared with the prediction against prevailing submarkets Last but not least, while we can empirically identify established as well as new submarkets, we also discover that there are condominium projects that do not belong to any submarket. The red dots in Map 1 show these projects which do not fit into any of the newly defined submarkets. On closer examination, these projects are either farther away from the CBD and, hence, have different locational attributes or that they possess characteristics which do not fit into any of the defined submarkets. These include age and the lack of facilities and amenities. This finding is important as most previous studies have tended to group all properties into one submarket or another even if they do not quite belong. As demographic, economic and technological factors change at an increasing pace, there will be properties which are out of place or time with the surrounding. V Conclusions This research has contributed to our understanding of the urban housing price determination process. The conceptualization of incorporating spatial auto correlation into housing submarket identification as well as the use of spatial models to estimate hedonic functions provides a way to define housing submarkets through statistical modeling rather than through an ad hoc selection of housing product groups. The juxtaposition of the new submarkets to the existing established submarkets, especially the 27

29 prime residential districts, confirms the appropriateness of the methodology. More importantly, the revelation of new and more specifically defined submarkets for private condominiums in Singapore in this study can be reasonably explained. Most of the emerging submarkets, for instance, can be attributed to the activities of the residential market in Singapore over the last decade. The concept of defining submarket by the aggregate of the neighborhood characteristics also implies that location may no longer be the sole determinant of house price as transportation infrastructure improves over time. The submarket structure identified in this way provides a better framework for planning and economic analysis, appraisal and property tax assessment, mortgage evaluation as well as price prediction and forecasting. The emergence of distinctive submarkets will provide a deeper understanding of demand and supply at the micro level and hence allow the planning authority to fine tune their supply of residential lands in the future. More direct applications of the submarkets are in price prediction, appraisal and property tax assessment. The new submarket structure may well provide better justification for the assessment of annual values carried out by the tax authority. The limitation in using spatial autocorrelation structure to group dwellings into clusters is the lack of likelihood consideration. The consequence may be that it is possible that two contiguous neighborhoods are combined into one, which may increase the dissimilarities within a cluster. Another limitation is that there is evidence (Gillen et al 2001) to show that there are actually anisotropic autocorrelations among urban housing prices, meaning that spatial autocorrelation is a function of both the distance and the direction separating 28

30 points in space. However, adopting a parametric approach, estimating anisotropic Semivariogram needs a prior knowledge about compass directional class (Simon 1997), which limits its application to the current study. Non-parametric statistical approaches (see an example in Clapp and Wang, 2003) may provide a new angle to attempt the issue, which is also our future research direction. 29

31 References Adair, A.S., Berry, J.N. and McGreal, W.S. (1996) Hedonic Modelling, Housing Submarkets and Residential Valuation, Journal of Property Research, 13, ; Allen, M. T., Springer, T. M., and Waller, N. G. (1995) Implicit Pricing Across Residential Submarkets, Journal of Real Estate Finance and Economics 11(2) Basu, S. and Thibodeau, T. (1998) Analysis of Spatial Autocorrelation in House Prices, Journal of Real Estate Finance and Economics, 17(1), Bourassa, S., Hamelink, F., Hoseli, M. and MacGregor, B. (1999) Defining Housing Submarkets, Journal of Housing Economics, 8, Bourassa, S. C., Hoesli, M. and Peng, V. S. (2003) Do Housing Submarkets Really Matter? Journal of Housing Economics 12: Capone, C. A., and Goldberg, L. (2001) Renter Mobility and Multifamiliy Mortgage Default Risk, Journal of Housing Economics, 10(1) Clapp, J. M., Kim, H. J. and Gelfand, A.E. (2002) Predicting Spatial patterns of House Prices Using LPR and Bayesian Smoothing. Real Estate Economics 30(4): Clapp, J. and Y. Wang (2004) Defining Neighborhood Boundaries: are census tracts obsolete? Working paper. Cliff, A. and Ord, J. (1981) Spatial Processes, Models and Applications. London: Pion. Dale-Johnson, D. (1982) An Alternative Approach to Housing Market Segmentation Using Hedonic Price Data, Journal of Urban Economics, 11, Dubin, R.A. (1992) Spatial Autocorrelation and Neighbourhood Quality, Regional Science and Urban Economics, 22,

32 Dubin, R.A., Pace, R.K. and Thibodeau, T.G. (1999) Spatial Autoregression Techniques for Real Estate Data, Journal of Real Estate Literature, 7, Dunse, N., Leishman, C. and Watkins, C. (2002) Testing for the Existence of Office Submarkets: a Comparison of Evidence from Two Cities, Urban Studies, 39(3), Galster G. G. (2003) Neighborhood Dynamics and Housing Markets. In Tony O Sullivan and Kenneth Gibb (eds) Housing Economics and Public Policy. Oxford: Blackwell. Goodman, A.C. and Thibodeau, T.G. (1998) Housing Market Segmentation, Journal of Housing Economics 7, ` Gillen, K., Thibodeau, T. G. and Wachter, S. (2001) Anisotropic Autocorrelation in House Prices. Journal of Real estate Finance and Economics 23(1): Halvorsen, R. and Pollakowski, H. (1981) Choice of Functional Form for Hedonic Price Functions, Journal of Urban Economics 10: Jones, C. (2002) The Definition of housing Market Areas and Strategic Planning, Urban Studies, 39(3), Maclnnan, D. and Tu Y, (1996) Economics Perspectives on the Structure of Local Housing Markets, Housing Studies, 11, Matheron, G. (1963) Principles of Geostatistics, Economic Geology, 58, Michaels, R. G., and Smith, V. K. (1990) Market Segmentation and valuing Amenities with Hedonic Models: the Case of Hazardous Waste Sities, Journal of Urban Economics 28, Pace, R.K., R. Barry and J.M. Clapp and M. Rodriquez (1998) Spatiotemporal Autoregresive Models of Neighbourhood Effects, Journal of Real Estate Finance and Economics, 17(1),

33 Palm, R. (1978) Spatial Segmentation of the Urban Housing Market, Economic Geography 54, Schnare, A. B., and Struyk, R. J. (1976) Segmentation in Urban Housing Markets, Journal of Urban Economics 3, Straszheim, M. (1975) Hedonic Estimation of the Housing Market Prices: a further comment, Review of Economics and Statistics 56, Simon, G. (1997) An Angular Version of Spatial Correlations, with Exact Significance Test, Geographical Analysis 29(3) Tu, Y and Goldfinch, J. (1996) A two Stages Housng Choice Forecasting Model, Urban Studies, 33(3), Watkin, G. (2001) The Definition and Identification of Housing Submarkets, Environment and Planning A, 33,

34 Appendix Table A1 Variable Definitions Variables Description Price Dwelling transaction price (Unit: S$) Size Floor area in each condominium flat (unit: m 2 ) Age The age of the condominium project (Unit: year) Level The floor level where the flat is (Unit: number) Freehold Dummy variable with ONE indicating freehold, otherwise ZERO. units Total number of dwelling units in the condominium project (Unit: number) swimming, 15 Dummy variables, each with ONE indicating having the squash, respective facility, otherwise ZERO. The facilities are: tennis, swimming pool, squash court, tennis court, sauna, sauna, playground, multi-purpose hall, gym, covered car park, and playgrou, barbeque area, jacuzzi, wadding pool, 24 hours security mph, and others gym, car park, BBQ Jacuzzi Wadding Security Others Primary Dummy variable with ONE indicating the property is with 1 km to the 1 st and nearest top 30 primary schools, otherwise ZERO. Dist_secondary Distance to the 1 st nearest top 10 secondary schools (Unit: km) Dist_Junior Distance to the 1 st nearest top 10 junior college (Unit: km) Dist_MRT Distance to the nearest MRT station (Unit: km) Dist_CBD Distance to the central of CBD (Unit: km) 33

35 Table A2 Market Wide Hedonic Function (OLS estimation) Variables Coefficient (Std) Constant (0.295) Size 0.490(0.088) Size (0.001) Level 0.006(0.001) Age (0.001) Freehold 0.576(0.054) Unit (0.19) Unit*Freehold (0.022) Gym 0.063(0.009) Mph 0.026(0.008) Playgrou 0.018(0.011) Squash 0.084(0.010) Swimming 0.168(0.021) Wadding 0.106(0.011) Security 0.080(0.016) Dis_Sec (0.003) Dis_jc (0.002) Mrt (0.004) Primary 0.023(0.008) Adjusted R Mean Square of Residual Sample size

36 Table A3-1 Submarket Wide Hedonic Function (GLS) Variables Constant ( ) Size ( ) Freehold (4.1698) Gym (3.0435) Swimming 0.307(3.199) Adjusted R Mean Square of residual Sample size 813 Coefficient (T-stat) Table A3-2 Submarket Wide Hedonic Function (GLS) Variables Coefficient (T-stat) Constant ( ) Size ( ) Freehold (4.5743) Unit ( ) Gym (3.2846) Squash (2.9306) Swimming (1.896) Wadding (2.4179) Adjusted R Mean Square of residual Sample size 1063 Table A3-3 Submarket Wide Hedonic Function (GLS) Variables Coefficient (T-stat) Constant ( ) Size 0.858( ) Age ( ) Freehold (5.8526) Primary (3.1825) Adjusted R Mean Square of residual Sample size

37 Table A3-4 Submarket Wide Hedonic Function (GLS) Variables Coefficient (T-stat) Constant 9.653( ) Size ( ) Freehold 0.294(3.5963) Adjusted R Mean Square of residual Sample size 171 Table A3-5 Submarket Wide Hedonic Function (OLS) Variables Coefficient (T-stat) Constant ( ) Size (5.6384) Wadding (5.6756) Adjusted R Mean Square of residual Sample size 78 Table A3-6 Submarket Wide Hedonic Function (OLS) Variables Coefficient (T-stat) Constant ( ) Size ( ) Freehold ( ) Unit ( ) Squash (9.9612) Adjusted R Mean Square of residual Sample size 215 Table A3-7 Submarket Wide Hedonic Function (OLS) Variables Coefficient (T-stat) Constant (55.217) Size 0.663( ) Age ( ) Freehold (6.8722) Adjusted R Mean Square of residual Sample size 65 36

38 Table A3-8 Submarket Wide Hedonic Function (GLS) Variables Coefficient (T-stat) Constant ( ) Size ( ) Freehold (4.0029) Mph ( ) Playgrou (2.2181) Adjusted R Mean Square of residual Sample size 122 Table A4 Selected characteristics for the condominiums that don t belong to any submarkets. Min Max Mean Std Price (S$) 296,000 2,859, ,673,98 335, Size(sqm) Level Age (year) Total_units Dist_MRT (km) Dist_CBD (km) Dist_Secondary (Km) Dist_Junior (km) Frequency (%) Freehold 45.5 BBQ 61.3 CarPark 84.1 GYM 55.5 Jacuzzi 27.7 Fitness 50.5 Minimart 5.3 Mph 34.5 Playgrou 83.1 Sauna 43.9 Squash 65.2 Swimming 90.6 Tennis 85.8 Wading 80.7 Security 90.4 Others 74.6 Primary 21.7 Note: the definitions of these variables are given in Table A1 37

39 Map A1 Property Clusters in Singapore Condominium Market Map A2 Prevailing Singapore Private Housing Submarkets 38