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The structure of Housing Submarkets in a Metropolitan Region
BOURASSA, Steven C., HOESLI, Martin E.
Abstract
In this paper, it is examined whether the structure of constrained submarkets constructed according to three a priori classifications (property type, house value and geographical areas) differs from that of unconstrained submarkets constructed by means of principal component analysis and cluster analysis. This procedure makes it possible to assess the impact of imposing a priori constraints when housing submarkets are constructed. Data for Auckland, New Zealand, are used. The structure of housing submarkets in the Auckland region is found to be related primarily to the physical characteristics of properties. The other dimensions of housing submarkets gain more importance only when classifications with several submarkets are considered. The a priori classifications are found to lead to submarkets whose structure does not reflect the dimensions of housing submarkets in this metropolitan region.
BOURASSA, Steven C., HOESLI, Martin E. The structure of Housing Submarkets in a Metropolitan Region. 1999
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The Structure of Housing Submarkets in a Metropolitan Region
Steven C. Bourassa* & Martin Hoesli**
*Department of Urban and Public Affairs, University of Louisville, USA
**HEC, University of Geneva, Switzerland and Department of Accountancy, University of Aberdeen, Scotland
November 17, 1999
Correspondence
Martin Hoesli, University of Geneva, HEC, 40 boulevard Carl-Vogt, CH-1211 Geneva 4, Switzerland
Tel: ++4122 705 8122, Fax: ++4122 705 8104, email: martin.hoesli@hec.unige.ch
The Structure of Housing Submarkets in a Metropolitan Region
ABSTRACT
In this paper, it is examined whether the structure of constrained submarkets constructed according to three a priori classifications (property type, house value and geographical areas) differs from that of unconstrained submarkets constructed by means of principal component analysis and cluster analysis. This procedure makes it possible to assess the impact of
imposing a priori constraints when housing submarkets are constructed. Data for Auckland, New Zealand, are used. The structure of housing submarkets in the Auckland region is found to be related primarily to the physical characteristics of properties. The other dimensions of housing submarkets gain more importance only when classifications with several submarkets are considered. The a priori classifications are found to lead to submarkets whose structure does not reflect the dimensions of housing submarkets in this metropolitan region.
1. INTRODUCTION
Given the spatial immobility, stock durability, and heterogeneity of housing services, as well as the inelastic demand and supply of housing over the short- and medium-term, it is unlikely that the housing market is a uniform entity. This is true across metropolitan areas, but is also valid within a metropolitan area. The interaction of inelastic demands for particular types of housing and relatively inelastic supplies may disrupt the equilibrium market conditions in the housing market, and segment the market into a set of fairly independent sectors or submarkets. Houses will be close substitutes within a submarket and poor substitutes across submarkets.
Traditionally, submarkets are defined in either spatial or structural terms. When spatial dimensions are used, housing market segmentation can use pre-existing geographic or political boundaries (Schnare and Struyk, 1976; Goodman and Kawai, 1982; Adair et al., 1996) or spatial partitions based on socio-economic or environmental characteristics of an area (Schnare, 1980; Galster, 1987; Harsman and Quigley, 1995). Another way of delineating submarkets in spatial terms is offered by Palm (1978). She argues that information constraints and search costs may segment the market into different submarkets, within which it is probable that housing information is exchanged at low costs, and between which little information is available without the investment of relatively more time and effort. Similarly, Palm (1976) and Michaels and Smith (1990) investigate submarkets delineated by real estate agents. The use of structural dimensions to define housing submarkets has been on the basis of the number of rooms (Schnare and Struyk, 1976), lot and floor area (Bajic, 1985), or the type of dwelling, such as detached versus attached (Allen et al., 1995; Adair et al., 1996).
Some researchers have used statistical techniques to define housing submarkets. Dale- Johnson (1982) uses factor analysis on 13 variables (including price), and extracts five factors which are used to define 10 submarkets. In all but one case, the hypothesis of similarity of the hedonic regression coefficients across submarkets is rejected. Maclennan and Tu (1996) investigate the structure of housing submarkets in Glasgow. They use principal component analysis (PCA) to identify the individual variables that explain the highest proportion of the variation in the data. These variables are then used as the basis for cluster analysis. Goodman and Thibodeau (1998) use hierarchical methods to define submarkets in a study that focuses on the role of school districts in Dallas. Bourassa et al. (1999) use PCA to extract the
relevant factors or dimensions of residential submarkets. The significant factors are then used in a series of cluster analyses to form submarkets. Unlike Maclennan and Tu (1996), Bourassa et al. apply cluster analysis to factor scores, which are linear functions of all of the variables,
rather than individual variable values. The empirical analysis is performed using data for Sydney and Melbourne, Australia.
The aim of this paper is to analyse the structure of housing submarkets in a metropolitan region. In particular, it is examined whether the structure of constrained a priori submarkets differs from that of unconstrained submarkets which are constructed by means of statistical methods. In other words, we want to assess the validity of a priori definitions of the sort commonly used in housing submarket analysis. For this purpose, data for the Auckland, New Zealand, housing market are used. Three classifications of a priori submarkets are defined:
property type (detached versus attached); house value (according to approximate quartiles);
and six geographical areas defined by the local government boundaries. Unconstrained submarkets are constructed as follows. First, PCA is used to extract factors from the
variables. Second, standardised factor scores are calculated, and these scores are weighted by the percentage of variance explained by each factor. Third, cluster analysis is used on the weighted factor scores to construct housing submarkets.
There is no presumption in this analysis that statistically defined submarkets are spatially contiguous. Although it is probably desirable for most practical applications to impose some form of spatial contiguity, here we allow the data to determine which dwellings are the closest substitutes without imposing any such constraints. This is of particular interest as the aim of the paper is to analyse the structure of submarkets. Thus, the structure of constrained submarkets (the a priori submarkets) can be compared to that of unconstrained submarkets (the statistically defined submarkets).
The data set includes the transaction prices and an extensive list of structural
characteristics for all dwelling sales in Auckland in 1996. An important advantage of the Auckland data set is that the co-ordinates of properties are available, so that the distance from the central business district (CBD) can be measured for each property. This is made possible
by the use of a geographic information system (GIS). Chen (1994) has shown, using a GIS for the greater Boston area, that the street distance of the shortest path or the Euclidean distance from the house to the CBD has more explanatory power in hedonic regressions than has the Euclidean distance from the centroid of a tract or a block group to the CBD. The other locational attributes of the properties used in this study are drawn from the 1996 census. The census variables are not property-specific but refer to small geographic areas (the area units, AUs). The average size of the AUs is 18 square kilometres.
The paper is organised as follows. The construction of submarkets and data are presented in sections 2 and 3, respectively. In section 4, the dimensions of housing submarkets are presented, while the results of an analysis of the structure of constrained and unconstrained submarkets are discussed in section 5. Section 6 contains the conclusions.
2. CONSTRUCTION OF SUBMARKETS
Three a priori classifications of housing submarkets are considered in this paper. The first refers to property type and comprises of two categories: detached and attached units. The housing market is also segmented on the basis of house values. Four categories are considered based on the quartiles of the distribution of values. Finally, a geographic
classification based on the local government areas is used. There are six local governments in the Auckland metropolitan region: Auckland City, Manukau City, North Shore City, Papakura District, Rodney District and Waitakere City.
The statistically defined submarkets are constructed as follows. Principal component analysis (PCA) is used to extract orthogonal factors from the variables. Principal component or factor analysis is a procedure by which to derive a small number of linear combinations (the principal components or factors) of the original variables which retain a substantial amount of the information contained in these variables. The first component is the linear combination of
the original variables that explains the maximum variance in the data. The second component is the linear combination of the original variables that is orthogonal to the first and that
explains the maximum proportion of the variance unexplained by the first component. The ith component is orthogonal to the first i-1 components and explains the maximum proportion of the variance unexplained by those components. It is possible to extract as many components as there are original variables.
The components that jointly account for at least 80 percent of the variance are retained, and for interpretation purposes, these components are rotated using a VARIMAX procedure.
By VARIMAX rotation, the new principal components and the factor scores calculated on these components remain uncorrelated, which meets the requirement of using only non- collinear variables for cluster analysis. Factor scores, however, need to be weighted.
Otherwise, the variables which have high loadings on less important factors will have the same impact in the cluster analysis as variables which load highly on important factors. This would not be making full use of the information concerning the dimensions of housing submarkets contained in the PCA results. One obvious way of weighting the factor scores is to use the percentage of variance explained by each factor. This procedure is used in this paper.1
Weighted factor scores are then used in cluster analysis to construct homogeneous submarkets. Cluster analysis is a procedure for allocating observations to groups, based on the data rather than on a priori classifications, so that observations in a cluster tend to be similar to one another but different from observations in other clusters. The number of clusters is set to equal the number of a priori constrained submarkets, i.e. two, four and six, respectively. As concluded by Afifi and Clark (1990), if the number of clusters to be grouped is known, a particularly appropriate method of clustering is the K-means method of MacQueen (1967). Therefore, a version of K-means clustering, for which the metric is squared Euclidean distance, is used in this study.
3. DATA
The sale prices and physical characteristics of housing are drawn from Valuation New Zealand (VNZ) sales data. The VNZ data contain such information about housing as: exact location, floor area, age, construction material and exterior condition, an assessment of overall quality, sale date, total sale price and value of chattels. Dwelling type (attached or detached) is also derived from the VNZ data. All of the data used for this study refer to dwellings with separate freehold titles that transacted individually and at “arm’s length”.
The census is conducted in New Zealand every five years, and the data used in this study are from the latest census conducted in 1996. Each property in the VNZ data set was assigned to a census polygon using the standard GIS technique of overlay, which allows a polygon to be assigned to each property. This was then related to associated census variables for that tract. Census data provide socio-economic characteristics of geographic areas at various scales, including the area units (AUs) used in this study. There are 326 AUs in the Auckland region. The average area and population are 18 square kilometres, as noted previously, and 1,000 to 1,500 persons, respectively. For each area unit, the following information was extracted and calculated: the densities of population and dwellings, home ownership rate, median household income, percentage of people receiving income support, average number of cars per household, average number of bedrooms per house, percentage unemployed, as well as ethnic composition.
The use of a GIS also allowed the data set to be supplemented with the measure of the Euclidean distance between each property and the CBD. Houses have been geo-coded using offset street addresses that provide location with a general accuracy of plus or minus 20 meters for urban properties.
There were 34,753 freehold residential properties sold in the Auckland metropolitan area
in 1996, of which 25,653 sales were suitable for the present analysis. The majority of the discarded sales had missing or aberrant values for variables used in the analysis.2 The balance of the observations were omitted because they could not be geo-coded and thus could not be matched with variables extracted from the census and the distance from the CBD could not be calculated. Table 1 presents summary statistics of the VNZ and distance from the CBD data for individual dwellings, and census data for AUs.
[Insert Table 1 (Summary statistics) here]
The average sale price of houses is approximately NZ$262,000 with NZ$9,400 of chattels (approximately 4% of sales price on average). The average size of dwellings is 132 square metres, yielding an average price per square metre of NZ$1,990. Most houses are detached and their average age is 27 years. Dwellings are usually of good roof and wall quality, and have a tile roof and wooden walls and an average quality of the principal structure. The average distance to the CBD is approximately 12 kilometres. The average home ownership rate in the Auckland region is above 70%, and approximately 70% of the population is of European descent. Maori, Pacific Islanders and Asians account for the remaining 30% of the population.3 Approximately one third of house sales are in the city of Auckland.
4. DIMENSIONS OF HOUSING SUBMARKETS
Principal component analysis is used to extract information contained in the available data.
Applying PCA allows the uncorrelated factor scores for each of the components, rather than individual variables with potential multicollinearity problems, to be used in the cluster analysis.
The PCA is also interesting in its own right because it identifies the underlying dimensions that distinguish housing submarkets.
Twelve principal components were retained by the 80 percent total variance criterion. The lowest communality of the retained components is 0.53, which means that all variables have
been well represented by the retained components, and enough components have been retained to capture sufficient information from these variables. These principal components disclose the underlying dimensions, or factors, that distinguish Auckland residential submarkets.
Table 2 presents the 12 factors retained in the principal component analysis. Panel A indicates the percentage of variance explained by each factor, the cumulative percentage of variance and the eigenvalue for each factor. The percentages of variances explained by each factor are used as weights to calculate weighted factor scores to be used in the cluster analysis. Panel B lists the variables with the highest loadings for each factor. Each factor stands for a specific dimension that distinguishes housing submarkets. These dimensions can be classified into three categories.
[Insert Table 2 (Principal components and dimensions of housing submarkets) here]
The first category relates to the physical characteristics of the dwellings. Nearly half of the total variance in the data is explained by factors that load heavily on physical characteristics.
Two of the three most important factors (Factors 1 and 3) fit into this category. Factor 1 is related to the age of the house and the condition of the walls and roof. Factor 3 is related to the value of the house and the chattels, and the size of the dwelling. Four other factors have high scores on structural characteristics: Factor 5 is related to roof material, Factor 6 to the design of the property, Factor 9 to wall material and property type and Factor 11 to wall material only.
This dimension of housing submarkets finds an interpretation in residential location theory, particularly in the work by Grigsby et al. (1987). These authors draw attention to the fixed nature of housing stock and the difficulty in modifying that stock. Thus, the nature of the housing stock should have an impact on housing location decisions and the degree to which dwellings are substitutable.
Five factors are related to the neighbourhood in which properties are located. Several census variables for the neighbourhoods load highly on Factor 2: the home ownership rate, the average number of bedrooms, the percentage of people driving to work, the median income, the percentage of Pacific Islanders, the percentage unemployed and the percentage receiving income support. Factors 7, 8 and 10 are related to the geographic segmentation of the Auckland region. Factor 8, for instance, is related to the Papakura District in which the percentage of Maori is the highest (24.6%). Finally, Factor 12 is also a neighbourhood factor on which two variables from the census have high loadings: the average number of cars per household and the dwelling density.
This dimension of residential markets is consistent with the theory by Wheaton (1977). He argues that neighbourhood characteristics are important in explaining residential patterns.
Using the Boston area as an example, DiPasquale and Wheaton (1996) demonstrate that environmental characteristics, including proximity to various amenities and neighbourhood quality, can account for more than half of the overall value of the house.
A third dimension of residential location theory is accessibility. According to Alonso (1964) and Muth (1969), there is a trade-off between accessibility and consumption of land.
In the Alonso-Muth model, the relationship between the income elasticity of demand for space and the income elasticity of commuting costs determines the geographical distribution of households within an urban area. With income elastic space demand and inelastic commuting costs, higher-income households will have much larger lots and only slightly greater
commuting costs. In this case, they will outbid other households at peripheral locations. For US cities, it is assumed that the first elasticity exceeds the second, thus accounting for the location of wealthier households at the periphery and poorer households in the centre. With income inelastic space demand and elastic commuting costs, higher-income households have steeper bid rent curves and should locate centrally— a result that is consistent with observed
location patterns in Auckland. Consistent with Wheaton’s critique of the Alonso-Muth model, however, neighbourhood and environmental characteristics seem more likely explanations for the location of Auckland’s higher-income households.
This accessibility dimension does not seem to be as important as that reported in other studies, for instance in Sydney and Melbourne (Bourassa et al., 1999). Only the fourth factor is related to distance from the CBD. The Rodney District variable has a high loading on this factor. This is not surprising as this area has the highest average distance from the CBD (approximately 32 kilometres). The population density variable has a negative loading on this factor as the more central locations are also more densely populated.
After the factors were retained, weighted factor scores were calculated and used for clustering housing submarkets. Three sets of submarkets, consisting of two, four, and six submarkets, respectively, were formed using the K-means clustering method.
5. THE STRUCTURE OF SUBMARKETS 5.1 Two Submarket Classification
Table 3 reports averages for selected variables both for the constrained classification of submarkets by property type (detached vs. attached) and unconstrained two submarket
classification. When the property type a priori classification is considered, it is quite clear that the variables which differ across the two submarkets are related to the type of property. The detached submarket contains larger and more expensive houses. The home ownership rate is also higher for the detached submarket. A substantial percentage of detached houses are in Waitakere City.
[Insert Table 3 (Selected characteristics of the two submarket classifications) here]
As mentioned in the previous section, the principal component analysis results suggest that physical characteristics of properties (in particular, age and condition of walls and roof) are the
most important dimensions of housing submarkets in Auckland. It is therefore not surprising that the two statistically defined submarkets differ according to these variables. Submarket 1 contains dwellings which are more recent and consequently in better condition than in
Submarket 2. The quality of the principal structure is also better for houses in Submarket 1, and units are larger. A large proportion of houses in Submarket 2 is in Auckland city, while houses in Submarket 1 are almost evenly distributed across Auckland City, Manukau City, North Shore City and Waitakere City.
Both classifications appear to be driven mostly by variables related to the physical
characteristics of dwellings. This is not surprising given that the a priori classification is based on property type and that physical characteristics are also the most important dimension in the PCA results. This does not imply, however, that houses are in the same submarkets with both classifications. Table 4 shows that this is far from being the case.
[Insert Table 4 (Cross-tabulation of a priori and statistically defined submarkets) here]
5.2 Four Submarket Classification
Table 5 contains the cross-tabulations for statistically defined submarkets. It shows inter alia the relationship between the statistically defined classifications of two and four
submarkets. In the four submarket solution, most houses from the first submarket of the two submarket classification are allocated to Submarket 1, but also to Submarkets 2 and 3, whereas houses of the second submarket are allocated almost exclusively to Submarket 4.
[Insert Table 5 (Cross-tabulation of statistically defined submarkets) here]
The structure of submarkets for the four submarket classifications are reported in Table 6.
Not surprisingly, the constrained classification by house value is related to structural,
neighbourhood and distance variables as all these variables should impact on house prices. As the average house price rises, so does the floor size, the percentage of detached houses, the
quality of walls and roof, the design of the property, the median household income, and the percentage of population of European and Asian descent. The average distance from the CBD decreases as the house value increases. Expensive houses are located primarily in Auckland City, while inexpensive dwellings are situated mostly in Waitakere City.
[Insert Table 6 (Selected characteristics of the four submarket classifications) here]
The unconstrained submarkets do not cluster primarily according to sales price.
Submarket 3 has a much higher average house price (98% of houses in Submarket 2 are in the most expensive house category, see Table 4), but the other three submarkets have
approximately the same average house value. Submarket 2 was defined not only according to house value: only 22.2% of houses in the most expensive a priori submarket are allocated to that submarket. As compared with the other submarkets, Submarket 3 contains a larger proportion of detached houses. These dwellings are large, close to the CBD, located in areas with low unemployment, low percentage of population receiving income support, high median income, high percentage of population of European descent and low percentages of Maoris and Pacific Islanders. Most houses are in Auckland City.
Submarket 4 is very different from the other three submarkets. It contains older houses with walls and roofs in poorer condition. Houses in that submarket are predominantly from Submarket 2 in the two submarket classification. Submarket 3 has a high proportion of attached dwellings. The ownership rate and the median income are low. The proportion of units located in areas with a high percentage of Maori and Pacific Islanders is greater than for the other submarkets. Submarket 1 contains dwellings which are far from the CBD where ownership rates are high. Houses are located mainly in Manukau City, North Shore City and Waitakere City.
The three dimensions of housing submarkets are less obvious in the statistically defined submarkets than in the a priori submarkets. In the statistically defined groups, the physical
characteristics remain the most important dimension, whereas other characteristics have a lesser impact than in the a priori classification. When the cross-tabulations between both classifications are considered (Table 4), it is quite clear that the structure of submarkets is different across classifications. Submarkets 1 and 3 have approximately one quarter of observations in each of the house value groups. Submarket 2 almost exclusively contains expensive houses, while the number of houses per price group decreases with house value in the case of Submarket 4.
5.3 Six Submarket Classification
Table 5 also gives the cross-tabulations between the four and six statistically defined classifications. It indicates that dwellings in Submarkets 2 and 3 of the four submarket classification are mostly assigned to Submarkets 4 and 1, respectively. Most units from Submarket 1 are assigned to Submarket 2 and to a lesser extent Submarket 1. Submarket 4 is broken down into two submarkets (3 and 6) in the six submarket classification.
Table 7 contains the averages of the variables for each submarket according to both classifications. The results for the a priori classification suggest that mainly socio-economic and demographic variables, and the distance from the CBD differ across submarkets. Rodney District, for instance, has a low median income and a low percentage of population
unemployed. The population is primarily of European descent. Papakura District has a high percentage of Maori and a high unemployment rate. Pertaining to the physical attributes of properties, some differences exist across submarkets but these are limited. Waitakere City has a high percentage of detached houses. Houses in Auckland City are usually older and more expensive.
[Insert Table 7 (Selected characteristics of the six submarket classifications) here]
The statistically defined submarkets are again strongly discriminated according to age and to the quality of walls and roof. Submarkets 1, 2, 4 and 5 contain more recent units than Submarkets 3 and 6. The walls and roof of units in these submarkets are also, on average, in better condition. Other structural characteristics, such as floor size and quality of the principal structure, also vary across submarkets. Submarket 5 contains only four houses. These units are large and expensive. The other dimensions of housing submarkets also appear clearly in this submarket classification. Distance from the CBD and socio-economic characteristics vary, in some cases quite substantially, across submarkets. Submarket 2 has a high percentage of Asians and Submarket 3 a high percentage of Maori and Pacific Islanders.
Table 4 shows that statistically defined submarkets are related to the local government areas. Submarkets 1, 3 and 4 contain large proportions of Auckland City dwellings, while Submarkets 2 and 6 have more diversity. The local government areas, however, can only very imperfectly discriminate house sales into the statistically defined submarkets as there is no clear pattern in the cross-tabulations of both classifications. This again suggests that in the six submarket classification, the statistically defined groups have a strong structural dimension, but also socio-economic, demographic and accessibility dimensions. The a priori groups, because of the constraint placed by the a priori assumption, differ mostly according to the location of properties.
6. CONCLUSIONS
This paper has compared the structure of constrained housing submarkets with that of unconstrained submarkets. The constrained submarkets were constructed on the basis of three a priori criteria: property type, house value and geographical areas. Principal component analysis and cluster analysis were used to construct unconstrained submarkets. Thus, the
impact of imposing a priori constraints on the structure of housing submarkets in a metropolitan region can be assessed.
There are three main dimensions to housing submarkets. These dimensions are related to the physical characteristics of the properties, socio-economic and other characteristics of neighbourhoods, and accessibility to central locations. The results have shown that the structural dimension of housing dominates in the Auckland metropolitan region. The a priori classifications, because of the constraint placed on them, in most cases do not reflect the structure of housing submarkets. The geographic a priori which was considered in this paper places too much emphasis on socio-economic, demographic and accessibility characteristics.
On the other hand, the a priori classification according to house value emphasises all dimensions of housing markets because house values reflect the various attributes of properties.
As Auckland housing submarkets are dominated by structural characteristics, the
classification by property type constitutes the best a priori grouping of properties of the three which have been considered in this paper. This is true for Auckland, but may not be true in other metropolitan regions. The statistical procedure which is used in this paper permits the construction of housing submarkets whose structure is based on the important dimensions of these submarkets. The structure of housing submarkets in Auckland is dominated by the physical characteristics of dwellings. When a classification with a larger number of
submarkets is considered, however, the other dimensions of housing submarkets also appear to be important in the Auckland metropolitan region.
Further work in this area could apply the techniques outlined here to analysis of the dimensions of housing submarkets in other metropolitan regions. Comparative analysis could then be undertaken to determine the causes of differences or similarities in the most important dimensions. Similarly, the methods could be applied to a single housing market using data
from different points in time. In both cases, the analysis should help to advance understanding of the structure of urban housing markets. The methods may also have practical applications.
In particular, it should be investigated whether statistically defined submarkets could lead to better house price predictions in the context of hedonic pricing models. This could lead to improvements in mass appraisal methods.
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TABLE 1 Summary Statistics
Variable Mean
Standard
deviation Minimum Maximum VNZ data for individual dwellings
Total sale price (NZ$) 262,166 138,348 77,500 2,950,000
Value of chattels (NZ$) 9,401 6,653 0 300,000
Age of dwelling 27 22 3 111
Floor size (m2) 132 60 30 1280
Detached houses (%) 73 44 0 100
Roof condition (%)
Good 58 49 0 100
Average 40 49 0 100
Poor 2 15 0 100
Wall condition (%)
Good 59 49 0 100
Average 39 49 0 100
Bad 2 15 0 100
Roof material (%)
Tile 52 50 0 100
Iron 44 50 0 100
Other 4 19 0 100
Wall material (%)
Wood 37 48 0 100
Brick 22 41 0 100
Fibrolite 17 37 0 100
Other 24 43 0 100
Quality of principal structure (%)*
Superior 18 38 0 100
Average 77 42 0 100
Poor 6 23 0 100
GIS data for individual dwellings
Distance from the CBD (km) 12.4 8.2 0 73.7
TABLE 1 (continued) Summary Statistics
Variable Mean
Standard
deviation Minimum Maximum Census data for area units
Density of dwellings (/km2) 677 212 45 1,326
Density of population (/km2) 2,224 1,083 3 8,184
Home ownership rate (%) 71.2 13.0 19.1 92.2
Average number of bedrooms 2.95 0.29 1.94 3.75
Average number of cars 2.00 0.004 1.96 2.03
Persons driving to work (%) 73.2 8.3 31.1 85.6
Median household income (NZ$) 45,199 11,118 24,167 81,578
Persons unemployed (%) 4.6 1.8 0 13.3
Persons receiving income support (%) 30.8 8.3 12.7 58.9
Ethnic structure (%)
European 70 15 5 95
Maori 10 7 2 44
Pacific Islander 8 9 0 67
Asian 11 7 0 45
Local government area (%)
Auckland City 33 47 0 100
Manukau City 19 39 0 100
North Shore City 21 40 0 100
Papakura District 4 20 0 100
Rodney District 5 23 0 100
Waitakere City 18 38 0 100
*Quality of the Principal Structure: Superior – the design is superior and the quality of fixtures and fittings is first class; Average – the design is typical of its era and the quality of the fixtures and fittings is average to good; Poor – the design is below the level generally expected for the era, or the level of fixtures and fittings is barely adequate and possibly of below average quality.
TABLE 2
Principal Components and Dimensions of Housing Submarkets
A. VARIANCE EXPLAINED AND EIGENVALUES
Component
Percentage variance explained
Cumulative percentage
Eigenvalue
1 19.1 19.1 6.50
2 11.9 31.0 4.05
3 8.8 39.8 2.99
4 7.1 47.0 2.42
5 6.5 53.4 2.19
6 6.1 59.5 2.07
7 4.5 64.0 1.53
8 4.0 68.0 1.34
9 3.4 71.4 1.16
10 3.3 74.6 1.11
11 3.3 77.9 1.11
12 2.7 80.6 0.93
B. DIMENSIONS OF SUBMARKETS
Component Variable Factor loadings
1: Physical characteristics Average wall condition 0.95
Average roof condition 0.95
Age 0.57
Good roof condition -0.96
Good wall condition -0.96
2: Socio-economic Ownership rate 0.92
Average number of bedrooms 0.85 Persons driving to work 0.83 Median household income 0.54
Pacific Islander -0.51
Persons unemployed -0.62
Persons receiving income support
-0.68
3: Physical characteristics and house value
Value of chattels 0.88
Total sale price 0.87
Floor size 0.60
4: Accessibility and density Rodney District 0.89
Distance from the CBD 0.70
Population density -0.53
TABLE 2 (continued)
Principal Components and Dimensions of Housing Submarkets
Component Variable Factor loadings
5: Physical characteristics Tile roof 0.95
Iron roof -0.93
6: Physical characteristics superior quality of the principal structure
0.86 average quality of the
pricincipal structure
-0.89
7: Socio-economic North Shore City 0.89
8: Socio-economic Papakura District 0.89
Maori 0.57
9: Physical characteristics Detached 0.72
Walls in wood 0.61
Walls in brick -0.58
10: Socio-economic Manukau City 0.67
Asian 0.53
Waitakere City -0.75
11: Physical characteristics Walls in fibrolite 0.88
12: Socio-economic Average number of cars 0.67
Density of dwellings 0.61
TABLE 3
Selected Characteristics of the Two Submarket Classifications
Submarkets by property type Statistically defined submarkets
Attached Detached 1 2
Variable n=6,928 n=18,725 n=15,053 n
=
10,600Total sale price (NZ$) 221,660 277,153 274,323 244,903
Age of dwelling 20 29 16 42
Floor size (m2) 105 142 143 116
Detached houses (%) 0 100 71 76
Roof condition (%)
Good 63 57 98 2
Average 37 41 2 93
Wall condition (%)
Good 64 58 99 4
Average 35 40 1 93
Quality of the principal structure (%)
Superior 9 21 25 7
Average 90 72 73 83
Distance to CBD (km) 11.9 12.5 13.3 11.0
Home ownership rate (%) 67.4 72.6 73.2 68.3
Median household income (NZ$) 44,597 45,422 46,192 43,789
Persons unemployed (%) 4.6 4.6 4.4 4.9
Persons receiving income support (%) 31.9 30.4 29.6 32.6
Ethnic structure (%)
Asian 11 10 11 10
European 71 70 71 69
Maori 10 11 10 11
Pacific Islander 7 8 7 9
Local government area (%)
Auckland City 39 31 24 45
Manukau City 26 16 22 14
North Shore City 17 22 22 19
Papakura District 6 4 4 5
Rodney District 6 5 7 3
Waitakere City 6 22 21 14
TABLE 4
Cross-tabulation of A Priori and Statistically Defined Submarkets
A priori submarkets Statistically defined submarkets
By property type 1 2 Total
Attached 4,394 2,534 6,928
Detached 10,659 8,066 18,725
Total 15,053 10,600 25,653
By house value 1 2 3 4 Total
1st quartile 2,247 0 943 3,163 6,353
2nd quartile 2,688 1 788 2,799 6,276
3rd quartile 3,139 33 987 2,454 6,613
4th quartile 2,192 1,422 929 1,868 6,411
Total 10,266 1,456 3,647 10,284 25,653
Local government area 1 2 3 4 5 6 Total
Auckland City 2,028 462 2,661 1,169 3 2,110 8,433
Manukau City 486 2,838 143 51 0 1,318 4,836
North Shore City 839 2,231 329 180 0 1,702 5,281
Papakura District 273 329 231 24 0 262 1,119
Rodney District 932 47 15 56 1 348 1,399
Waitakere City 881 2,194 110 22 0 1,378 4,585
Total 5,439 8,101 3,489 1,502 4 7,118 25,653
TABLE 5
Cross-tabulation of Statistically Defined Submarkets
Two submarket classification Four submarket
classification
1 2 Total
1 10,210 56 10,266
2 1,280 176 1,456
3 3,548 99 3,647
4 15 10,269 10,284
Total 15,053 10,600 25,653
Two submarket classification
Six submarket classification 1 2 Total
1 5,438 1 5,439
2 8,074 27 8,101
3 150 3,339 3,489
4 1,387 115 1,502
5 3 1 4
6 1 7,117 7,118
Total 15,053 10,600 25,653
Four submarket classification
Six submarket classification 1 2 3 4 Total
1 2,128 28 3,282 1 5,439
2 8,051 49 0 1 8,101
3 9 51 224 3,205 3,489
4 48 1,312 141 1 1,502
5 0 4 0 0 4
6 30 12 0 7,076 7,118
Total 10,266 1,456 3,647 10,284 25,653
26
TABLE 6
Selected Characteristics of the Four Submarket Classifications
Submarkets by house value quartile Statistically defined submarkets
1st 2nd 3rd 4th 1 2
Variable n=6,353 n=6,276 n=6,613 n=6,411 n=10,266 n=1,456
Total sale price (NZ$) 146,487 201,936 262,938 434,963 244,163 569,252
Age of dwelling 26 26 27 28 15 24
Floor size (m2) 86 107 141 192 140 224
Detached houses (%) 57 70 79 85 75 85
Roof condition (%)
Good 48 54 62 69 98 91
Average 49 45 36 29 2 7
Wall condition (%)
Good 49 55 63 70 99 93
Average 48 43 35 29 1 5
Quality of principal structure (%)
Superior 1 3 19 46 24 49
Average 87 90 78 53 74 50
Distance to CBD (km) 15.5 13.1 11.8 9.1 14.9 7.9
Home ownership rate (%) 68.3 71.7 72.8 72.0 78.9 70.3
Median household income (NZ$) 39,314 42,088 46,056 53,192 47,562 58,625
Persons unemployed (%) 5.8 4.7 4.2 3.8 4.1 3.6
Persons receiving income support (%) 34.8 32.1 29.7 26.8 27.1 26.4
Ethnic structure (%)
Asian 8 10 11 12 11 11
European 62 70 73 77 73 79
Maori 16 11 8 6 10 5
Pacific Islander 13 9 6 4 6 4
Local government area (%)
Auckland City 22 26 34 49 8 76
Manukau City 21 19 20 15 30 5
North Shore City 9 22 25 26 25 10
Papakura District 11 4 2 1 4 2
Rodney District 5 7 7 3 7 5
Waitakere City 32 23 11 5 26 2
27
TABLE 7
Selected Characteristics of the Six Submarket Classifications
Submarkets by territorial local authority Statistically defined submarkets
Auckland Manukau North Shore Papakura Rodney Waitakere 1 2
Variable n=8,433 n=4,836 n=5,281 n=1,119 n=1,399 n=4,585 n=5,439 n=8,101
Total sale price (NZ$) 307,997 240,876 286,228 177,013 237,946 200,786 236,007 252,251
Age of dwelling 37 20 23 23 17 22 17 14
Floor size (m2) 127 143 142 122 130 120 118 146
Detached houses (%) 68 63 78 61 70 91 57 78
Roof condition (%)
Good 43 69 61 56 74 66 99 98
Average 53 30 37 42 24 32 1 2
Wall condition (%)
Good 45 71 62 56 74 67 99 99
Average 52 27 37 40 24 31 0 1
Quality of principal structure (%)
Superior 15 30 19 21 10 9 15 28
Average 82 63 78 65 74 86 83 70
Distance to CBD (km) 6.2 16.4 8.9 28.8 32.0 13.3 13.9 14.1
Home ownership rate (%) 60.0 79.6 76.2 69.1 77.9 75.6 64.1 80.5
Median household inc. (NZ$) 46,787 47,984 47,311 41,148 32,718 41,706 37,325 50,339
Persons unemployed (%) 5.2 4.4 3.4 6.0 2.9 5.2 5.2 4.0
Persons receiving income support (%) 32.5 27.1 27.6 35.1 40.7 31.2 37.3 24.7
Ethnic structure (%)
Asian 13 15 9 4 2 7 9 12
European 66 66 80 65 89 66 68 73
Maori 9 11 7 25 8 14 12 9
Pacific Islander 11 7 3 6 1 12 10 5
Local govern. area (%)
Auckland City 100 0 0 0 0 0 37 6
Manukau City 0 100 0 0 0 0 9 35
North Shore City 0 0 100 0 0 0 15 28
Papakura District 0 0 0 100 0 0 5 4
Rodney District 0 0 0 0 100 0 17 1
Waitakere City 0 0 0 0 0 100 16 27
NOTES
1 Our results show that the weights have a substantial impact on cluster membership.
2 A sale was identified as aberrant and discarded from the analysis as unrepresentative if it fell into one of the following categories: (a) the property had a land area larger than 0.25 hectares (this excluded properties that may have been sold primarily for redevelopment purposes); (b) the property had a floor area less than 30 square meters (this value is the first percentile in the size distribution); (c) the property sold for less than NZ$77,500 (first percentile in the sale price distribution); (d) the price per square metre of the property is either less than NZ$850 or larger than NZ$5,600; or (e) the property had chattels accounting for more than 20 percent of the total price.
3 The averages of the census data reported in Table 1 are not exact averages for the Auckland region, but rather averages of the neighbourhood characteristics of dwellings which were sold in 1996.
