Space and Residential Values Modelling Interactions Between Geographical Patterns and Property Attri

1
Space and Residential ValuesModelling
Interactions Between Geographical Patterns and
Property Attributes
First Congress of the International Real Estate
Society Anchorage, Alaska, July 25-28, 2001

• Marius Thériault, François Des Rosiers, Paul
  Villeneuve Yan Kestens

2
Problem Statement (1)

• Handling Interaction Between Spatial Factors and
  Values of Specific Housing Attributes
• In hedonic modelling, values are usually
  specified using fixed coefficients
• The assumption is that values of attributes are
  invariant across the city
• However, various types of households have
  different needs and tastes
• These households form the market of home buyers
  (demand)
• They are not distributed evenly over space
  (spatial heterogeneity)
• This could locally distort the demand for
  specific structural attributes
• There is a need to test, the interaction between
  the structural features of physical and urban
  space and those housing attributes which are
  putatively influenced by these structural
  features spatially adjusted coefficients
• This paper presents a methodology to handle
  interactions between geographical factors and the
  marginal contribution of each property attribute
  (model its variation over space)

3
Problem Statement (2)

• Spatial Autocorrelation Among Residuals of the
  Hedonic Model
• Spatial autocorrelation is highly detrimental to
  the efficiency of standard statistical tests used
  to assess the statistical significance of OLS
  regression coefficients
• A city-wide hedonic modelling approach must (1)
  test for the presence of spatial heterogeneity
  (2) implement alternative estimation techniques
  to handle spatial autocorrelation
• In 1990, Casettis expansion method was used by
  Can for investigating spatial drifts in housing
  markets
• We extend the procedure using several
  neighbourhood quality indexes, and combining them
  with comparisons of each property with its
  immediate neighbours
• thus allowing for a locally sensitive assessment
  of spatial dependence and for a significant step
  towards an efficient control of spatial
  autocorrelation

4
Conceptual Framework (1)

• Increasing Social Diversity
• During the last 40 years, rapid social and
  economic changes have been restructuring housing
  demand in North American cities
• Three tendencies capable of profoundly modifying
  residential markets
• Rapid increase in female labour force during the
  seventies has diversified household profiles and
  needs (dual earners, domestic outsourcing)
• Rising income inequalities between households now
  counting on varying numbers of working members
  produce social polarisation into urban space
• Development of the service sector of metropolitan
  areas and decentralisation of manufacturing
  activities has affected the social profile of
  many neighbourhoods, especially by redistributing
  services locations
• All these changes have an effect on residential
  relocation behaviour, which is highly related to
  household structure and cycles
• Social diversity and decentralisation of services
  increases the complexity of rent gradients
  influencing housing markets

5
Conceptual Framework (2)

• Tree types of gradients
• City-wide gradients related to structural factors
  (E.g. urban form, socio-economic status of
  neighbourhoods, location rent)
• Local gradients linked to externalities (E.g.
  noise caused by the proximity of a motorway)
• Local gradients reflecting local market internal
  dynamics (E.g. diffusion of home renovation among
  neighbours) and /or emulation among neighbours
  (E.g. adding a swimming pool in the backyard)
• First two are true gradients (exogenous
  effects), last one is false gradient
  (endogenous effect)
• True gradients violate the stationarity
  assumption (fixed coefficient) and produce
  spatial autocorrelation among residuals of the
  hedonic model if their effect is not
  appropriately handled
• False gradients are reflecting evolution of
  market trends and do not yield significant
  spatial autocorrelation among model residuals

6
Conceptual Framework (3)

• Socio-demographic profiles and housing market
• Socio-demographic profiles of the population are
  certainly major determinants of housing market
  differentiation and form city-wide trends
  (exogenous effect)
• However, the distribution of population is also
  constrained by the housing market (endogenous
  effect)
• Those effects are intermingled as demand and
  supply are driven by availability and
  affordability of housing
• Therefore, these interactions with housing
  attributes should be modelled explicitly and
  translated into space-varying coefficients using
  Casettis expansion method
• Conceptually, household formation and household
  income are major determinants of housing demand.
  The rate of household formation has a
  quantitative effect on the demand level, while
  income has a qualitative effect on the type of
  demand and selection of needed attributes

7
Conceptual Framework (4)

• Endogenous Market Effects
• As pointed out by Can (1990), most people prefer
  to live in neighbourhoods where they think the
  return for their housing investment will be
  highest
• People are then willing to invest in maintaining
  dwelling where the return on such expenditures is
  sufficiently high
• This suggest that home owners are observing their
  immediate neighbours and will be more prone to
  improve their property if the neighbourhood
  itself is upgrading
• Conversely, home buyers generally try to find
  homes in neighbourhoods having socio-economic
  status similar to their own, implying that
  similar people, with the same needs, tend to
  agglomerate at specific locations
• Hence the intrinsic nature of spatial dependence
  which governs real estate markets, each social
  group tending to value specific sets of housing
  attributes, while specific attributes may be
  valued differently by various segments of the
  population

8
Objectives

• Main Objectives
• Measuring the effect of social differentiation
  and residential segregation on the valuation of
  specific amenities
• Assess the impact of the conformity/difference of
  a house with its neighbours when put on the
  market
• Example of research issues
• A cosy house surrounded by poorly-maintained
  properties will loose a large part of its value,
  eventually more if it belongs to the higher
  segment of the local market (buyers with high
  socio-economic status)
• Provide a procedure to integrate those ecological
  effects in hedonic models methods to isolate the
  marginal impact of this spatial mismatch on the
  sale price and means to identify which specific
  attributes will loose their value

9
Test Case

• Market, Geographical Location and Social Status
• 4040 bungalows (one-story single family house)
  sold within the Quebec Urban Community from
  January 1990 et December 1991
• Each property is described using a large set
  (nearly 80) of property-specific attributes
  (Table 3) and neighbourhood-related attributes
  (more than 100) computed using GIS functions
  (Tables 1, 2 and 3)
• Among these neighbourhood characteristics, travel
  times to services (schools and shopping centres)
  and census socio-economic data are linked to each
  property through selecting the nearest street
  corner (accessibility) or using point-in-polygon
  algorithm (census data)
• Neighbourhood-related attributes are replaced by
  factor scores derived from principal component
  analysis and orthogonal Varimax rotations (Tables
  1 and 2, Maps 1 and 2)
• Principal components avoid multicollinearity
  problems among independent variables and they
  summarize structural factors behind accessibility
  to services and heterogeneity of households needs

10
ModellingApproach

• Sub-Samples
• Models are built using 3633 cases (90 of total)
  selected at random with proportional
  stratification by municipality (13), keeping the
  407 remaining observations from an independent
  model effectiveness assessment
• Tests to Avoid
• Multicollinearity
• Autocorrelation
• Heteroskedasticity
• Problem solving strategies

11
Spatial Autocorrelation (1)

• Spatial autocorrelation
• Significance tests and measures of fit that
  ignore spatial autocorrelation may be misleading
• The presence of spatial error autocorrelation can
  make the indication tests for heteroskedasticity
  highly unreliable
• Ecological fallacy effects often arise strictly
  from the precence of spatial dependency
• Spatial autocorrelation is based on positional
  information of geo-referenced data which is not
  captured by classical statistics, ncluding OLS
  multiple regression
• Spatial autocorrelation is a measure of true but
  masked information needed to understand
  mechanisms of urban dynamics its is an artifact
  of specification error in spatial modelling
• If an important variable is missing from a
  regression equation, the spatial distribution of
  this variable constitutes a communality across
  regression residuals, causing them to appear to
  be autocorrelated

12
Spatial Autocorrelation (2)

• Measuring spatial autocorrelation
• Morans I formula to assess spatial
  autocorrelation (Table 4)
• Implemented within a GIS software (MapInfo)
  providing a network of 15 nearest neighbours
• Measuring similarity/difference with the 15
  nearest neighbours
• Average status of the 15 nearest neighbours
• Departure form the neighbours

13
Models and Results (1)

• Five Steps (Table 5)
• 1) Standard Hedonic model using property
  specifics and principal components of
  geographical factors (Model A, Table 6)
• 2) Try to replace each property specific by a
  combination of the 15 nearest neighbours weighted
  average and specific departure from the
  neighbourhood trend (Model B not shown)
• 3) Compute interactions between each principal
  component and each property attribute and
  externality index using Casettis expansion
  method (
  ) try to add interactions to property
  specifics (model C not shown)
• 4) Integrate models A, B and C specific
  attributes, neighbourhood trends/specific
  departures and spatial interactions (Model D,
  Table 7)
• 5) Model the perceived tax burden/opportunity for
  over/under-assessed property (by the
  municipality) using a two-stage approach - Using
  estimates of Model D as proxy to house values
  (Model E, Table 8)

14
Models and Results (2)

• Adjusted R-square is increasing from 0.768 to
  0.822
• Adding 23 spatial variables has a rather marginal
  effect on explanatory power (R-square increase)
• Standard deviation of residuals are falling very
  slowly, from 0.118 to 0.103 (0.125 to 0.106
  control sample)
• F ratios are decreasing until Model D (366 to
  277) but show a net improvement for Model E (56
  variables)
• Morans I for Model E are closer to that of
  actual sale price (Graph 1) and shows the same
  distance range (1125 m)
• The most important improvement concerns the
  reduction of spatial autocorrelation among
  residuals Model A (0.16) to Model E (0.08)
• The inclusion of spatial interactions (expansion
  method) and the relative tax differential is
  generating this improvement, reducing the range
  of spatial autocorrelation to about 375 metres
  (Graph 3)

15
Discussion (1)

• Space-dependent values of attributes
• They generate significant interactions (exogenous
  socio-economic or externality effects) using
  Casettis expansion method
• Their effect can be split in two parts, that of
  the property itself, that of the weighted average
  of its 15 nearest neighbours (endogenous effects)
• Isolating functional form of the spatial
  relationships
• Annex 1 shows the mathematical specification of
  Model E (multiplicative form)
• Each space-dependent attribute may be isolated to
  define a spatially adjusted coefficient
• 15 were found, most of them being very important
  attribute of the house (living area, lot size,
  age), attributes that could be seen outdoor
  (Skylight, Veranda, Shed), taxation rates, or
  internal attributes that are highly
  representative of the general maintenance of the
  property

16
Discussion (2)

• Computing spatially adjusted coefficients
• Since interactions and neighbours adjustments
  involve geographical factors that can be mapped,
  it is possible to compute local values of
  space-Varying coefficients and to build map of
  their distribution controlling for both location
  and size-related (or presence) attributes
• Map 4 shows an interpolated view of the location
  rent effect of a bungalow situated on a larger
  than average lot (1000 sq. m. versus a geometric
  mean of 622 sq. m. for all sold properties in
  1990-91)
• The absolute effect is very strong, from 44 to
  60 of house value
• The relative value of land increases with
  socio-economic status and is also related to life
  cycles, favouring mature suburbs inhabited by
  empty-nesters
• Map 5 and 6 show depreciation-related spatial
  trends for a 10 years-old and a 40 years-old
  house
• These functions integrate endogenous and
  exogenous gradients
• The household maintenance/repair decisions are
  determined by income levels, but also by
  households perception concerning the future
  value of their asset, in turn determined by the
  signals they receive from their immediate
  neighbours, but mediated by their own age

17
Discussion (3)

• Map 7 shows the marginal effect of adding a
  second washroom
• The spatial trend estimator is regional-level
  accessibility to services
• Per se, a washroom adds 5,4 to the house value
• There was an average of 1.25 washroom per house
  in that market
• Young families with middle income far away from
  regional services are forced to go to new suburbs
  to access home ownership and often trade off the
  second washrooms
• In older neighbourhoods, the second washroom is
  prevalent and there is a penalty for house having
  only one
• Map 8 shows the marginal effect of having a shed
  on the lot
• The value of a shed is highly variable in space
  and is increasing home value in sectors that are
  showing less than average household income and
  where the proportion of blue collar is higher
  than average

18
Conclusion

• These worked examples clearly show the benefits
  of including interactions with urban dynamics
  within hedonic models
• The purpose is to enhance our understanding on
  the complex linkages between housing prices and
  the socio-economic evolution of North American
  cities
• An important side benefit it helps reduce
  spatial autocorrelation among models residuals
• We can further improve handling of spatial
  dependence
• 1) by considering a wider range of spatial
  attributes (E.g. environment)
• 2) by defining more flexible ways of measuring
  spatial dependence (E.g. non linear functions,
  multivariate interactions)
• 3) by considering information about home buyers
  (E.g. socio-economic status, revealed
  perceptions)
• 4) by splitting principal components scores to
  distinguish city-wide trends (E.g. trend surface)
  and peculiarities of specific areas (departure
  from the trend)

19
Acknowledgements

• This project is funded by
• the Quebec Provinces FCAR program
• the Canadian Social Sciences and Humanities
  Research Council
• the Canadian Network of Centres of excellence in
  Geomatics (GEOIDE)
• the Canadian Natural Sciences and Engineering
  Research Council
• The research was realised in co-operation with
• the Quebec Urban Community Appraisal Division
  (CUQ)
• the Quebec Ministry of Transport (MTQ)
• the Quebec Urban Community Transit Society
  (STCUQ)