Spatial modelling of property prices: The case of Aberdeen - Wolfgang Karl H ardle Maria Osipenko Humboldt-Universit at zu Berlin Rainer Schulz ...
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Spatial modelling of property prices:
The case of Aberdeen
Wolfgang Karl Härdle
Maria Osipenko
Humboldt-Universität zu Berlin
Rainer Schulz
University of Aberdeen Business School
Spatial Modelling
Introduction 2
Introduction
Value of residential dwelling will depend on
I structural characteristics
– number of (bed)rooms, bathrooms, garden etc.
I location characteristics
– amenities
· green space, parks, water, nice surrounding buildings
– disamenities
· busy roads, rail tracks, dense built environment
Spatial Modelling
Introduction 3
Who should be interested in models of the effect of characteristics and
location on prices?
I market participants (households, banks, valuers)
I tax authorities and assessors
I environmental economists and (hopefully) policymakers
Why should we be interested in new modelling approaches?
I data of real estate transactions often include geo-coordinates
I map and location information becomes electronically available
Spatial Modelling
Introduction 4
Why Aberdeen?
Contains Ordnance Survey data c Crown copyright and database right 2013.
Figure 1: Aberdeen City
Spatial Modelling
Introduction 5
Figure 2: Aberdeen is known for oil, a successful manager,...
Spatial Modelling
Introduction 6
Figure 3: ... and the material of its buildings.
Spatial Modelling
Introduction 7
Why not Aberdeen?
Real estate markets are always local
I good data availability
– transaction information including geo-codes
– geo-coded location information available (for research)
∗ city border and electoral wards
∗ building footprints
∗ roads, railtracks, tunnels
∗ woodland
I homogenous buildings, high turnover, limited construction ⇒
facilitates interpretation
Spatial Modelling
Data 8
Data
Transaction data comes from the Aberdeen Solicitors Property Centre
(ASPC)
I covers most residential property transactions in Aberdeen
I detailed information on individual properties
I information provided by residential agents and solicitors
Cleaned sample from 2000-2012 contains 53788 observations.
Spatial Modelling
Data 9
Data
Table 1: Summary statistics. 53788 sales, 2000-2012.
Mean Median Std. Min Max
Price (000) 137.46 112.41 101.65 10.00 1550.00
Ask (000) 123.25 96.00 93.62 9.00 1500.00
Rooms 3.62 3.00 1.55 2.00 10.00
Bedrooms 2.22 2.00 1.02 1.00 6.00
Public rooms 1.40 1.00 0.72 1.00 5.00
Wash rooms 1.22 1.00 0.49 1.00 4.00
Bathrooms 0.90 1.00 0.35 0.00 3.00
Shower rooms 0.32 0.00 0.52 0.00 3.00
Floors 1.41 1.00 0.54 1.00 3.00
Garages 0.29 0.00 0.54 0.00 3.00
continued on next slide
Spatial Modelling
Data 10
Table 1 continued.
Mean
Central heating 0.81
Double glazing 0.89
Garden 0.55
New built 0.00
Detached 0.11
Semi-detached 0.29
Flat 0.60
Spatial ModellingData 11
Figure 4: Transactions of flats, semi-, and detached properties.
Spatial ModellingData 12
Figure 5: Transaction prices.
Spatial ModellingData 13
Figure 6: Transaction prices in boom years 2007-2008
Spatial ModellingData 14
Figure 7: Transaction prices in bust years 2009-2010
Spatial ModellingData 15
Figure 8: Number of rooms.
Spatial ModellingData 16
Inspection of data reveals
I large cross-sectional variation of prices and property characteristics
I indication of spatial clustering of prices and characteristics
I general economic conditions impact on prices (temporal variation)
Factors that could contribute to spatial price variation
I variation of characteristics
I variation of local amenities
– indirect impact via local variation of implicit prices of
characteristics
– direct impact via (dis)amenities
Spatial ModellingModels 17
Models
Parametric hedonic regression (Palmquist 1991)
yi = α + di δ + xi β + εi (1)
yi (log) price of property i sold in period t
di (T − 1) row vector with 1 in period of sale, 0 else
xi row vector with characteristics of i, includes district dummies
δ models temporal, coefficients for district dummies in β model spatial
variation.
Caveats: spatially constant implicit prices (β), potential for omitted
variable bias, efficiency loss if errors have spatial dependence.
Spatial ModellingModels 18
Parametric spatial models (LeSage and Pace 2009)
Spatial autoregression model (SAR)
yi = α + di δ + ρwi y + xi β + εi (2)
wi row vector spatial weights, element i is zero
y column vector with log prices
Elements of wi could depend on spatial or economic distance, here the
former.
ρwi y could be motivated as latent variable for neighborhood quality.
Eq. 2 is in line with the sales comparison approach used in the financial
industry.
Spatial ModellingModels 19
Spatial lag of X model (SLX)
yi = α + di δ + wi Xγ + xi β + εi (3)
X matrix of stacked xi s
Eq. 3 can be motivated by positive/negative externalities of
characteristics of neighbouring buildings.
Spatial error model (SEM)
yi = α + di δ + xi β + ui (4)
ui = ρwi u + εi (5)
u column vector with errors ui
Eq. 5 can be motivated with omitted variables.
Spatial ModellingModels 20
Spatial Durbin model (SDM)
yi = α + di δ + ρwi y + wi Xγ + xi β + εi (6)
nests SAR and SLX.
Can be motivated with omitted variables that are correlated with
elements in X.
Other models have been proposed in the literature
I interpretation of models often not straightforward
I similar to lags in time series models
I usefulness depends on intended application
Spatial ModellingModels 21
Semiparametric spatial models
Standard hedonic regression with location function
yi = di δ + xi β + m(li ) + εi . (7)
xi vector without district dummies
li vector with geo-codes (east, north) for property i
Varying coefficient model
yi = di δ(li ) + xi β(li ) + m(li ) + εi . (8)
Example: geographically-weighted regression (GWR) (Fotherington et al.
2002)
Spatial ModellingModels 22
Specification
Potential to reduce explanatory variables (characteristics bundles)
Some implicit prices
I might vary spatially (garden)
I others might not (number of bathrooms)
Omitted variable bias will be a problem (e.g. age is not observed)
Choice of weights (bandwidth) should be adaptive (see Fig. 4)
Spatial ModellingWhat has been done? 23
What has been done? An incomplete review
Semiparametric hedonic model, continuous variables considered
nonparametrically (size, age, distance to CBD), implicit prices for
categorial variables are constant (Anglin and Gencay 1996, Bin 2004,
Gençay and Yang 1996, Iwata et al. 2000, McMillen and Thorsnes 2000,
Meese and Wallace 1991)
Model from Eq. 7 with m(l, t), effectively Eq. 8 with constant β. (Clapp
2004)
Spatial Modelling24
References
Anglin, P. M. and Gencay, R.: 1996, Semiparametric estimation of a
hedonic price function, Journal of Applied Econometrics 11, 633–648.
Bin, O.: 2004, A prediction comparison of housing sales prices by
parametric versus semi-parametric regressions, Journal of Housing
Economics 13, 68–84.
Clapp, J. M.: 2004, A semiparametric method for estimating local house
price indices, Real Estate Economics 32, 127–160.
Fotherington, A. S., Brunsdon, C. and Charlton, M.: 2002,
Geographically weighted regression: the analysis of spatially varying
relationships, John Wiley & Sons, Chichester.
Gençay, R. and Yang, X.: 1996, A forecast comparision of residential
Spatial Modelling25
housing prices by parametric versus semiparametric conditional mean
estimators, Economic Letters 52(2), 129–135.
Iwata, S., Murao, H. and Wang, Q.: 2000, Nonparametric assessment of
the effects of neighborhood land uses on residential house values, in
T. B. Fomby and R. C. Hill (eds), Applying Kernel and Nonparametric
Estimation to Economic Topics, Vol. 14 of Advances in Econometrics,
JAI Press Inc., Stamford CT, pp. 229–257.
LeSage, J. and Pace, R. K.: 2009, Introduction to Spatial Econometrics,
Statistics: Textbooks and Monographs, Chapman & Hall, Boca Raton.
McMillen, D. P. and Thorsnes, P.: 2000, The reaction of housing prices
to information on superfund sites: A semiparametric analysis of the
Tacoma, Washington market, in T. B. Fomby and R. C. Hill (eds),
Applying Kernel and nonparametric estimation to economic topics,
Vol. 14 of Advances in econometrics, JAI Press Inc., pp. 201–228.
Spatial Modelling26
Meese, R. and Wallace, N.: 1991, Nonparametric estimation of dynamic
hedonic price models and the construction of residential housing price
indices, Journal of the American Real Estate and Urban Economics
Association 19, 308–332.
Palmquist, R. B.: 1991, Hedonic methods, in J. B. Braden and C. D.
Kolstad (eds), Measuring the demand for environmental quality,
Contributions to Economic Analysis, North Holland, Amsterdam,
chapter 4, pp. 77–120.
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