TI 2013-171/VIII
Tinbergen Institute Discussion Paper
Spatial Heterogeneity in Hedonic House Price
Models:
The Case of Austria
Marco Helbich
1
Wolfgang Brunauer
2
Eric Vaz
3
Peter Nijkamp
4
1
University of Heidelberg, Germany;
2
UniCredit Bank Austria AG, Austria;
3
Ryerson University, Canada;
4
Faculty of Economics and Business Administration, VU University Amsterdam, and Tinbergen
Institute.
Tinbergen Institute is the graduate school and research institute in economics of Erasmus University
Rotterdam, the University of Amsterdam and VU University Amsterdam.
More TI discussion papers can be downloaded at http://www.tinbergen.nl
Tinbergen Institute has two locations:
Tinbergen Institute Amsterdam
Gustav Mahlerplein 117
1082 MS Amsterdam
The Netherlands
Tel.: +31(0)20 525 1600
Tinbergen Institute Rotterdam
Burg. Oudlaan 50
3062 PA Rotterdam
The Netherlands
Tel.: +31(0)10 408 8900
Fax: +31(0)10 408 9031
Duisenberg school of finance is a collaboration of the Dutch financial sector and universities, with the
ambition to support innovative research and offer top quality academic education in core areas of
finance.
DSF research papers can be downloaded at: http://www.dsf.nl/
Duisenberg school of finance
Gustav Mahlerplein 117
1082 MS Amsterdam
The Netherlands
Tel.: +31(0)20 525 8579
1
Spatial Heterogeneity in Hedonic House Price Models:
The Case of Austria
Marco Helbich, Wolfgang Brunauer, Eric Vaz, Peter Nijkamp
Abstract
Modeling spatial heterogeneity (SH) is a controversial subject in real estate economics. Single-family-
home prices in Austria are explored to investigate the capability of global and locally weighted
hedonic models. Even if regional indicators are not fully capable to model SH and technical
amendments are required to account for unmodeled SH, the results emphasize their importance to
achieve a well-specified model. Due to SH beyond the level of regional indicators, locally weighted
regressions are proposed. Mixed geographically weighted regression (MGWR) prevents the
limitations of fixed effects by exploring spatially stationary and non-stationary price effects. Besides
reducing prediction errors, it is concluded that global model misspecifications arise from improper
selected fixed effects. Reported findings provide evidence that SH of implicit prices is more complex
than can be modeled by regional indicators or purely local models. The existence of both stationary
and non-stationary effects imply that the Austrian housing market is economically connected.
1 Introduction
In real estate research, it is well established that hedonic prices may vary across space such as
stratifications of metropolitan areas, regions, and counties (e.g., Bourassa et al., 1999; Goodman and
Thibodeau, 2003; Bischoff and Maennig, 2011; Helbich et al., 2013a). However, this parametric
modeling approach has some restrictions: Spatial units have to be defined exogenously, SH is
modeled in a discrete fashion where continuous changes across space can be expected, and usually
the same definition of spatial units is used for all spatially varying effects (e.g., Redfearn, 2009;
McMillen and Redfearn, 2010).
By preventing these limitations, non-parametric locally weighted regression procedures (LWR;
Cleveland and Devlin, 1988) offer significant advantages (McMillen and Redfearn, 2010; McMillen,
2010). In this context, the slowly growing body of literature on LWR primarily use the geographically
weighted regression (GWR; Fotheringham et al., 2002), which inherently assumes SH in the hedonic
price function and all involved predictors (e.g., Bitter et al., 2007; Yu et al., 2007; Hanink et al., 2010).
However, in situations where only some of the variables vary spatially, GWR results in inefficient
estimations and possibly incorrect conclusions (Wei and Qi; 2012). This is particularly true for
relatively small countries like Austria where real estate markets are economically connected through
common federal policies such as governmental subsidies etc. Economic ties might also be relevant
for structural housing features where Austrian-wide equilibrium conditions between supply and
demand are a rational outcome. On the other side, spatially varying implicit prices are expected
where local legislation and regulation (e.g., through spatial planning policies) are effective and/or
where local supply consequence scarcity (e.g., plot area). Consequently, some price determining
effects are expected to vary across space, while others are spatially homogenous. Both aspects are
modeled simultaneously in the so-called MGWR (Fotheringham et al., 2002). Although the MGWR
model seems to be rational, it has not yet been considered in real estate studies.
2
Therefore, the overall objective of this research is to explore SH in cross-sectional housing price
functions. Using Austrian housing data, following contributions to the literature are established: First,
the efficiency of fixed effects is evaluated in the context of global models, considering additionally
iteratively technical corrections for spatial autocorrelation (SAC) and SH. Second, switching to fully
local non-parametric modeling, it is demonstrated that SH is only inadequately captured by imposing
spatially fixed effects and that systematic parameter variation is evident which deviates substantially
from globally estimated marginal prices. Finally, due to an absence of empirical consensus which
predictor enters the model globally or locally, the data-driven MGWR procedure is proposed. As
such, following research questions are addressed:
• Are standard hedonic regressions equipped with spatial indictors suitable to model SH? Are
technical corrections required to archive a well-specified model?
• Is SH beyond the regional fixed effects present? If this is the case, does a semi-local model
outperform its global and fully local counterparts?
The rest of the paper is structured as follows. Section 2 reviews the theoretical foundations of
hedonic pricing theory and discusses methodologies to account for SH. Following this, Section 3
introduces the empirical models. Section 4 presents the study area and the dataset. The results are
summarized in section 5, before Section 6 highlights major conclusions and implications.
2 Background
2.1 Hedonic pricing theory
The theoretical basis of hedonic price modeling (Rosen 1974) is derived from Lancaster's (1966)
consumer behavior theory, which argues that not the good itself creates utility, but its individual
characteristics. As housing characteristics are non-separable and traded in bundles, real estate is
usually treated as a heterogeneous good. Houses are valued for their utility-bearing characteristics
with implicit prices, which can be considered as the component's specific prices (McDonald, 1997).
Thus, a household implicitly chooses a set of different goods and services by selecting a specific
object (Sheppard, 1997; Malpezzi, 2003). In the course of their purchase decisions, households aim
to maximize their utility depending on their own social and economic characteristics. Households'
utilities are also increasingly influenced by the absolute location of the house. Urban economic
theory, in particular the monocentric Alonso-Muth-Mills model, provide a uniform framework to
explain the spatial organization of housing (Anas et al. 1998). Briefly stated, the model claims that
distance to the core city is the exclusively determinant causing spatial variation in housing prices and
that prices, among other things, smoothly tend to decline with distance. Due to this reductionist use
of commuting costs, the model has attracted some criticism. However, in a recent empirical study of
real estate commodities, Ahlfeldt (2011) concludes that the model still performs satisfactorily.
Methodologically, a hedonic price function describes the functional relationship between the real
estate price and associated physical characteristics
, … ,
as well as neighborhood
characteristics
, … ,
. The former depicts the fabric of the dwelling (e.g., floor area); the latter
defines the dwelling's surroundings, often based on census data (e.g., educational level; see Can,
1998). Usually the equation is estimated by means of multiple regression analysis. In practice, most
empirical research uses a semi-log or log-log specification, having the advantage that prices vary with
the quantity of housing characteristics and further corrects for heteroskedastic tendencies (Malpezzi
3
2003). Can and Megbolugbe (1997) assess that a wrong functional form results in unreliable and
biased estimates.
2.2 Spatial effects in hedonic models
SAC and SH are two challenges in hedonic modeling. Since Dubin (1992; 1998) and a wealth of
subsequent research (e.g., Can and Megbolugbe, 1997; Pace et al., 1998; LeSage and Pace, 2009;
McMillen, 2010), it is now accepted that such spatial effects should be taken into account when
estimating hedonic price functions. SAC describes the coincidence of locational and attribute
similarity (Anselin 1988) caused by analogous neighborhood characteristics, similar socio-economic
characteristics of their residents, and the quality of services (Dubin, 1992). As a consequence, the
traditional ordinary least squares (OLS) estimator is inefficient and statistical inference is invalid
(Dubin, 1998).
Although the price function assumes spatial equilibrium between supply and demand for dwelling
characteristics, as real estate is fixed in space, and because of its durability and consistent properties,
supply becomes largely inelastic (Malpezzi, 2003). Furthermore, different socio-economic and
demographic conditions of households cause spatial variation in dwelling demand (Sheppard, 1997).
Functional disequilibria, which manifest themselves in the emergence of heterogeneous market
structures, might result as a consequence (McMillen and Redfearn, 2010). Therefore, SH should be
considered in hedonic models. As LeSage and Pace (2009) pointed out, non-modeled heterogeneity
can lead to biased results and falsely induced SAC.
2.3 Modeling spatial heterogeneity
SH can either be considered in a discrete way or in a continuous manner. Both approaches are
discussed in this Section.
2.3.1 Discrete approaches
Discrete attempts model SH based on predefined spatial units (e.g., federal states) which are usually
considered within the regression as fixed or random effects.
Fixed effects model
Within the regression framework, fixed effects or spatial indicators for regions can be integrated,
which let the intercepts vary over space. Slope heterogeneity can be controlled through spatial
interaction effects of the spatial indicators with explanatory covariates (e.g., Kestens et al., 2004).
However, they implicitly assume prior knowledge about the actual spatial process. Modeling
heterogeneity using a large number of fixed effects can result in insufficient observations within
regions for parameter estimations which, due to the loss of degrees of freedom, decrease the
prediction accuracy. Therefore, it is common practice to interact in an ad-hoc fashion where only
"one-variable-at-a-time" is considered (McMillen and Redfearn, 2010, p. 713). Thus, a trade-off
between both data fidelity and reduction of prediction accuracy is required which is partially solved
by the random effects model (Orford, 2000; Goldstein, 2011).
