Spatial effects and non-linearity in hedonic modeling. Will large data sets change our assumptions?

Date05 February 2018
Published date05 February 2018
Pages32-49
DOIhttps://doi.org/10.1108/JPIF-10-2016-0080
AuthorMarcelo Cajias,Sebastian Ertl
Subject MatterProperty management & built environment,Real estate & property,Property valuation & finance
Spatial effects and non-linearity
in hedonic modeling
Will large data sets change our assumptions?
Marcelo Cajias
Department of Research, PATRIZIA Immobilien AG, Augsburg, Germany, and
Sebastian Ertl
IRE/BS International Real Estate Business School, University of Regensburg,
Regensburg, Germany
Abstract
Purpose The purpose of this paper is to test the asymptotic properties and prediction accuracy of two
innovative methods proposed along the hedonic debate: the geographically weighted regression (GWR) and
the generalized additive model (GAM).
Design/methodology/approach The authors assess the asymptotic properties of linear, spatial and
non-linear hedonic models based on a very large data set in Germany. The employed functional form is based
on the OLS, GWR and the GAM, while the estimation methodology was chosen to be iterative in forecasting,
the fitted rents for each quarter based on their 1-quarter-prior functional form. The performance accuracy is
measured by traditional indicators such as the error variance and the mean squared (percentage) error.
Findings The results provide evidence for a clear disadvantage of the GWR model in out-of-sample
forecasts. There exists a strong out-of-sample discrepancy between the GWR and the GAM models, whereas
the simplicity of the OLS approach is not substantially outperformed by the GAM approach.
Practical implications For policymakers, a more accurate knowledge on market dynamics via hedonic
models leads to a more precise market control and to a better understanding of the local factors affecting
current and future rents. For institutional researchers, instead, the findings are essential and might be used as
a guide when valuing residential portfolios and forecasting cashflows. Even though this study analyses
residential real estate, the results should be of interest to all forms of real estate investments.
Originality/value Samplesize is essential when derivingthe asymptotic propertiesof hedonic models. Whit
this studycovering more than 570,000 observations, this studyconstitutes to the authorsknowledgeone of
the largest data sets used forspatial real estate analysis.
Keywords Housing, Generalized additive model (GAM), Geographically weighted regression (GWR),
German residential market, Hedonic model, Semi-parametric regression
Paper type Research paper
Introduction
What are the three most important things when dealing with real estate? location, location,
location. This is a pretty common saying about real estate, which makes the statement that
the location of a property is one of the most important factors in defining its value.
Traditional models for defining the value of properties make use of regression methods in
order to decompose the underlying value drivers of properties considering a series of
attributes and of course their location within a certain market. The estimation of hedonic
regression models has indeed grown substantially over the last years integrating new
approaches for modeling spatial heterogeneity, which is essential in the explanation of real
estate prices across space. With the list of spatially estimation techniques being very
extensive, the geographically weighted regression (GWR) has established itself as a
widely used method that expands the restrictive traditional ordinary least squares (OLS)
Journal of Property Investment &
Finance
Vol. 36 No. 1, 2018
pp. 32-49
© Emerald PublishingLimited
1463-578X
DOI 10.1108/JPIF-10-2016-0080
Received 25 October 2016
Revised 10 April 2017
Accepted 18 April 2017
The current issue and full text archive of this journal is available on Emerald Insight at:
www.emeraldinsight.com/1463-578X.htm
The authors especially thank PATRIZIA Immobilien AG for contributing the data set and large
computational infrastructure necessary to conduct this study. All statements of opinion reflect the
current estimations of the authors and do not necessarily reflect the opinion of PATRIZIA Immobilien
AG or its associated companies.
32
JPIF
36,1
by considering spatially varying effects. Based on the assumption that real estate prices
vary over space within a certain market, the GWR method estimates local regressions in
order to identify spatially varying parameters and therefore different marginal price
functions. The rationale behind the GWR method is plausible since real estate prices are
mainly determined by neighborhood effects, the proximity to common amenities and lastly
by household's income distribution. In this context, a major part of the empirical research
encourages the assumption that the explanatory power as well as the forecasting accuracy
of hedonic models increases when their functional form accounts for spatial effects, thus
emphasizing the potentials of the GWR in explaining real estate prices.
Beyond this scope, a series of semi-parametric methods which are able to capture spatial
effectshave been proposed recently and (theoretically) allow a moreflexible modeling between
the regressor and the predictor without any a priori assumptions regarding the underlying
data generating process. In particular methods, like the generalized additive model (GAM),
capture spatial effects based on smooth functions and expand the traditional hedonic model
by identifying latent nonlinear effects. Since the main goal of any hedonic model is the
reduction of misspecification in the estimated coefficients, the GAM model allows covariates
to take a nonlinear functional form in order to reduce the error variance (EV) and thus
enhance the model quality. With GAM models being popular in natural sciences, their usage
in the empirical real estate research has been very limited and not been extensively studied.
Given the uncertainty about the statistical advantages of GAM models in hedonic
equations,this paper estimates hedonicregressions via OLS, GWR and GAMbased on a large
data set including more than 570,000 observations of rental flats in 46 NUTS3 regions in
Germany. The aim of the present study is to test their explanatory power by means of
out-of-sample validation approaches. The results show primarily that the explanatory power
and predictability of rents in the observed German markets increases significantly when a
non-linear and spatially-variant functional form like the GAM procedure is chosen.
The paper is organized as follows: the upcoming section gives an overview on spatial
and non-linear effects in hedonic pricing methods from a theoretical point of view together
with empirical evidence. The subsequent section covers the database, whereas the following
section explains the econometric methods used for estimating hedonic prices via OLS, GWR
and GAM. In the next sections the research design and the parameterization of the models is
described, as well as the consequential statistical results and implications of the entire
analysis. The final section concludes.
Spatial modeling of real estate prices
Regardless of whether it is building up hedonic real estate indices, forecasting prices or
analyzing different markets, a significant share of empirical real estate research does not
take spatial variables or non-linearity into account. This may be due to different reasons.
In the most cases, the lack of the needed data to capture spatial heterogeneity should
be the cause. Another possibility may be that spatial models are considered to be
complex and difficult to estimate or interpret and that they are not integrated in standard
econometric programs.
But why does spatial heterogeneity matter? The locational immobility of real estate
makes its price formation different from traditional commodities. Real estate prices
theoretically reflect their explicit building attributes, neighborhood characteristics and
finally the share of directly available amenities. Moreover, real estate prices respond to
the demand of households for housing, which in turn is based on their disposable income,
transport costs and on their own preferences. Spatial variation in rents arises since
households disposable income varies across a city and since some regions or submarkets
are able to attract households with higher purchasing power than others. Furthermore, each
one of these submarkets provides a different set of local characteristics like green areas,
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Spatial
effects and
non-linearity

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