# RECORD 5d5481f1bdb4441dc2691f3437c1456c28db4354
# TITLE: A Grid Based Approach to Analysing Spatial Weighting Matrix Specification
# YEAR: 2019.0  VENUE: nan  DOI: 10.31235/osf.io/nt2yq
# AUTHORS: C. Rahal
# PAGES: 9  CANDIDATE TABLE PAGES (1-based): []
# ABSTRACT: We outline a grid-based approach to provide further evidence against the misconception that the results of spatial econometric models are sensitive to the exact specification of the exogenously set weighting matrix (otherwise known as the 'biggest myth in spatial econometrics'). Our application estimates three large sets of specifications using an original dataset which contains information on the Prime Central London housing market. We show that while posterior model probabilities may indicate a strong preference for an extremely small number of models, and while the spatial autocorrelation parameter varies substantially, median direct effects remain stable across the entire permissible spatial weighting matrix space. We argue that spatial econometric models should be estimated across this entire space, as opposed to the current convention of merely estimating a cursory number of points for robustness.


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A Grid Based Approach to Analysing Spatial
Weighting Matrix Speciﬁcation
Charles Rahal‡
‡Leverhulme Centre for Demographic Science, University of Oxford, OX1 3UQ
E-mail: charles.rahal@sociology.ox.ac.uk
8th October, 2017
Abstract:
We outline a grid-based approach to provide further evidence against the miscon-
ception that the results of spatial econometric models are sensitive to the exact speciﬁcation of
the exogenously set weighting matrix (otherwise known as the ‘biggest myth in spatial economet-
rics’). Our application estimates three large sets of speciﬁcations using an original dataset which
contains information on the Prime Central London housing market. We show that while posterior
model probabilities may indicate a strong preference for an extremely small number of models,
and while the spatial autocorrelation parameter varies substantially, median direct eﬀects remain
stable across the entire permissible spatial weighting matrix space. We argue that spatial econo-
metric models should be estimated across this entire space, as opposed to the current convention
of merely estimating a cursory number of points for robustness.
Keywords:
Spatial Econometrics, Real Estate Economics, Model Selection, Data Visualisation
1. INTRODUCTION
The most frequently asked question when discussing spatial econometric models regards the sensi-
tivity of the results to the speciﬁcation of the spatial weighting matrix (W ). A recent introduction
to a special issue of Papers in Regional Science summarizes this succinctly, stating: ‘Critics of spa-
tial econometrics almost always in our experience home in on the arbitrary nature of the weights’
(Arbia and Fingleton, 2008, p.316). This misconception that spatial regression models are sensi-
tive to W is pervasive and may have arisen from previous research incorrectly interpreting model
coeﬃcients as if they were partial derivatives, or from the use of misspeciﬁed models (even in cases
where the spatial weighting matrix will not theoretically change coeﬃcient point estimates). The
perceived issue of sensitivity is highlighted directly within a housing context in an early inﬂu-
ential article which claims: ‘There does not appear to be any consensus regarding which scheme
represents the best realization of the correlation structure appearing in the housing market. This
is problematic because all of the results are conditional on the researcher’s a priori speciﬁcation
of the spatial structure’ (Dubin, 1998, p.88). LeSage and Pace (2014) convincingly conclude that
‘the notion that estimates and inferences are sensitive to use of a particular weight matrix as per-
haps the biggest myth about spatial regression models’ [p.5]. Amongst others, they attack a well
cited study (Bell and Bockstael (2000)) which claims that their results are more sensitive to the
speciﬁcation of the spatial weight matrix than to estimation technique. However, for a correctly
speciﬁed Spatial Error Model (SEM – the type used in that paper), changes in W only change the
measures of dispersion: not the point estimates. More generally, methods for specifying W have
been discussed extensively, dating back to as early as Kooijman (1976) who proposed choices based
on maximizing Moran’s coeﬃcient. Much work has since followed aiming to reduce the degree of
arbitrariness in the choice of W , and LeSage and Parent (2007) develop a Bayesian model averag-
ing procedure (using posterior model probabilities as weights) to incorporate uncertainty. Rather