1# RECORD 5d5481f1bdb4441dc2691f3437c1456c28db43542# TITLE: A Grid Based Approach to Analysing Spatial Weighting Matrix Specification3# YEAR: 2019.0 VENUE: nan DOI: 10.31235/osf.io/nt2yq4# AUTHORS: C. Rahal5# PAGES: 9 CANDIDATE TABLE PAGES (1-based): []6# 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.789===== PAGE 1 (score 4, numeric-paren 0, table-words 0, var-words 4) =====1011A Grid Based Approach to Analysing Spatial12Weighting Matrix Specification13Charles Rahal‡14‡Leverhulme Centre for Demographic Science, University of Oxford, OX1 3UQ15E-mail: charles.rahal@sociology.ox.ac.uk168th October, 201717Abstract:18We outline a grid-based approach to provide further evidence against the miscon-19ception that the results of spatial econometric models are sensitive to the exact specification of20the exogenously set weighting matrix (otherwise known as the ‘biggest myth in spatial economet-21rics’). Our application estimates three large sets of specifications using an original dataset which22contains information on the Prime Central London housing market. We show that while posterior23model probabilities may indicate a strong preference for an extremely small number of models,24and while the spatial autocorrelation parameter varies substantially, median direct effects remain25stable across the entire permissible spatial weighting matrix space. We argue that spatial econo-26metric models should be estimated across this entire space, as opposed to the current convention27of merely estimating a cursory number of points for robustness.28Keywords:29Spatial Econometrics, Real Estate Economics, Model Selection, Data Visualisation301. INTRODUCTION31The most frequently asked question when discussing spatial econometric models regards the sensi-32tivity of the results to the specification of the spatial weighting matrix (W ). A recent introduction33to a special issue of Papers in Regional Science summarizes this succinctly, stating: ‘Critics of spa-34tial econometrics almost always in our experience home in on the arbitrary nature of the weights’35(Arbia and Fingleton, 2008, p.316). This misconception that spatial regression models are sensi-36tive to W is pervasive and may have arisen from previous research incorrectly interpreting model37coefficients as if they were partial derivatives, or from the use of misspecified models (even in cases38where the spatial weighting matrix will not theoretically change coefficient point estimates). The39perceived issue of sensitivity is highlighted directly within a housing context in an early influ-40ential article which claims: ‘There does not appear to be any consensus regarding which scheme41represents the best realization of the correlation structure appearing in the housing market. This42is problematic because all of the results are conditional on the researcher’s a priori specification43of the spatial structure’ (Dubin, 1998, p.88). LeSage and Pace (2014) convincingly conclude that44‘the notion that estimates and inferences are sensitive to use of a particular weight matrix as per-45haps the biggest myth about spatial regression models’ [p.5]. Amongst others, they attack a well46cited study (Bell and Bockstael (2000)) which claims that their results are more sensitive to the47specification of the spatial weight matrix than to estimation technique. However, for a correctly48specified Spatial Error Model (SEM – the type used in that paper), changes in W only change the49measures of dispersion: not the point estimates. More generally, methods for specifying W have50been discussed extensively, dating back to as early as Kooijman (1976) who proposed choices based51on maximizing Moran’s coefficient. Much work has since followed aiming to reduce the degree of52arbitrariness in the choice of W , and LeSage and Parent (2007) develop a Bayesian model averag-53ing procedure (using posterior model probabilities as weights) to incorporate uncertainty. Rather54