Applied Spatial Econometrics: Raising The Bar

Spatial Economic Analysis, Vol. 5, No. 1, March 2010Applied Spatial Econometrics: Raising the BarJ. PAUL ELHORSTDownloaded by [Portland State University] at 15:35 06 October 2013(Received December 2009; accepted December 2009)This paper places the key issues and implications of the new ‘introductory’ book onspatial econometrics by James LeSage & Kelley Pace (2009) in a broader perspective: the argument infavour of the spatial Durbin model, the use of indirect effects as a more valid basis for testing whetherspatial spillovers are significant, the use of Bayesian posterior model probabilities to determine whichspatial weights matrix best describes the data, and the book’s contribution to the literature on spatiotemporal models. The main conclusion is that the state of the art of applied spatial econometrics hastaken a step change with the publication of this book.ABSTRACTRelever le niveau de l’économetrie spatial appliquéeLa pre sente communication place les principales questions et implications du nouvel ouvraged’introduction sur l’économe tries spatiale de James LeSage & Kelley Pace (2009) dans un contexteplus général: l’argument favorisant le modèle spatial de Durbin, l’emploi d’effets indirects comme baseplus valable pour évaluer l’aspect significatif des de versements spatiaux, l’emploi des probabilite s d’unmodèle baysien poste rieur pour évaluer laquelle des matrices de poids spatiaux de crit le mieux lesdonnes, et la contribution de l’ouvrage la documentation sur les modèles spatio-temporels. La principaleconclusion est qu’avec la publication de cet ouvrage, l’état de l’art de l’e conome tries spatiale applique aeffectue un grand pas en avant.RÉSUMÉAlzar el nivel de la econometrı́a espacial aplicadaEste trabajo plantea las cuestiones e implicaciones clave del nuevo libro introductorio sobreeconómetra espacial de James LeSage & Kelley Pace (2009) dentro de una perspectiva más amplia: elargumento a favor del modelo espacial Durbin, el uso de efectos indirectos como una base más válidapara poner a prueba si los desbordamientos espaciales son significativos, el uso de probabilidadesposteriores bayesianas para descubrir que matriz de pesos espaciales describe mejor los datos, y lacontribución del libro a la bibliógrafa sobre modelos espaciotemporales. La principal conclusión es que laeconometrı a espacial aplicada más avanzada ha experimentado un cambio radical con la publicación deeste libro.RÉSUMÉFaculty of Economics and Business, University of Groningen, PO Box 800, 9700 AV Groningen, TheNetherlands. Email: j.p.elhorst@rug.nl. The author would like to thank Jan Jacobs and Jan Oosterhaven and theeditors of this journal Bernard Fingleton and Harry Garretsen for valuable comments on a previous version of thispaper.ISSN 1742-1772 print; 1742-1780 online/10/010009-20# 2010 Regional Studies AssociationDOI: 10.1080/17421770903541772

10J. P. ElhorstKEYWORDS: Spatial Durbin model; spatial spillovers; posterior model probabilities; spatio-temporalDownloaded by [Portland State University] at 15:35 06 October 2013modelsJEL CLASSIFICATION: C21; R101. IntroductionThe year 2007 marks a sea change in spatial econometricians’ way of thinking.Prior to this they were interested mainly in models containing one type of spatialinteraction effect: the spatial lag model and the spatial error model. The first modelcontains a spatially lagged dependent variable, while the second model incorporatesa spatial autoregressive process in the error term. The seminal book by Anselin(1988) and the testing procedure for a spatial error or a spatial lag model based onrobust Lagrange multiplier tests developed by Anselin et al. (1996) may beconsidered as the main pillars behind this way of thinking. After 2007 the interest inmodels containing more than one spatial interaction effect increased. In his keynotespeech at the first World Conference of the Spatial Econometrics Association in2007, Harry Kelejian advocated models that include both a spatially laggeddependent variable and a spatially autocorrelated error term (based on Kelejian &Prucha, 1998 and related work), while James LeSage, in his presidential address atthe 54th North American Meeting of the Regional Science Association International in 2007, advocated models that include both a spatially lagged dependentvariable and spatially lagged explanatory variables. In analogy to Durbin (1960)for the time series case, Anselin (1988) labelled the latter model the spatialDurbin model.The argument in favour of the spatial Durbin model is now laid down in anew ‘introductory’ book on spatial econometrics by James LeSage & Kelley Pace(2009), and may be considered a landmark in raising the bar in the field ofapplied spatial econometrics. One strength of the spatial Durbin model is that itproduces unbiased coefficient estimates also if the true data-generation process is aspatial lag or a spatial error model. Another strength is that it does not imposeprior restrictions on the magnitude of potential spatial spillover effects. In contrastto other spatial regression specifications, these spillover effects can be global orlocal and be different for different explanatory variables. These and otherimportant issues put forward in LeSage & Pace’s book (hereinafter with pagenumbers shown in parentheses) will be summarized in this paper. This paper,however, is more than just a book review. In each of the following sections,I will first give my own view of the state of the art of one theme inapplied spatial econometrics, and then I will discuss the contribution of LeSage &Pace’s book.

Applied Spatial Econometrics112. A Taxonomy of Linear Spatial Dependence Models for Cross-sectionDataTo give a full explanation of the claim that the spatial Durbin model producesunbiased coefficient estimates, also if the true data-generation process is a spatial lagor a spatial error model, I first consider a taxonomy of linear spatial dependencemodels for cross-section data.The standard approach in most empirical work is to start with a non-spatiallinear regression model and then to test whether or not the model needs to beextended with spatial interaction effects. This approach is known as the specific-togeneral approach. The non-spatial linear regression model takes the formDownloaded by [Portland State University] at 15:35 06 October 2013Y aiN Xb o;(1)where Y denotes an N 1 vector consisting of one observation on thedependent variable for every unit in the sample (i 1, . . ., N), iN is an N 1vector of ones associated with the constant term parameter a, X denotes anN K matrix of exogenous explanatory variables, with the associated parametersb contained in a K 1 vector, and o (o 1 ; :::; o N )T is a vector of disturbanceterms,1 where oi are independently and identically distributed error terms for all iwith zero mean and variance s2. Since the linear regression model is commonlyestimated by ordinary least squares (OLS), it is often labelled the OLS model.Furthermore, even though the OLS model in most studies focusing on spatialinteraction effects is rejected in favour of a more general model, its results oftenserve as a benchmark.The opposite approach is to start with a more general model containing, nestedwithin it as special cases, a series of simpler models that ideally should represent allthe alternative economic hypotheses requiring consideration. Manski (1993) pointsout that three different types of interaction effects may explain why an observationassociated with a specific location may be dependent on observations at otherlocations: (i) endogenous interaction effects, where the decision of a spatial unit (orits economic decision makers) to behave in some way depends on the decisiontaken by other spatial units; (ii) exogenous interaction effects, where the decision ofa spatial unit to behave in some way depends on independent explanatory variablesof the decision taken by other spatial units*if the number of independentexplanatory variables in a linear regression model is K, then the number ofexogenous interaction effects is also K, provided that the intercept is considered as aseparate variable; and (iii) correlated effects, where similar unobserved environmental characteristics result in similar behaviour.The Manski model takes the formY rWY aiN Xb WXu u;(2a)u lWu o;(2b)where the variable WY denotes the endogenous interaction effects among thedependent variables, WX the exogenous interaction effects among the independentvariables, and Wu the interaction effects among the disturbance terms of thedifferent spatial units. r is called the spatial autoregressive coefficient, l the spatial