space and growth: a survey of empirical evidence ... - ResearchGate

28 Maria Abreu, Henri L.F. de Groot and Raymond J.G.M. Floraxinterpretation of the coefficients. We also mention some common misconceptionsthat are prevalent in the literature, and suggest areas where improvementscan be made.3.1. Operationalisation3.1.1. Lattice and geostatistical approachesThere are two alternative approaches for spatial statistical analysis. Thelattice or spatial process approach assumes that the unit of analysis is a discreteentity or object. Objects are linked by a spatial pattern, expressed in terms of aspatial weights matrix. Inference is based on "expanding domain" asymptotics,which is, adding more and more objects to the sample. Prediction is byextrapolation, that is, for a different set of spatial units, or for another timeperiod (Anselin, 2002). The variance-covariance matrix is indirectly determinedby the model and by the exogenous spatial weights matrix (discussed in the nextsection). The spatial error and spatial lag models are examples of the spatialprocess approach, as are most of the models used in the spatial econometricsliterature within economics. The reason is that most economic models are basedon discrete objects: individuals, firms, sectors, countries. A problem with thisapproach is that it is difficult to deal with missing observations, since everyobject in the model must be connected to every other via the spatial weightsmatrix.In contrast, the geostatistical or direct representation approach takes as theunit of analysis data points on a continuous field or surface. Examples of a fieldin this sense are land prices, or average yearly rainfall. Geostatistical models donot use spatial weights matrices to summarize the spatial relationship. Thevariance-covariance matrix must be modeled directly, typically as a function ofthe distance between observations. There is no equivalent of the spatial lagmodel with this approach; geostatistical models apply only to the error term. Oneadvantage of this method is that it allows "interpolation", i.e. making predictionsfor missing values (known as kriging).Some studies have used the average value of proximate observations as anexplanatory variable, with the degree of proximity modeled as a distance decayfunction (e.g., Keller, 2002). The resulting model is non-linear, but can beestimated if the data is available as a panel, or at the sectoral level7.7 It should be noted that growth studies that include a physical distance function on the right-handsideof the regression are not generally considered to be examples of the geostatistical approachunless they also model the spatial autocorrelation in the error term directly by making the variancecovariancematrix a function of distance.