Spatial Weighting Matrix Selection in Spatial Lag Econometric Model

Abstract

This paper investigates the choice of spatial weighting matrix in a spatial lag model framework. In the empirical literature the choice of spatial weighting matrix has been characterized by a great deal of arbitrariness. The number of possible spatial weighting matrices is large, which until recently was considered to prevent investigation into the appropriateness of the empirical choices. Recently Kostov (2010) proposed a new approach that transforms the problem into an equivalent variable selection problem. This article expands the latter transformation approach into a two-step selection procedure. The proposed approach aims at reducing the arbitrariness in the selection of spatial weighting matrix in spatial econometrics. This allows for a wide range of variable selection methods to be applied to the high dimensional problem of selection of spatial weighting matrix. The suggested approach consists of a screening step that reduces the number of candidate spatial weighting matrices followed by an estimation step selecting the final model. An empirical application of the proposed methodology is presented. In the latter a range of different combinations of screening and estimation methods are employed and found to produce similar results. The proposed methodology is shown to be able to approximate and provide indications to what the ‘true’ spatial weighting matrix could be even when it is not amongst the considered alternatives. The similarity in results obtained using different methods suggests that their relative computational costs could be primary reasons for their choice. Some further extensions and applications are also discussed.