Interaction matrix selection in spatial autoregressive models with an application to growth theory

Abstract

The interaction matrix, or spatial weight matrix, is the fundamental tool to model cross-sectional interdependence between observations in spatial autoregressive models. However, it is most of the time not derived from theory, as it should be ideally, but chosen on an ad hoc basis. In this paper, we propose a modified version of the J test to formally select the interaction matrix. Our methodology is based on the application of the robust against unknown heteroskedasticity GMM estimation method, developed by Lin and Lee (2010). We then implement the testing procedure developed by Hagemann (2012) to overcome the decision problem inherent to non-nested models tests. An application of the testing procedure is presented for the Schumpeterian growth model with worldwide interactions developed by Ertur and Koch (2011) using three different types of interaction matrices: genealogic distance, linguistic distance and bilateral trade flows. We find that the interaction matrix based on trade flows is the most adequate.