The spatial lag of X model, a linear regression model extended to include explanatory variables observed on neighboring cross-sectional units, is the simplest spatial econometric model producing flexible spatial spillover effects and the easiest model to parameterize the spatial weights matrix, denoted by W, describing the spatial arrangement of the units in the sample. Nevertheless, it has received relatively little attention in the theoretical and applied spatial econometrics literature. This study fills this gap by considering several extensions of its basic form. It is found that the claim made in many empirical studies that their results are robust to the specification of W. In addition, it is found that the common practice to adopt the same W for every spatial lag should be rejected. These findings are illustrated using a cigarette demand model based on panel date of 46 U.S. states over the period 1963 to 1992.
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