Model Specification in the Analysis of Spatial Dependence

The recent surge in studies analyzing spatial dependence in political science has gone hand in hand with increased attention paid to the choice of estimation technique. In comparison, specification choice has been largely neglected, even though it leads to equally, if not more, important inference problems. In this article we discuss four issues. Two pitfalls can simply be avoided if researchers adequately control for common trends and shocks and refrain from inferring anything on the validity of the chosen weighting matrix from the estimation results of the spatial lag. The two remaining specification choices have no easy solution, however. First, row-standardization of the weighting matrix changes the relative weight of observations that make up the spatial effect and thereby impacts on statistical inference of the spatial lag. It should therefore only be applied if theoretically warranted, not as a general default rule. Second, seemingly small changes to the functional form of the weighting matrix can change dramatically the coefficient sign, size and standard error of the spatial lag. This creates the temptation of choosing a functional form that generates results consistent with the hypothesis to be tested. Only a more developed theoretical model can defend researchers against verification bias by providing guidance on the functional form of the weighting matrix. We demonstrate the importance of all four specification issues by replicating a prominent model of spatial dependence in international capital tax rate competition.