Lag or Error? - Detecting the Nature of Spatial Correlation

The attractiveness of spatial autoregressive models has increased significantly. The awareness of important spatial interactions arose in various fields. In economics, interactions can be due to interdependencies between entities such as states, firms, or consumers. Examples are spatial interactions due to network effects, due to environmental circumstances, due to contagion problems, or due to market interdependencies. In politics the propagation of opinions has a spatial dimension. Even more naturally is the spatial correlation of geographical units. Vegetation patterns and snow cover distributions are specific examples in the latter vein. For many applications estimating a spatial correlation coefficient is useful to obtain white noise errors and therefore valid hypothesis test. However, often theory suggests the existence of spatial dependence in the endogeneous variable as in the examples of strategic behavior and the propagation of opinions. In these cases the parameter of the spatial dependent variable is of interest per se. Estimating spatial models – like the spatial lag model, the spatial error model or even spatial autoregressive model with spatial autoregressive disturbances – requires the specification of an appropriate weighting matrix. The necessary weighting matrix to capture the spatial dimension will be very different for each application. Dubin (2003) analyzed the severeness of a (model) misspecification resulting from an improper weighting matrix. Additionally, McMillen (2003) investigated the impact of an improper functional form of the model. In this article we analyze whether it is empirically possible to separate the effect of a spatial lag in the dependent variable from a spatial lag in the error term using maximum likelihood and generalized method of moments as estimation techniques. Therefore, a large Monte Carlo study is set up to investigate the consequences of a weighting matrix misspecification for the finite sample properties. Various specification tests are applied to check the models and to detect the most suitable weighting scheme using the information in the data