Measurement Error and the Specification of the Weights Matrix in Spatial Regression Models

While the spatial weights matrix boldsymbol W is at the core of spatial regression models, there is a scarcity of techniques for validating a given specification of boldsymbol W. I approach this problem from a measurement error perspective. When boldsymbol W is inflated by a constant, a predictable form of endogeneity occurs that is not problematic in other regression contexts. I use this insight to construct a theoretically appealing test and control for the validity of boldsymbol W that is tractable in panel data, which I call the K test. I demonstrate the utility of the test using Monte Carlo simulations.