Spatial regression models are becoming increasingly popular across the social sciences as a means of modeling spatial dependencies within data. At the core of these models is W, a connectivity matrix between observations. Despite the centrality of W in spatial regression models, however, there is a scarcity of techniques for evaluating the validity of a given specification of W. I argue that approaching the specification of W as a measurement error problem leads to some important insights. I demonstrate that when W is misspecified, a predictable form of omitted variable bias occurs. I also construct a theoretically appealing test for the validity of W which, while intractable in cross-sectional settings, is easily applied in settings featuring multiple cross-sections like panel data. I demonstrate the validity of this test using simulations with an examination of the models in Williams and Whitten (2015). By demonstrating the utility of the approach, I simultaneously provide scholars a means of testing their modelling assumptions and advance a larger theoretical framework for dependence across data that will be fruitful for future research.
Vande Kamp, G. N. (2018). Measurement Error and the Specification of W.
