Bias from Network Misspecification Under Spatial Dependence

The prespecification of the network is one of the biggest hurdles for applied researchers in undertaking spatial analysis. In this letter, we demonstrate two results. First, we derive bounds for the bias in nonspatial models with omitted spatially-lagged predictors or outcomes. These bias expressions can be obtained without prior knowledge of the network, and are more informative than familiar omitted variable bias formulas. Second, we derive bounds for the bias in spatial econometric models with nondifferential error in the specification of the weights matrix. Under these conditions, we demonstrate that an omitted spatial input is the limit condition of including a misspecificed spatial weights matrix. Simulated experiments further demonstrate that spatial models with a misspecified weights matrix weakly dominate nonspatial models. Our results imply that, where cross-sectional dependence is presumed, researchers should pursue spatial analysis even with limited information on network ties.