📌 The Challenge

Prespecifying the network of ties is a major obstacle for applied spatial analysis. When networks are unknown or misspecified, researchers face bias from omitted spatial inputs or from errors in the spatial weights matrix.

🔍 What the paper shows

• Derives bounds on bias in nonspatial models that omit spatially lagged predictors or outcomes.
• Derives bounds on bias in spatial econometric models when the weights matrix is misspecified with nondifferential error.

🧭 How the bounds work

• The bias expressions for nonspatial models can be computed without prior knowledge of the underlying network.
• These expressions are more informative than standard omitted-variable bias formulas because they explicitly account for spatially-lagged inputs.
• For spatial models, the analysis shows that an omitted spatial input is the limiting case of including a misspecified spatial weights matrix.

🧪 Evidence from simulations

• Simulated experiments compare nonspatial models, correctly specified spatial models, and spatial models with misspecified weights.
• Results show that spatial models with a misspecified weights matrix weakly dominate nonspatial models: they perform at least as well, and often better, in terms of bias.

⚖️ Key findings

• Bias bounds are available even without knowing network ties.
• Misspecifying the weights matrix does not generally make spatial models worse than ignoring spatial dependence entirely.
• The omitted-spatial-input case is the extreme limit of weight-matrix misspecification.

📣 Why it matters

Where cross-sectional dependence is plausible, pursuing spatial analysis is recommended even with limited information about network ties. The derived bounds give practical guidance on expected bias and support the use of spatial econometric techniques when dependence is suspected.