Spatial interdependence and instrumental variable models

Instrumental variable (IV) methods are widely used to address endogeneity concerns. Yet, a specific kind of endogeneity – spatial interdependence – is regularly ignored. We show that ignoring spatial interdependence in the outcome results in asymptotically biased estimates even when instruments are randomly assigned. The extent of this bias increases when the instrument is also spatially clustered, as is the case for many widely used instruments: rainfall, natural disasters, economic shocks, and regionally- or globally-weighted averages. Because the biases due to spatial interdependence and predictor endogeneity can offset, addressing only one can increase the bias relative to ordinary least squares. We demonstrate the extent of these biases both analytically and via Monte Carlo simulation. Finally, we discuss a general estimation strategy – S-2SLS – that accounts for both outcome interdependence and predictor endogeneity, thereby recovering consistent estimates of predictor effects.