A Design-Based Approach to Spatial Correlation

When observing spatial data, what standard errors should we report? With the finite population framework, we identify three channels of spatial correlation: sampling scheme, assignment design, and model specification. The Eicker-Huber-White standard error, the cluster-robust standard error, and the spatial heteroskedasticity and autocorrelation consistent standard error are compared under different combinations of the three channels. Then, we provide guidelines for whether standard errors should be adjusted for spatial correlation for both linear and nonlinear estimators. As it turns out, the answer to this question also depends on the magnitude of the sampling probability.