Inference for Regression with Clustered or Spatially Correlated Data II: Spatial Correlation

This article presents inference for regression with data that are correlated across some measure of distance; most often geographic distance. Failure to appropriately adjust standard errors can lead to confidence intervals that are too narrow, and hypothesis tests that over-reject.
If spatial correlation exists within region but not across regions then one can use cluster-robust inference methods presented in the companion paper, Cameron and Miller (2026).
In this paper we focus on methods when spatial correlation is dampening in distance. Then the standard inference method is the spatial HAC of Conley (1999). This method does not work well when spatial persistence is high, and alternative inference methods are needed. Additionally it is important that regression models control for any spatial trends to avoid finding spurious correlation.