A Design-Based Approach to Spatial Correlation

TL;DR

This paper examines how different sources of spatial correlation affect standard error estimation in spatial data analysis, providing guidelines for when adjustments are necessary based on the data collection and model specifics.

Contribution

It introduces a design-based framework to identify sources of spatial correlation and compares various standard error estimators under different conditions.

Findings

Eicker-Huber-White, cluster-robust, and spatial HAC standard errors are compared.

Guidelines are provided for adjusting standard errors based on spatial correlation sources.

The importance of sampling probability magnitude in standard error adjustment is highlighted.

Abstract

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.