Spatial Correlation Robust Inference

TL;DR

This paper introduces a new method for constructing confidence intervals that effectively account for various forms of spatial correlation, ensuring reliable inference in large samples and outperforming previous methods in practical applications.

Contribution

It develops a novel approach to spatially robust inference using population principal components and benchmark critical values, improving coverage and efficiency.

Findings

Controls coverage under weak spatial correlation as sample size grows

Provides valid coverage for certain strong spatial correlations

Outperforms previous methods in U.S. state economic data

Abstract

We propose a method for constructing confidence intervals that account for many forms of spatial correlation. The interval has the familiar `estimator plus and minus a standard error times a critical value' form, but we propose new methods for constructing the standard error and the critical value. The standard error is constructed using population principal components from a given `worst-case' spatial covariance model. The critical value is chosen to ensure coverage in a benchmark parametric model for the spatial correlations. The method is shown to control coverage in large samples whenever the spatial correlation is weak, i.e., with average pairwise correlations that vanish as the sample size gets large. We also provide results on correct coverage in a restricted but nonparametric class of strong spatial correlations, as well as on the efficiency of the method. In a design calibrated to match economic activity in U.S. states the method outperforms previous suggestions for spatially robust inference about the population mean.