Local Statistics for Spatial Panel Models with Application to the US Electorate

TL;DR

This paper introduces a fast permutation testing methodology for detecting spatial correlations in spatial panel models, demonstrated on US electoral data, enhancing model validation techniques.

Contribution

It extends univariate spatial association statistics to multivariate and panel data, providing a new tool for model checking in spatial econometrics.

Findings

Method successfully applied to US electoral data from 2000 to 2016.

Identifies significant spatial correlations in electoral results.

Enhances the robustness of spatial panel model validation.

Abstract

The spatial panel regression model has shown great success in modelling econometric and other types of data that are observed both spatially and temporally with associated predictor variables. However, model checking via testing for spatial correlations in spatial-temporal residuals is still lacking. We propose a general methodology for fast permutation testing of local and global indicators of spatial association. This methodology extends past statistics for univariate spatial data that can be written as a gamma index for matrix similarity to the multivariate and panel data settings. This includes Moran's $I$ and Geary's $C$ among others. Spatial panel models are fit and our methodology is tested on county-wise electoral results for the five US presidential elections from 2000 to 2016 inclusive. County-wise exongenous predictor variables included in this analysis are voter population density, median income, and percentage of the population that is non-Hispanic white.