The Effect of Spatial Autoregressive Structures on Statistical Efficiency and Model Specification Accuracy

Posted: Feb 25, 2022

• Paisley Wood
• Patrick Evans
• Penelope Parker

Abstract

Spatial econometric models have become increasingly prevalent across numerous disciplines, including economics, geography, environmental science, and public health. These models explicitly account for spatial dependence, recognizing that observations from proximate locations often exhibit correlation patterns that violate the independence assumption of classical regression analysis. The spatial autoregressive (SAR) model, in particular, has emerged as a workhorse specification for capturing such dependencies through a spatially lagged dependent variable. Despite the widespread adoption of SAR models, fundamental questions remain regarding how the specification of spatial dependence structures affects statistical efficiency and model selection accuracy. Traditional approaches to spatial econometrics have primarily focused on estimation techniques and inference procedures, with comparatively less attention devoted to understanding how the choice of spatial weight matrices influences the statistical properties of resulting estimators. The spatial weight matrix, which formalizes the connectivity structure between observational units, represents a crucial—yet often arbitrary—modeling decision that can substantially impact empirical results. Current practice typically relies on ad hoc specifications or convenience-based selections, with limited theoretical guidance on optimal weight matrix construction for given research contexts. This paper addresses this critical gap by systematically investigating how different spatial autoregressive structures affect both statistical efficiency and model specification accuracy. We develop a novel analytical framework that examines the interplay between spatial connectivity patterns, estimation precision, and model selection performance. Our approach moves beyond conventional treatments of spatial dependence by considering how the topological properties