The correlation structure of spatial autoregressions on graphs

Abstract

This paper studies the correlation structure of spatial autoregressions defined over arbitrary configurations of observational units. We derive a number of new properties of the models and provide new interpretations of some of their known properties. A little graph theory helps to clarify how the correlation between two random variables observed at two units depends on the walks connecting the two units, and allows to discuss the statistical consequences of the presence (or, more importantly in econometrics, the absence) of symmetries or regularities in the configuration of the observational units. The analysis is centered upon one-parameter models, but extensions to multi-parameter models are also considered. Keywords: exponential families; graphs; quadratic subspace; spatial autoregressions; spatial weights matrices. JEL Classification: C12, C21