Low rank spatial econometric models

TL;DR

This paper introduces low rank spatial econometric models within a linear mixed model framework, enabling robust, fast estimation and inference even with noisy data, validated through simulations and implemented in an R package.

Contribution

It proposes a novel low rank spatial econometric modeling approach that improves robustness and efficiency, especially in noisy data scenarios, with practical implementation in R.

Findings

High accuracy in estimating direct and indirect effects.

Lower root mean squared errors in noisy data conditions.

Effective parameter estimation using Type II restricted likelihood.

Abstract

This article presents a re-structuring of spatial econometric models in a linear mixed model framework. To that end, it proposes low rank spatial econometric models that are robust to the existence of noise (i.e., measurement error), and can enjoy fast parameter estimation and inference by Type II restricted likelihood maximization (empirical Bayes) techniques. The small sample properties of the proposed low rank spatial econometric models are examined using Monte Carlo simulation experiments, the results of these experiments confirm that direct effects and indirect effects a la LeSage and Pace (2009) can be estimated with a high degree of accuracy. Also, when data are noisy, estimators for coefficients in the proposed models have lower root mean squared errors compared to conventional specifications, despite them being low rank approximations. The proposed approach is implemented in an R package "spmoran".