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<p>Model selection is critical in spatial econometrics, particularly when specifying the degree of spatial dependence in regression models. Traditional criteria such as Akaike’s Information Criterion (AIC), Bayesian Information Criterion (BIC), and the Hannan-Quinn Criterion (HQC) are widely applied but do not adaptively account for the complexity introduced by spatial autocorrelation. This paper develops and evaluates the Renormalized Maximum Likelihood (RNML) criterion, which incorporates a data-driven penalty derived from the Fisher Information Matrix to balance model fit and complexity. Through extensive Monte Carlo simulations, we demonstrate RNML’s superior capacity to recover the true spatial dependence structure, particularly under strong spatial autocorrelation. Three empirical applications, regional GDP in Europe, COVID-19 spread in Italy, and foreign-born populations in Germany, show that RNML consistently selects higher spatial autoregressive coefficients than classical criteria. Crucially, our spillover effects analysis reveals that these differences, while numerically modest, translate into substantively different interpretations of cross-regional dependencies. RNML systematically attributes greater importance to indirect effects, providing more realistic assessments of spatial spillovers in economic, epidemiological, and demographic contexts. The criterion’s geometry-aware penalty, computational simplicity, and improved finite-sample performance make it a valuable addition to the spatial econometric toolkit.</p>

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Renormalized Maximum Likelihood for Spatial Lag Models

  • 期刊论文

  • 发表日期：

    2025年11月12日

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  • Saïd Maanan

摘要

Model selection is critical in spatial econometrics, particularly when specifying the degree of spatial dependence in regression models. Traditional criteria such as Akaike’s Information Criterion (AIC), Bayesian Information Criterion (BIC), and the Hannan-Quinn Criterion (HQC) are widely applied but do not adaptively account for the complexity introduced by spatial autocorrelation. This paper develops and evaluates the Renormalized Maximum Likelihood (RNML) criterion, which incorporates a data-driven penalty derived from the Fisher Information Matrix to balance model fit and complexity. Through extensive Monte Carlo simulations, we demonstrate RNML’s superior capacity to recover the true spatial dependence structure, particularly under strong spatial autocorrelation. Three empirical applications, regional GDP in Europe, COVID-19 spread in Italy, and foreign-born populations in Germany, show that RNML consistently selects higher spatial autoregressive coefficients than classical criteria. Crucially, our spillover effects analysis reveals that these differences, while numerically modest, translate into substantively different interpretations of cross-regional dependencies. RNML systematically attributes greater importance to indirect effects, providing more realistic assessments of spatial spillovers in economic, epidemiological, and demographic contexts. The criterion’s geometry-aware penalty, computational simplicity, and improved finite-sample performance make it a valuable addition to the spatial econometric toolkit.