Efficient parametric estimation of the spatial autoregressive model

Nicolas Debarsy, Vincenzo Verardi and Catherine Vermandele
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Nicolas Debarsy: LEM - Lille économie management - UMR 9221 - UA - Université d'Artois - UCL - Université catholique de Lille - Université de Lille - CNRS - Centre National de la Recherche Scientifique
Vincenzo Verardi: Louvain Research Institute in Management and Organizations (LouRIM)
Catherine Vermandele: LMTD - Laboratoire de méthodologie du traitement des données - ULB - Université libre de Bruxelles

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Abstract: This paper introduces a new one-step parametric estimation method for spatial autoregressive (SAR) models, providing an efficient estimator for any error distribution with a defined quantile function. Based on Le Cam's Local Asymptotic Normality (LAN) theory, it extends the maximum likelihood approach to cases like the Laplace distribution, which lacks a globally defined first derivative.\We further develop this estimator for two highly flexible distributions: Tukey's gand-h and Pewsey and Jones's sinh-arcsinh (SAS), designed to capture skewness and non-normal tail weight. These flexible distributions mitigate the risks of distributional misspecification by approximating a wide range of parametric distributions. Monte Carlo simulations assess finite-sample performance, showing that our estimator outperforms traditional parametric spatial methods when the error distribution deviates from normality and is well-approximated by these flexible alternatives.

Keywords: spillovers; Local Asymptotic Normality; Flexible distributions; efficiency (search for similar items in EconPapers)
Date: 2025-03-11
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