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Estimation of spatial panel data models with random effects using Laplace approximation methods

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  • Yuheng Ling
  • Kaixuan Bai
  • Yue Yang

Abstract

This paper proposes using integrated nested Laplace approximations (INLAs), a full Bayesian approach, for estimating spatial panel data models with random effects. These models encompass Anselin’s model, Kapoor’s model and the generalised spatial random effects model. We show that a spatial autoregressive process in the error terms is a special case of Gaussian Markov random fields (GMRFs), thereby reducing computational costs. The computational benefit is further enhanced through the use of INLAs to compute the posterior marginals of model parameters. Finite sample properties of the INLA-GMRF approach are assessed through comprehensive Monte Carlo simulations. We also compare its computational efficiency with classic estimation methods. Finally, we demonstrate this approach with an empirical study on renewable energy production in China.

Suggested Citation

  • Yuheng Ling & Kaixuan Bai & Yue Yang, 2026. "Estimation of spatial panel data models with random effects using Laplace approximation methods," Spatial Economic Analysis, Taylor & Francis Journals, vol. 21(2), pages 364-385, April.
    • Handle: RePEc:taf:specan:v:21:y:2026:i:2:p:364-385
    DOI: 10.1080/17421772.2025.2504503
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