Bayesian Estimation of Spatial Lagged Panel Quantile Regression Model

This paper proposes a Bayesian estimation method for spatial lagged panel quantile models. The proposed model simultaneously considers spatial lag effects of the dependent variable and the quantile regression framework, enabling effective capture of spatial dependence and conditional distribution heterogeneity. The research constructs a Bayesian estimation framework based on the asymmetric Laplace distribution by decomposing the random disturbance term into a combination of normal and exponential distributions, successfully developing a probabilistic model with both thick tail robustness and computational efficiency. On this basis, the study derives the full conditional posterior probability distributions of model parameters and designs a hybrid Markov Chain Monte Carlo (MCMC) sampling algorithm integrating Gibbs sampling and Metropolis–Hastings algorithm for parameter estimation. Numerical simulation experiments demonstrate that, compared with traditional estimation methods, the proposed Bayesian estimation approach exhibits superior estimation accuracy and robustness across different quantiles, with particularly pronounced advantages in small sample and heavy-tailed distribution scenarios. This methodology provides a more reliable theoretical tool for analyzing panel data with spatial dependencies. This method can not only accurately quantify the spatial spillover effect, but also identify the different effects of the same influencing factor at different emission levels, which provides a strong methodological support for formulating differentiated and precise emission reduction policies.