Bayesian Estimation of the Dynamic Spatial Durbin Panel Model Theory and Simulation Evidence from a Comparison with Quasi- Maximum Likelihood and the General Method of Moments

In this paper, we develop a Bayesian estimator (BE) in a hierarchical structure for the Dynamic Spatial Durbin Panel Model (DSDPM). The model is specified as a latent state–space model allowing its likelihood to jointly include the covariates, temporal dynamics, spatial dependence, spatiotemporal effects and the stochastic processes governing the errors. Estimation is implemented using the Integrated Nested Laplace Approximation (INLA). To evaluate its performance, we carried out a Monte Carlo simulation study comparing BE with the Generalized Method of Moments (GMM) and Quasi-Maximum Likelihood (QML) estimators across a range of spatial, temporal and spatiotemporal autoregressive parameters within the stability boundaries of [0, 0.4] determined by the spectral radius of the spatial weights matrix. The main result was that BE outperformed its alternatives in terms of bias and estimation variance for the regression coefficients and the dependence parameters. QMLE was frequently biased and GMM often displayed large estimation variance, especially for increasing spatial, temporal and spatiotemporal dependence, reflecting identification and numerical challenges near the stability boundaries. For values of the autoregressive parameters larger than 0.4 the estimates for all three estimators became unstable and took highly implausible.