Comparison of the blocked sampling approaches for the spatial dynamic panel data model

This study investigates Bayesian posterior sampling for a spatial dynamic panel data (SDPD) model using a mode-based blocked Metropolis–Hastings approach. The model’s stationarity depends on three parameters governing contemporaneous spatial dependence, lagged spatial dependence, and serial correlation. Because these parameters are interdependent under the stationarity restrictions, separate sampling using the random-walk Metropolis-Hastings (RW-MH) algorithm can produce highly autocorrelated posterior draws and require many MCMC iterations. To address this issue, we adapt a mode-based blocking strategy based on a Taylor approximation of the SDPD model and implement it as a blocked Metropolis–Hastings algorithm, referred to as TaB-MH. We compare TaB-MH with RW-MH and the No-U-Turn sampler (NUTS) using simulated and empirical data. The simulation results show that TaB-MH achieves satisfactory convergence across the parameter configurations considered, while NUTS also performs well after unconstrained reparameterization, with its convergence and sampling efficiency depending on the parameter configuration and warm-up length. Using Japanese prefectural panel data, we find stronger spatial than serial dependence in both private consumption and private investment, although the relative strength of spatial dependence is weaker for private investment. The estimated marginal effects indicate that government consumption reduces private-sector activity through both direct and indirect effects, whereas government investment has no statistically significant effects.