This paper extends the Baltagi et al. (2018, 2021) static and dynamic ε-contamination papers to dynamic space-time models. We investigate the robustness of Bayesian panel data models to possible misspecification of the prior distribution. The proposed robust Bayesian approach departs from the standard Bayesian framework in two ways. First, we consider the ε-contamination class of prior distributions for the model parameters as well as for the individual effects. Second, both the base elicited priors and the ε-contamination priors use Zellner (1986)’s g-priors for the variance-covariance matrices. We propose a general “toolbox” for a wide range of specifications which includes the dynamic space-time panel model with random effects, with cross-correlated effects à la Chamberlain, for the Hausman-Taylor world and for dynamic panel data models with homogeneous/heterogeneous slopes and cross-sectional dependence. Using an extensive Monte Carlo simulation study, we compare the finite sample properties of our proposed estimator to those of standard classical estimators. We illustrate our robust Bayesian estimator using the same data as in Keane and Neal (2020). We obtain short run as well as long run effects of climate change on corn producers in the United States.