Before revision:  We establish two robustness properties of posterior estimators under misspecification of the assumed distribution of unobservables: they are optimal in terms of local worst-case bias, and their global bias is no larger than twice the minimum worst-case bias that can be achieved within a large class of estimators.
After revision:  We establish two robustness properties of posterior average effects under misspecification of the assumed distribution of unobservables: they are optimal in terms of local worst-case bias, and their global bias is no larger than twice the minimum worst-case bias that can be achieved within a large class of estimators.