Before 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 at most twice the minimum worst-case bias within a large class of estimators .
After revision:  We show that PAE have minimum worst-case bias under local misspecification of the assumed distribution of unobservables : they are optimal in terms of local worst-case bias, and their global bias is at most twice the minimum worst-case bias within a large class of estimators .