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 . We establish related robustness results for posterior predictors. In addition, we suggest a simple measure of the information contained in the posterior conditioning. Lastly, we present two empirical illustrations, to estimate the distributions of neighborhood effects in the US, and of permanent and transitory components in a model of income dynamics.
After revision:  We establish two robustness properties of posterior average effects under misspecification of the assumed distribution of unobservables . This provides a rationale for reporting these estimators in applications. We introduce a measure of informativeness of the posterior conditioning, which quantifies the bias of PAE relative to parametric model-based estimators, and we study other robustness properties of PAE for estimation and prediction. As illustrations, we report PAE estimates of distributions of neighborhood effects in the US, and of permanent and transitory components in a model of income dynamics.