Economists are often interested in computing averages with respect to a distribution of unobservables. Examples are moments or distributions of individual fixed-effects, average partial effects in discrete choice models, or counterfactual policy simulations based on a structural model. We consider posterior estimators of such effects , where the average is computed conditional on the observation sample. While in various settings it is common to "shrink" individual estimates -- e.g., of teacher value-added or hospital quality -- toward a common mean to reduce estimation noise, a study of the frequentist properties of posterior average estimators is lacking. 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. These results provide a theoretical foundation for the use of posterior average estimators . In addition, our theory suggests a simple measure of the information contained in the posterior conditioning. For illustration, we consider two empirical settings: the estimation of the distribution of neighborhood effects in the US, and the estimation of the densities of permanent and transitory components in a model of income dynamics.
Economists are often interested in estimating averages with respect to distributions of unobservables. Examples are moments of individual fixed-effects, average effects in discrete choice models, or counterfactual simulations in structural models. For such quantities, we propose and study "posterior average effects" , where the average is computed conditional on the sample, in the spirit of empirical Bayes and shrinkage methods. While the usefulness of shrinkage for prediction is well-understood, a justification of posterior conditioning to estimate population averages is currently lacking. 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.
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computing
estimating
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a distribution
distributions
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or distributions
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partial
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policy simulations based on a structural model. We consider posterior estimators of such effects
simulations in structural models. For such quantities, we propose and study "posterior average effects"
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observation sample. While in various settings it is common to "shrink" individual estimates -- e.g., of teacher value-added or hospital quality -- toward a common mean to reduce estimation noise, a study of the frequentist properties of posterior average estimators is
sample, in the spirit of empirical Bayes and shrinkage methods. While the usefulness of shrinkage for prediction is well-understood, a justification of posterior conditioning to estimate population averages is currently
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estimators
average effects
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no larger than
at most
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that can be achieved
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These results provide a theoretical foundation for the use of posterior average estimators
We establish related robustness results for posterior predictors
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our theory suggests
we suggest
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For illustration, we consider two empirical settings: the estimation of the distribution of
Lastly, we present two empirical illustrations, to estimate the distributions of
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the estimation of the densities