Posterior average effects

Stéphane Bonhomme () and Martin Weidner ()
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Stéphane Bonhomme: Institute for Fiscal Studies and University of Chicago
Martin Weidner: Institute for Fiscal Studies and University College London

No CWP49/20, CeMMAP working papers from Centre for Microdata Methods and Practice, Institute for Fiscal Studies

Abstract: Economists are often interested in estimating averages with respect to distributions of unobservables. Examples are moments of individual fixed-effects, average partial effects in discrete choice models, and counterfactual simulations in structural models. For such quantities, we propose and study posterior average effects (PAE), 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 show that PAE have minimum worst-case bias under local misspecification of the parametric 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.

Date: 2020-10-09
New Economics Papers: this item is included in nep-dcm
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