Bruce E. Hansen

"Model Averaging, Asymptotic Risk, and Regressor Groups"
Quantitative Economics (2014)


This paper examines the asymptotic risk of nested least-squares averaging estimators when the averaging weights are selected to minimize a penalized least-squares criterion. We find conditions under which the asymptotic risk of the averaging estimator is globally smaller than the unrestricted least-squares estimator. For the Mallows averaging estimator under homoskedastic errors the condition takes the simple form that the regressors have been grouped in sets of four or larger. This condition is a direct extension of the classic theory of James-Stein shrinkage. This discovery suggests the practical rule that implementation of averaging estimators be restricted to models in which the regressors have been grouped in this manner. Our simulations show that this new recommendation results in substantial reduction in mean-squared error relative to averaging over all nested sub-models. We illustrate the method with an application to the regression estimates of Fryer and Levitt (2013).

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Some of the above material is based upon work supported by the National Science Foundation under Grants No. SES-9022176, SES-9120576, SBR-9412339, and SBR-9807111. Any opinions, findings, and conclusions, or recommendations expressed in this material are those of the author(s), and do not necessarily reflect the views of the NSF.