Bruce E. Hansen

"Averaging Estimators for Regressions with a Possible Structural Break"

Econometric Theory (2009) vol. 25, 6, 1498-1514

November 2007
Revised: March 2008


This paper investigates selection and averaging of linear regressions with a possible structural break. Our main contribution is the construction of a Mallows criterion for the structural break model. We show that the correct penalty term is non-standard and depends on unknown parameters, but it can be approximated by an average of limiting cases to yield a feasible penalty with good performance. Following Hansen (2007) we recommend averaging the structural break estimates with the no-break estimates where the weight is selected to minimize the Mallows criterion. This estimator is simple to compute, as the weights are a simple function of the ratio of the penalty to the Andrews SupF test statistic.

To assess performance we focus on asymptotic mean-squared error (AMSE) in a local asymptotic framework. We show that the AMSE of the estimators depends exclusively on the parameter variation function. Numerical comparisons show that the unrestricted least-squares and pretest estimators have very large AMSE for certain regions of the parameter space, while our averaging estimator has AMSE close to the infeasible optimum..

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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.