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AVERAGING ESTIMATORS FOR REGRESSIONS WITH A POSSIBLE STRUCTURAL BREAK

Published online by Cambridge University Press:  01 December 2009

Bruce E. Hansen
Bruce E. Hansen*
Affiliation:
University of Wisconsin
*
*Address correspondence to Bruce E. Hansen. Department of Economics, 1180 Observatory Drive, University of Wisconsin, Madison, WI 53706, USA; e-mail: bhansen@ssc.wisc.edu.
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Abstract

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 nonstandard 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, Econometrica 75, 1175–1189) 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, whereas our averaging estimator has AMSE close to the infeasible optimum.

Type
ARTICLES
Information
Econometric Theory , Volume 25 , Issue 6: Newbold Conference Special Issue , December 2009 , pp. 1498 - 1514
Copyright
Copyright © Cambridge University Press 2009

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References

REFERENCES

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