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FUNCTIONAL FORM MISSPECIFICATION IN REGRESSIONS WITH A UNIT ROOT

Published online by Cambridge University Press:  13 September 2010

Abstract

We examine the limit properties of the nonlinear least squares (NLS) estimator under functional form misspecification in regression models with a unit root. Our theoretical framework is the same as that of Park and Phillips (2001, Econometrica 69, 117–161). We show that the limit behavior of the NLS estimator is largely determined by the relative orders of magnitude of the true and fitted models. If the estimated model is of different order of magnitude than the true model, the estimator converges to boundary points. When the pseudo-true value is on a boundary, standard methods for obtaining rates of convergence and limit distribution results are not applicable. We provide convergence rates and limit theory when the pseudo-true value is an interior point. If functional form misspecification is committed in the presence of stochastic trends, the convergence rates can be slower and the limit distribution different than that obtained under correct specification.

Type
Research Article
Copyright
Copyright © Cambridge University Press 2010

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Footnotes

This paper is based on Chapter 2 of my Ph.D. thesis at the University of Southampton. I am deeply indebted to Grant Hillier and Peter Phillips for invaluable advice and encouragement. I am grateful to Tassos Magdalinos and Jean-Yves Pitarakis for their support and for useful comments. In addition, I thank three referees for suggestions that have substantially improved the previous version.

References

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