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FUNCTIONAL FORM MISSPECIFICATION INREGRESSIONS WITH A UNIT ROOT

Published online by Cambridge University Press:  13 September 2010

Ioannis Kasparis
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Abstract

We examine the limit properties of the nonlinear leastsquares (NLS) estimator under functional formmisspecification in regression models with a unitroot. Our theoretical framework is the same as thatof Park and Phillips (2001,Econometrica 69, 117–161). Weshow that the limit behavior of the NLS estimator islargely determined by the relative orders ofmagnitude of the true and fitted models. If theestimated model is of different order of magnitudethan the true model, the estimator converges toboundary points. When the pseudo-true value is on aboundary, standard methods for obtaining rates ofconvergence and limit distribution results are notapplicable. We provide convergence rates and limittheory when the pseudo-true value is an interiorpoint. If functional form misspecification iscommitted in the presence of stochastic trends, theconvergence rates can be slower and the limitdistribution different than that obtained undercorrect specification.

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Type
Research Article
Information
Econometric Theory , Volume 27 , Issue 2 , April 2011 , pp. 285 - 311
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 amdeeply indebted to Grant Hillier and PeterPhillips for invaluable advice and encouragement.I am grateful to Tassos Magdalinos and Jean-YvesPitarakis for their support and for usefulcomments. In addition, I thank three referees forsuggestions that have substantially improved theprevious version.

References

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