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Functional Form Misspecification in Regressions with a Unit Root

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  • Ioannis Kasparis
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    Abstract

    We examine the limit properties of the Non-linear 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, Econometrica 2001. We show that the limit behaviour of the NLS estimator is largely determined by the relative order 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 distribution results, 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.

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    File URL: http://papers.econ.ucy.ac.cy/RePEc/papers/02-08.pdf
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    Bibliographic Info

    Paper provided by University of Cyprus Department of Economics in its series University of Cyprus Working Papers in Economics with number 2-2008.

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    Length: 29 pages
    Date of creation: Feb 2008
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    Handle: RePEc:ucy:cypeua:2-2008

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    Web page: http://www.econ.ucy.ac.cy

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    1. Donald W. K. Andrews, 1999. "Estimation When a Parameter Is on a Boundary," Econometrica, Econometric Society, vol. 67(6), pages 1341-1384, November.
    2. Park, Joon Y. & Phillips, Peter C.B., 1999. "Asymptotics For Nonlinear Transformations Of Integrated Time Series," Econometric Theory, Cambridge University Press, vol. 15(03), pages 269-298, June.
    3. Yoosoon Chang & Joon Y. Park & Peter C. B. Phillips, 2001. "Nonlinear econometric models with cointegrated and deterministically trending regressors," Econometrics Journal, Royal Economic Society, vol. 4(1), pages 1-36.
    4. Saikkonen, Pentti & Choi, In, 2004. "Cointegrating Smooth Transition Regressions," Econometric Theory, Cambridge University Press, vol. 20(02), pages 301-340, April.
    5. Domowitz, Ian & White, Halbert, 1982. "Misspecified models with dependent observations," Journal of Econometrics, Elsevier, vol. 20(1), pages 35-58, October.
    6. Russell Davidson & James G. MacKinnon, 1980. "Several Tests for Model Specification in the Presence of Alternative Hypotheses," Working Papers 378, Queen's University, Department of Economics.
    7. P tscher, Benedikt M., 2004. "Nonlinear Functions And Convergence To Brownian Motion: Beyond The Continuous Mapping Theorem," Econometric Theory, Cambridge University Press, vol. 20(01), pages 1-22, February.
    8. Bierens, Herman J., 1984. "Model specification testing of time series regressions," Journal of Econometrics, Elsevier, vol. 26(3), pages 323-353, December.
    9. Wooldridge, Jeffrey M., 1986. "Estimation and inference for dependent processes," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 45, pages 2639-2738 Elsevier.
    10. Vuong, Quang H, 1989. "Likelihood Ratio Tests for Model Selection and Non-nested Hypotheses," Econometrica, Econometric Society, vol. 57(2), pages 307-33, March.
    11. White, Halbert & Domowitz, Ian, 1984. "Nonlinear Regression with Dependent Observations," Econometrica, Econometric Society, vol. 52(1), pages 143-61, January.
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