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Nonlinear estimators with integrated regressors but without exogeneity

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Author Info
Robert de Jong
Abstract

This paper analyzes nonlinear cointegrating regressions as have been recently analyzed in a paper by Park and Phillips in Econometrica. I analyze the consequences of removing Park and Phillips' exogeneity assumption, which for the special case of a linear model would imply the asymptotic validity of the least squares estimator for linear cointegrating regressions. For the linear model, the unlikeliness of such an exogeneity assumption to hold in practice has inspired the `fully modified' technique, the `leads and lags' technique, and Park's `canonical regressions'. In this paper, a `fully modified' type technique is proposed for nonlinear cointegrating regressions. The mathematical tool for proving this result is a new so-called `convergence to stochastic integrals' result. This result is proven for objects that are summations of a stationary random variable times an asymptotically homogeneous function of an integrated process. The increments of the integrated process are allowed to be correlated with the stationary random variable. This result is derived by extending a line of proof pioneered in work by Chan and Wei

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Paper provided by Econometric Society in its series Econometric Society 2004 North American Winter Meetings with number 324.

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Date of creation: 11 Aug 2004
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Handle: RePEc:ecm:nawm04:324

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Related research
Keywords: nonlinearity; integrated process; cointegration; fully modified;

Find related papers by JEL classification:
C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions

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References listed on IDEAS
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  1. Park, Joon Y, 1992. "Canonical Cointegrating Regressions," Econometrica, Econometric Society, vol. 60(1), pages 119-43, January. [Downloadable!] (restricted)
  2. Phillips, P.C.B., 1986. "Understanding spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 33(3), pages 311-340, December. [Downloadable!] (restricted)
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  3. Benedikt Pötscher & Ingmar Prucha, 1991. "Basic structure of the asymptotic theory in dynamic nonlinear econometric models," Econometric Reviews, Taylor and Francis Journals, vol. 10(3), pages 253-325. [Downloadable!] (restricted)
  4. 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. [Downloadable!]
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  5. Joon Y. Park & Peter C. B. Phillips, 1999. "Nonlinear Regressions with Integrated Time Series," Working Paper Series no6, Institute of Economic Research, Seoul National University. [Downloadable!]
    Other versions:
  6. de Jong, Robert M. & Davidson, James, 2000. "The Functional Central Limit Theorem And Weak Convergence To Stochastic Integrals I," Econometric Theory, Cambridge University Press, vol. 16(05), pages 621-642, October. [Downloadable!]
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  7. Yoosoon Chang, 2000. "Nonlinear IV Unit Root Tests in Panels with Cross-Sectional Dependency," CIRJE F-Series CIRJE-F-85, CIRJE, Faculty of Economics, University of Tokyo. [Downloadable!]
    Other versions:
  8. Peter C.B. Phillips & Bruce E. Hansen, 1988. "Statistical Inference in Instrumental Variables," Cowles Foundation Discussion Papers 869R, Cowles Foundation, Yale University, revised Apr 1989. [Downloadable!]
  9. Joon Y. Park & Peter C. B. Phillips, 2000. "Nonstationary Binary Choice," Econometrica, Econometric Society, vol. 68(5), pages 1249-1280, September.
    Other versions:
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