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Nonlinearity Induced Weak Instrumentation

Author

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  • Ioannis Kasparis
  • Peter C. B. Phillips
  • Tassos Magdalinos

Abstract

In regressions involving integrable functions we examine the limit properties of instrumental variable (IV) estimators that utilise integrable transformations of lagged regressors as instruments. The regressors can be either I (0) or nearly integrated ( NI ) processes. We show that this kind of nonlinearity in the regression function can significantly affect the relevance of the instruments. In particular, such instruments become weak when the signal of the regressor is strong, as it is in the NI case. Instruments based on integrable functions of lagged NI regressors display long range dependence and so remain relevant even at long lags, continuing to contribute to variance reduction in IV estimation. However, simulations show that ordinary least square (OLS) is generally superior to IV estimation in terms of mean squared error (MSE), even in the presence of endogeneity. Estimation precision is also reduced when the regressor is nonstationary.

Suggested Citation

  • Ioannis Kasparis & Peter C. B. Phillips & Tassos Magdalinos, 2014. "Nonlinearity Induced Weak Instrumentation," Econometric Reviews, Taylor & Francis Journals, vol. 33(5-6), pages 676-712, August.
  • Handle: RePEc:taf:emetrv:v:33:y:2014:i:5-6:p:676-712
    DOI: 10.1080/07474938.2013.825181
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    File URL: http://hdl.handle.net/10.1080/07474938.2013.825181
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    6. Park, Joon Y., 2002. "Nonstationary nonlinear heteroskedasticity," Journal of Econometrics, Elsevier, vol. 110(2), pages 383-415, October.
    7. Kasparis, Ioannis, 2008. "Detection Of Functional Form Misspecification In Cointegrating Relations," Econometric Theory, Cambridge University Press, vol. 24(5), pages 1373-1403, October.
    8. Joon Y. Park & Yoosoon Chang, 2004. "Endogeneity in Nonlinear Regressions with Integrated Time Series," Econometric Society 2004 North American Winter Meetings 594, Econometric Society.
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    10. Leeb, Hannes & Pötscher, Benedikt M., 2005. "Model Selection And Inference: Facts And Fiction," Econometric Theory, Cambridge University Press, vol. 21(1), pages 21-59, February.
    11. Phillips, Peter C.B. & Jin, Sainan & Hu, Ling, 2007. "Nonstationary discrete choice: A corrigendum and addendum," Journal of Econometrics, Elsevier, vol. 141(2), pages 1115-1130, December.
    12. Miller, J. Isaac & Park, Joon Y., 2010. "Nonlinearity, nonstationarity, and thick tails: How they interact to generate persistence in memory," Journal of Econometrics, Elsevier, vol. 155(1), pages 83-89, March.
    13. Wang, Qiying & Phillips, Peter C.B., 2009. "Asymptotic Theory For Local Time Density Estimation And Nonparametric Cointegrating Regression," Econometric Theory, Cambridge University Press, vol. 25(3), pages 710-738, June.
    14. Ibragimov, Rustam & Phillips, Peter C.B., 2008. "Regression Asymptotics Using Martingale Convergence Methods," Econometric Theory, Cambridge University Press, vol. 24(4), pages 888-947, August.
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    Cited by:

    1. Phillips, Peter C.B. & Li, Degui & Gao, Jiti, 2017. "Estimating smooth structural change in cointegration models," Journal of Econometrics, Elsevier, vol. 196(1), pages 180-195.
    2. Phillips, Peter C.B. & Lee, Ji Hyung, 2016. "Robust econometric inference with mixed integrated and mildly explosive regressors," Journal of Econometrics, Elsevier, vol. 192(2), pages 433-450.
    3. Kasparis, Ioannis & Andreou, Elena & Phillips, Peter C.B., 2015. "Nonparametric predictive regression," Journal of Econometrics, Elsevier, vol. 185(2), pages 468-494.

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    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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