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Non-linearity Induced Weak Instrumentation

Author Info

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

Abstract

In regressions involving integrable functions we examine the limit properties of IV estimators that utilise integrable transformations of lagged regressors as instruments. The regressors can be either I(0) or I(1) 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 I(1) case. Instruments based on integrable functions of lagged I(1) 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 OLS is generally superior to IV estimation in terms of MSE, even in the presence of endogeneity. Estimation precision is also reduced when the regressor is nonstationary.

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File URL: http://papers.econ.ucy.ac.cy/RePEc/papers/02-12.pdf
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Paper provided by University of Cyprus Department of Economics in its series University of Cyprus Working Papers in Economics with number 02-2012.

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Length: 37 pages
Date of creation: Jan 2012
Date of revision:
Handle: RePEc:ucy:cypeua:02-2012
Contact details of provider: Web page: http://www.econ.ucy.ac.cy

Keywords: Instrumental variables; Integrable function; Integrated process; Invariance principle; Local time; Mixed normality; Stationarity; Nonlinear cointegration; Unit roots; Weak Instruments.;

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Find related papers by 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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  1. Ibragimov, Rustam & Phillips, Peter C.B., 2008. "Regression asymptotics using martingale convergence methods," Scholarly Articles 2624459, Harvard University Department of Economics.
  2. Leeb, Hannes & P tscher, Benedikt M., 2005. "Model Selection And Inference: Facts And Fiction," Econometric Theory, Cambridge University Press, vol. 21(01), pages 21-59, February.
  3. 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.
  4. 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.
  5. Kasparis, Ioannis, 2008. "Detection Of Functional Form Misspecification In Cointegrating Relations," Econometric Theory, Cambridge University Press, vol. 24(05), pages 1373-1403, October.
  6. Joon Y. Park & Yoosoon Chang, 2004. "Endogeneity in Nonlinear Regressions with Integrated Time Series," Econometric Society 2004 North American Winter Meetings 594, Econometric Society.
  7. 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.
  8. 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.
  9. Offer Lieberman & Peter C.B. Phillips, 2002. "Error Bounds and Asymptotic Expansions for Toeplitz Product Functionals of Unbounded Spectra," Cowles Foundation Discussion Papers 1374, Cowles Foundation for Research in Economics, Yale University.
  10. Robert de Jong, 2004. "Nonlinear estimators with integrated regressors but without exogeneity," Econometric Society 2004 North American Winter Meetings 324, Econometric Society.
  11. Park, Joon Y., 2002. "Nonstationary nonlinear heteroskedasticity," Journal of Econometrics, Elsevier, vol. 110(2), pages 383-415, October.
  12. Qiying Wang & Peter C.B. Phillips, 2006. "Asymptotic Theory for Local Time Density Estimation and Nonparametric Cointegrating Regression," Cowles Foundation Discussion Papers 1594, Cowles Foundation for Research in Economics, Yale University.
  13. P. Jeganathan, 2006. "Limit Theorems for Functionals of Sums That Converge to Fractional Stable Motions," Cowles Foundation Discussion Papers 1558, Cowles Foundation for Research in Economics, Yale University, revised Mar 2006.
  14. P. Jeganathan, 2008. "Limit Theorems for Functionals of Sums that Converge to Fractional Brownian and Stable Motions," Cowles Foundation Discussion Papers 1649, Cowles Foundation for Research in Economics, Yale University.
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Cited by:

  1. 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.
  2. Ioannis Kasparis & Elena Andreou & Peter C.B. Phillips, 2012. "Nonparametric Predictive Regression," Cowles Foundation Discussion Papers 1878, Cowles Foundation for Research in Economics, Yale University.

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