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Non-linearity Induced Weak Instrumentation

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 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 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://cowles.econ.yale.edu/P/cd/d18b/d1872.pdf
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Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1872.

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Length: 38 pages
Date of creation: Sep 2012
Date of revision:
Publication status: Published in Econometric Reviews (2014), 33(5-6): 676-712
Handle: RePEc:cwl:cwldpp:1872
Note: CFP 1404
Contact details of provider: Postal: Yale University, Box 208281, New Haven, CT 06520-8281 USA
Phone: (203) 432-3702
Fax: (203) 432-6167
Web page: http://cowles.econ.yale.edu/

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Order Information: Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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  1. 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.
  2. Ibragimov, Rustam & Phillips, Peter C.B., 2008. "Regression Asymptotics Using Martingale Convergence Methods," Econometric Theory, Cambridge University Press, vol. 24(04), pages 888-947, August.
  3. 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.
  4. 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.
  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 & J. Isaac Miller, 2004. "Nonlinearity, Nonstationarity, and Thick Tails: How They Interact to Generate Persistency in Memory," Econometric Society 2004 North American Summer Meetings 597, Econometric Society.
  7. Joon Y. Park & Yoosoon Chang, 2004. "Endogeneity in Nonlinear Regressions with Integrated Time Series," Econometric Society 2004 North American Winter Meetings 594, Econometric Society.
  8. 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.
  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. 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(03), pages 710-738, June.
  11. Park, Joon Y., 2002. "Nonstationary nonlinear heteroskedasticity," Journal of Econometrics, Elsevier, vol. 110(2), pages 383-415, October.
  12. Robert de Jong, 2004. "Nonlinear estimators with integrated regressors but without exogeneity," Econometric Society 2004 North American Winter Meetings 324, Econometric Society.
  13. 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.
  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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