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Nonlinear instrumental variable estimation of an autoregression

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  • Phillips, Peter C. B.
  • Park, Joon Y.
  • Chang, Yoosoon

Abstract

Instrumental variable (IV) estimation methods that allow for certain nonlinear functions of the data as instruments are studied. The context of the discussion is the simple unit root model where certain advantages to the use of nonlinear instruments are revealed. In particular, certain classes of IV estimators and associated t-tests are shown to have simpler (standard) limit theory in contrast to the least squares estimator, providing an opportunity for the study of optimal estimation in certain IV classes and furnishing tests and confidence intervals that allow for unit root and stationary alternatives. The Cauchy estimator studied in recent work by So and Shin (1999) is shown to have such an optimality property in the class of certain IV procedures with bounded instruments.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 118 (2004)
Issue (Month): 1-2 ()
Pages: 219-246

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Handle: RePEc:eee:econom:v:118:y:2004:i:1-2:p:219-246

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Web page: http://www.elsevier.com/locate/jeconom

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References

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  1. Hyungsik R. Moon & Peter C.B. Phillips, 1999. "Estimation of Autoregressive Roots Near Unity Using Panel Data," Cowles Foundation Discussion Papers 1224, Cowles Foundation for Research in Economics, Yale University.
  2. Park, Joon Y & Phillips, Peter C B, 2001. "Nonlinear Regressions with Integrated Time Series," Econometrica, Econometric Society, vol. 69(1), pages 117-61, January.
  3. Peter C.B. Phillips & Joon Y. Park, 1998. "Asymptotics for Nonlinear Transformations of Integrated Time Series," Cowles Foundation Discussion Papers 1182, Cowles Foundation for Research in Economics, Yale University.
  4. Andrews, Donald W K, 1993. "Exactly Median-Unbiased Estimation of First Order Autoregressive/Unit Root Models," Econometrica, Econometric Society, vol. 61(1), pages 139-65, January.
  5. Phillips, Peter C B & Hansen, Bruce E, 1990. "Statistical Inference in Instrumental Variables Regression with I(1) Processes," Review of Economic Studies, Wiley Blackwell, vol. 57(1), pages 99-125, January.
  6. So, Beong Soo & Shin, Dong Wan, 1999. "Cauchy Estimators For Autoregressive Processes With Applications To Unit Root Tests And Confidence Intervals," Econometric Theory, Cambridge University Press, vol. 15(02), pages 165-176, April.
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Citations

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Cited by:
  1. 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.
  2. Meng, Ming & Lee, Hyejin & Cho, Myeong Hyeon & Lee, Junsoo, 2013. "Impacts of the initial observation on unit root tests using recursive demeaning and detrending procedures," Economics Letters, Elsevier, vol. 120(2), pages 195-199.
  3. Park, Joon, 2003. "Strong Approximations for Nonlinear Transformations of Integrated Time Series," Working Papers 2003-18, Rice University, Department of Economics.
  4. Matei Demetrescu & Christoph Hanck, 2013. "Nonlinear IV panel unit root testing under structural breaks in the error variance," Statistical Papers, Springer, vol. 54(4), pages 1043-1066, November.
  5. Lee, Hyejin & Meng, Ming & Lee, Junsoo, 2012. "Performance of nonlinear instrumental variable unit root tests using recursive detrending methods," Economics Letters, Elsevier, vol. 117(1), pages 214-216.
  6. Chang, Yoosoon, 2012. "Taking a new contour: A novel approach to panel unit root tests," Journal of Econometrics, Elsevier, vol. 169(1), pages 15-28.
  7. Kim, Chang Sik & Kim, In-Moo, 2008. "Nonlinear regression for unit root models with autoregressive errors," Economics Letters, Elsevier, vol. 100(3), pages 326-329, September.
  8. Paulo M. M. Rodrigues, 2004. "Properties of Recursive Trend-Adjusted Unit Root Tests," Economics Working Papers ECO2004/31, European University Institute.
  9. Kuzin, Vladimir, 2005. "Recursive demeaning and deterministic seasonality," Statistics & Probability Letters, Elsevier, vol. 72(3), pages 195-204, May.
  10. Chang, Yoosoon, 2003. "Nonlinear IV Panel Unit Root Tests," Working Papers 2003-06, Rice University, Department of Economics.
  11. Tsung-wu Ho, 2009. "The inflation rates may accelerate after all: panel evidence from 19 OECD economies," Empirical Economics, Springer, vol. 36(1), pages 55-64, February.
  12. Park, Joon, 2003. "Nonstationary Nonlinearity: An Outlook for New Opportunities," Working Papers 2003-05, Rice University, Department of Economics.
  13. Ho, Tsung-wu, 2008. "Testing seasonal mean-reversion in the real exchange rates: An application of nonlinear IV estimator," Economics Letters, Elsevier, vol. 99(2), pages 314-316, May.
  14. Kang, Wensheng, 2011. "Housing price dynamics and convergence in high-tech metropolitan economies," The Quarterly Review of Economics and Finance, Elsevier, vol. 51(3), pages 283-291, June.
  15. Hanck, Christoph & Demetrescu, Matei & Tarcolea, Adina, 2012. "IV-Based Cointegration Testing in Dependent Panels with Time-Varying Variance," Annual Conference 2012 (Goettingen): New Approaches and Challenges for the Labor Market of the 21st Century 62072, Verein für Socialpolitik / German Economic Association.

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