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Nonlinear Instrumental Variable Estimation of an Autoregression

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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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File URL: http://cowles.econ.yale.edu/P/cd/d13a/d1331.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 1331.

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Length: 30 pages
Date of creation: Sep 2001
Date of revision:
Publication status: Published in Journal of Econometrics (2004), 118(1-2): 219-246
Handle: RePEc:cwl:cwldpp:1331

Note: CFP 1087.
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Keywords: Cauchy estimator; instrumental variable autoregression; nonlinear instruments; sojourn time; unit root;

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References

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  1. Joon Y. Park & Peter C. B. Phillips, 1999. "Nonlinear Regressions with Integrated Time Series," Working Paper Series, Institute of Economic Research, Seoul National University no6, Institute of Economic Research, Seoul National University.
  2. Andrews, Donald W K, 1993. "Exactly Median-Unbiased Estimation of First Order Autoregressive/Unit Root Models," Econometrica, Econometric Society, Econometric Society, vol. 61(1), pages 139-65, January.
  3. Moon, Hyungsik R. & Phillips, Peter C.B., 2000. "Estimation Of Autoregressive Roots Near Unity Using Panel Data," Econometric Theory, Cambridge University Press, vol. 16(06), pages 927-997, December.
  4. Peter C.B. Phillips & Joon Y. Park, 1998. "Asymptotics for Nonlinear Transformations of Integrated Time Series," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 1182, Cowles Foundation for Research in Economics, Yale University.
  5. 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.
  6. Phillips, Peter C B & Hansen, Bruce E, 1990. "Statistical Inference in Instrumental Variables Regression with I(1) Processes," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 57(1), pages 99-125, January.
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Cited by:
  1. 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.
  2. 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.
  3. Rodrigues, Paulo M.M., 2006. "Properties of recursive trend-adjusted unit root tests," Economics Letters, Elsevier, vol. 91(3), pages 413-419, June.
  4. Yoosoon Chang, 2004. "Taking a New Contour: A Novel Approach to Panel Unit Root Tests," Econometric Society 2004 Far Eastern Meetings, Econometric Society 796, Econometric Society.
  5. 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.
  6. 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.
  7. Tsung-wu Ho, 2009. "The inflation rates may accelerate after all: panel evidence from 19 OECD economies," Empirical Economics, Springer, Springer, vol. 36(1), pages 55-64, February.
  8. Kang, Wensheng, 2011. "Housing price dynamics and convergence in high-tech metropolitan economies," The Quarterly Review of Economics and Finance, Elsevier, Elsevier, vol. 51(3), pages 283-291, June.
  9. 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.
  10. Park, Joon, 2003. "Strong Approximations for Nonlinear Transformations of Integrated Time Series," Working Papers 2003-18, Rice University, Department of Economics.
  11. Chang, Yoosoon, 2003. "Nonlinear IV Panel Unit Root Tests," Working Papers 2003-06, Rice University, Department of Economics.
  12. Matei Demetrescu & Christoph Hanck, 2013. "Nonlinear IV panel unit root testing under structural breaks in the error variance," Statistical Papers, Springer, Springer, vol. 54(4), pages 1043-1066, November.
  13. Kuzin, Vladimir, 2005. "Recursive demeaning and deterministic seasonality," Statistics & Probability Letters, Elsevier, vol. 72(3), pages 195-204, May.
  14. 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.
  15. Park, Joon, 2003. "Nonstationary Nonlinearity: An Outlook for New Opportunities," Working Papers 2003-05, Rice University, Department of Economics.

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