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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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  • Phillips, Peter C. B. & Park, Joon Y. & Chang, Yoosoon, 2004. "Nonlinear instrumental variable estimation of an autoregression," Journal of Econometrics, Elsevier, vol. 118(1-2), pages 219-246.
    • Handle: RePEc:eee:econom:v:118:y:2004:i:1-2:p:219-246
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    1. Moon, Hyungsik R. & Phillips, Peter C.B., 2000. "Estimation Of Autoregressive Roots Near Unity Using Panel Data," Econometric Theory, Cambridge University Press, vol. 16(6), pages 927-997, December.
    2. Peter C. B. Phillips & Bruce E. Hansen, 1990. "Statistical Inference in Instrumental Variables Regression with I(1) Processes," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 57(1), pages 99-125.
    3. Park, Joon Y & Phillips, Peter C B, 2001. "Nonlinear Regressions with Integrated Time Series," Econometrica, Econometric Society, vol. 69(1), pages 117-161, January.
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    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(2), pages 165-176, April.
    6. Andrews, Donald W K, 1993. "Exactly Median-Unbiased Estimation of First Order Autoregressive/Unit Root Models," Econometrica, Econometric Society, vol. 61(1), pages 139-165, January.
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    Cited by:

    1. 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.
    2. Park, Joon, 2003. "Nonstationary Nonlinearity: An Outlook for New Opportunities," Working Papers 2003-05, Rice University, Department of Economics.
    3. Kim, Jihyun & Meddahi, Nour, 2020. "Volatility regressions with fat tails," Journal of Econometrics, Elsevier, vol. 218(2), pages 690-713.
    4. Park, Joon, 2003. "Strong Approximations for Nonlinear Transformations of Integrated Time Series," Working Papers 2003-18, Rice University, Department of Economics.
    5. 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.
    6. Chang, Yoosoon, 2002. "Nonlinear IV unit root tests in panels with cross-sectional dependency," Journal of Econometrics, Elsevier, vol. 110(2), pages 261-292, October.
    7. Matei Demetrescu & Christoph Hanck, 2016. "Robust Inference for Near-Unit Root Processes with Time-Varying Error Variances," Econometric Reviews, Taylor & Francis Journals, vol. 35(5), pages 751-781, May.
    8. 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.
    9. Kyung So Im & Junsoo Lee & Vladimir Arcabic & Mansik Hur, 2018. "DF-IV Unit Root Tests Using Stationary Instrument Variables," Journal of Statistical and Econometric Methods, SCIENPRESS Ltd, vol. 7(1), pages 1-1.
    10. Chevillon, Guillaume & Mavroeidis, Sophocles & Zhan, Zhaoguo, 2016. "Robust inference in structural VARs with long-run restrictions," ESSEC Working Papers WP1702, ESSEC Research Center, ESSEC Business School.
    11. Chi‐Young Choi & Nelson C. Mark & Donggyu Sul, 2010. "Bias Reduction in Dynamic Panel Data Models by Common Recursive Mean Adjustment," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 72(5), pages 567-599, October.
    12. Matei Demetrescu & Christoph Hanck & Adina I. Tarcolea, 2014. "Iv-Based Cointegration Testing In Dependent Panels With Time-Varying Variance," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(5), pages 393-406, August.
    13. Chang, Yoosoon, 2003. "Nonlinear IV Panel Unit Root Tests," Working Papers 2003-06, Rice University, Department of Economics.
    14. 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.
    15. 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.
    16. Kim, Jihyun & Meddahi, Nour, 2020. "Volatility Regressions with Fat Tails," TSE Working Papers 20-1097, Toulouse School of Economics (TSE).
    17. Miller J. Isaac, 2010. "A Nonlinear IV Likelihood-Based Rank Test for Multivariate Time Series and Long Panels," Journal of Time Series Econometrics, De Gruyter, vol. 2(1), pages 1-38, September.
    18. Demetrescu Matei, 2009. "Panel Unit Root Testing with Nonlinear Instruments for Infinite-Order Autoregressive Processes," Journal of Time Series Econometrics, De Gruyter, vol. 1(2), pages 1-30, December.
    19. 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.
    20. Rodrigues, Paulo M.M., 2006. "Properties of recursive trend-adjusted unit root tests," Economics Letters, Elsevier, vol. 91(3), pages 413-419, June.
    21. Jihyun Kim & Nour Meddahi, 2020. "Volatility Regressions with Fat Tails," Post-Print hal-03142647, HAL.
    22. 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.
    23. Kuzin, Vladimir, 2005. "Recursive demeaning and deterministic seasonality," Statistics & Probability Letters, Elsevier, vol. 72(3), pages 195-204, May.
    24. 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.
    25. Neil Shephard, 2020. "An estimator for predictive regression: reliable inference for financial economics," Papers 2008.06130, arXiv.org.

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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
    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities

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