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Semiparametric estimation in triangular system equations with nonstationarity

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  • Gao, Jiti
  • Phillips, Peter C.B.

Abstract

A system of multivariate semiparametric nonlinear time series models is studied with possible dependence structures and nonstationarities in the parametric and nonparametric components. The parametric regressors may be endogenous while the nonparametric regressors are assumed to be strictly exogenous. The parametric regressors may be stationary or nonstationary and the nonparametric regressors are nonstationary integrated time series. Semiparametric least squares (SLS) estimation is considered and its asymptotic properties are derived. Due to endogeneity in the parametric regressors, SLS is not consistent for the parametric component and a semiparametric instrumental variable (SIV) method is proposed instead. Under certain regularity conditions, the SIV estimator of the parametric component is shown to have a limiting normal distribution. The rate of convergence in the parametric component depends on the properties of the regressors. The conventional n rate may apply even when nonstationarity is involved in both sets of regressors.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 176 (2013)
Issue (Month): 1 ()
Pages: 59-79

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Handle: RePEc:eee:econom:v:176:y:2013:i:1:p:59-79

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

Related research

Keywords: Endogeneity; Integrated process; Nonstationarity; Partial linear model; Simultaneity; Vector semiparametric regression;

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References

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  1. Phillips, Peter C B & Xiao, Zhijie, 1998. " A Primer on Unit Root Testing," Journal of Economic Surveys, Wiley Blackwell, vol. 12(5), pages 423-69, December.
  2. Peter C.B. Phillips & Joon Y. Park, 1986. "Statistical Inference in Regressions with Integrated Processes: Part 2," Cowles Foundation Discussion Papers 819R, Cowles Foundation for Research in Economics, Yale University, revised Feb 1987.
  3. Peter C. B. Phillips, 1998. "New Tools for Understanding Spurious Regressions," Econometrica, Econometric Society, vol. 66(6), pages 1299-1326, November.
  4. Whitney K. Newey & James L. Powell & Francis Vella, 1998. "Nonparametric Estimation of Triangular Simultaneous Equations Models," Working papers 98-6, Massachusetts Institute of Technology (MIT), Department of Economics.
  5. Peter C.B. Phillips, 1985. "Understanding Spurious Regressions in Econometrics," Cowles Foundation Discussion Papers 757, Cowles Foundation for Research in Economics, Yale University.
  6. Peter C.B. Phillips, 2008. "Local Limit Theory and Spurious Nonparametric Regression," Cowles Foundation Discussion Papers 1654, Cowles Foundation for Research in Economics, Yale University.
  7. Florens, Jean-Pierre & Johannes, Jan & Van Bellegem, Sébastien, 2009. "Instrumental Regression in Partially Linear Models," TSE Working Papers 10-167, Toulouse School of Economics (TSE).
  8. Gao, Jiti, 2007. "Nonlinear time series: semiparametric and nonparametric methods," MPRA Paper 39563, University Library of Munich, Germany, revised 01 Sep 2007.
  9. Ioannis Kasparis & Peter C. B. Phillips, 2009. "Dynamic Misspecification in Nonparametric Cointegrating Regression," University of Cyprus Working Papers in Economics 2-2009, University of Cyprus Department of Economics.
  10. Cai, Zongwu & Li, Qi & Park, Joon Y., 2009. "Functional-coefficient models for nonstationary time series data," Journal of Econometrics, Elsevier, vol. 148(2), pages 101-113, February.
  11. Park, Joon Y. & Phillips, Peter C.B., 1988. "Statistical Inference in Regressions with Integrated Processes: Part 1," Econometric Theory, Cambridge University Press, vol. 4(03), pages 468-497, December.
  12. Qiying Wang & Peter C. B. Phillips, 2009. "Structural Nonparametric Cointegrating Regression," Econometrica, Econometric Society, vol. 77(6), pages 1901-1948, November.
  13. Chunrong Ai & Xiaohong Chen, 2003. "Efficient Estimation of Models with Conditional Moment Restrictions Containing Unknown Functions," Econometrica, Econometric Society, vol. 71(6), pages 1795-1843, November.
  14. 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.
  15. Su, Liangjun & Ullah, Aman, 2008. "Local polynomial estimation of nonparametric simultaneous equations models," Journal of Econometrics, Elsevier, vol. 144(1), pages 193-218, May.
  16. Park, Joon Y. & Phillips, Peter C.B., 1999. "Asymptotics For Nonlinear Transformations Of Integrated Time Series," Econometric Theory, Cambridge University Press, vol. 15(03), pages 269-298, June.
  17. 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.
  18. Peter C. B. Phillips, 2001. "Descriptive econometrics for non-stationary time series with empirical illustrations," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 16(3), pages 389-413.
  19. Jiti Gao & Maxwell King & Zudi Lu & Dag Tjøstheim, 2009. "Nonparametric Specification Testing for Nonlinear Time Series with Nonstationarity," School of Economics Working Papers 2009-03, University of Adelaide, School of Economics.
  20. Peter C.B. Phillips & Joon Y. Park, 1998. "Nonstationary Density Estimation and Kernel Autoregression," Cowles Foundation Discussion Papers 1181, Cowles Foundation for Research in Economics, Yale University.
  21. Berkes, Istv n & Horv th, Lajos, 2006. "Convergence Of Integral Functionals Of Stochastic Processes," Econometric Theory, Cambridge University Press, vol. 22(02), pages 304-322, April.
  22. Peter C. B. Phillips & Liangjun Su, 2011. "Non‐parametric regression under location shifts," Econometrics Journal, Royal Economic Society, vol. 14(3), pages 457-486, October.
  23. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-54, July.
  24. Hardle, Wolfgang & LIang, Hua & Gao, Jiti, 2000. "Partially linear models," MPRA Paper 39562, University Library of Munich, Germany, revised 01 Sep 2000.
  25. Whitney K. Newey & James L. Powell, 2003. "Instrumental Variable Estimation of Nonparametric Models," Econometrica, Econometric Society, vol. 71(5), pages 1565-1578, 09.
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Citations

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Cited by:
  1. Degui Li & Peter C.B. Phillips & Jiti Gao, 2013. "Uniform Consistency of Nonstationary Kernel-Weighted Sample Covariances for Nonparametric Regression," Cowles Foundation Discussion Papers 1929, Cowles Foundation for Research in Economics, Yale University.
  2. Chaohua Dong & Jiti Gao & Dag Tjostheim & Jiying Yin, 2014. "Specification Testing for Nonlinear Multivariate Cointegrating Regressions," Monash Econometrics and Business Statistics Working Papers 8/14, Monash University, Department of Econometrics and Business Statistics.
  3. Biqing Cai & Jiti Gao, 2013. "Hermite Series Estimation in Nonlinear Cointegrating Models," Monash Econometrics and Business Statistics Working Papers 17/13, Monash University, Department of Econometrics and Business Statistics.
  4. Chaohua Dong & Jiti Gao, 2014. "Specification Testing in Structural Nonparametric Cointegration," Monash Econometrics and Business Statistics Working Papers 2/14, Monash University, Department of Econometrics and Business Statistics.
  5. Chaohua Dong & Jiti Gao & Dag Tjostheim, 2014. "Estimation for Single-index and Partially Linear Single-index Nonstationary Time Series Models," Monash Econometrics and Business Statistics Working Papers 7/14, Monash University, Department of Econometrics and Business Statistics.

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