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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.

Suggested Citation

  • Gao, Jiti & Phillips, Peter C.B., 2013. "Semiparametric estimation in triangular system equations with nonstationarity," Journal of Econometrics, Elsevier, vol. 176(1), pages 59-79.
  • Handle: RePEc:eee:econom:v:176:y:2013:i:1:p:59-79
    DOI: 10.1016/j.jeconom.2013.04.018
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    References listed on IDEAS

    as
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    Cited by:

    1. Dong, Chaohua & Linton, Oliver, 2018. "Additive nonparametric models with time variable and both stationary and nonstationary regressors," Journal of Econometrics, Elsevier, vol. 207(1), pages 212-236.
    2. Qiu, Guo & Xu, Wangtu (Ato) & Li, Ling, 2018. "Key factors to annual investment in public transportation sector: The case of China," Transportation Research Part A: Policy and Practice, Elsevier, vol. 107(C), pages 1-19.
    3. Wang, Qiying & Wu, Dongsheng & Zhu, Ke, 2018. "Model checks for nonlinear cointegrating regression," Journal of Econometrics, Elsevier, vol. 207(2), pages 261-284.
    4. Dong, Chaohua & Gao, Jiti & Tjøstheim, Dag & Yin, Jiying, 2017. "Specification testing for nonlinear multivariate cointegrating regressions," Journal of Econometrics, Elsevier, vol. 200(1), pages 104-117.
    5. Jiti Gao & Han Hong, 2014. "Nonparametric Regression Approach to Bayesian Estimation," Monash Econometrics and Business Statistics Working Papers 25/14, Monash University, Department of Econometrics and Business Statistics.
    6. Jia Chen & Jiti Gao & Degui Li & Zhengyan Lin, 2015. "Specification testing in nonstationary time series models," Econometrics Journal, Royal Economic Society, vol. 18(1), pages 117-136, February.
    7. Li, Degui & Phillips, Peter C. B. & Gao, Jiti, 2016. "Uniform Consistency Of Nonstationary Kernel-Weighted Sample Covariances For Nonparametric Regression," Econometric Theory, Cambridge University Press, vol. 32(3), pages 655-685, June.
    8. Feng, Guohua & Gao, Jiti & Peng, Bin & Zhang, Xiaohui, 2017. "A varying-coefficient panel data model with fixed effects: Theory and an application to US commercial banks," Journal of Econometrics, Elsevier, vol. 196(1), pages 68-82.
    9. 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.
    10. Dong, Chaohua & Gao, Jiti & Peng, Bin, 2015. "Semiparametric single-index panel data models with cross-sectional dependence," Journal of Econometrics, Elsevier, vol. 188(1), pages 301-312.
    11. Biqing Cai & Chaohua Dong & Jiti Gao, 2015. "Orthogonal Series Estimation in Nonlinear Cointegrating Models with Endogeneity," Monash Econometrics and Business Statistics Working Papers 18/15, Monash University, Department of Econometrics and Business Statistics.
    12. Lin, Yingqian & Tu, Yundong & Yao, Qiwei, 2020. "Estimation for double-nonlinear cointegration," Journal of Econometrics, Elsevier, vol. 216(1), pages 175-191.
    13. 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.
    14. Zhishui Hu & Peter C.B. Phillips & Qiying Wang, 2019. "Nonlinear Cointegrating Power Function Regression with Endogeneity," Cowles Foundation Discussion Papers 2211, Cowles Foundation for Research in Economics, Yale University.
    15. Connor, G. & Li, S. & Linton, O., 2020. "A Dynamic Semiparametric Characteristics-based Model for Optimal Portfolio Selection," Cambridge Working Papers in Economics 20103, Faculty of Economics, University of Cambridge.
    16. 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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    More about this item

    Keywords

    Endogeneity; Integrated process; Nonstationarity; Partial linear model; Simultaneity; Vector semiparametric regression;
    All these keywords.

    JEL classification:

    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities

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