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Inference on a Semiparametric Model with Global Power Law and Local Nonparametric Trends

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  • Jiti Gao
  • Oliver Linton
  • Bin Peng

Abstract

This paper studies a model with both a parametric global trend and a nonparametric local trend. This model may be of interest in a number of applications in economics, finance, ecology, and geology. The model nests the parametric global trend model considered in Phillips (2007) and Robinson (2012), and the nonparametric local trend model. We first propose two hypothesis tests to detect whether either of the special cases are appropriate. For the case where both null hypotheses are rejected, we propose an estimation method to capture both aspects of the time trend. We establish consistency and some distribution theory in the presence of a large sample. Moreover, we examine the proposed hypothesis tests and estimation methods through both simulated and real data examples. Finally, we discuss some potential extensions and issues when modelling time effects.

Suggested Citation

  • Jiti Gao & Oliver Linton & Bin Peng, 2017. "Inference on a Semiparametric Model with Global Power Law and Local Nonparametric Trends," Monash Econometrics and Business Statistics Working Papers 10/17, Monash University, Department of Econometrics and Business Statistics.
    • Handle: RePEc:msh:ebswps:2017-10
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    References listed on IDEAS

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    1. Li, Qi, 1999. "Consistent model specification tests for time series econometric models," Journal of Econometrics, Elsevier, vol. 92(1), pages 101-147, September.
    2. Phillips, Peter C.B. & Li, Degui & Gao, Jiti, 2017. "Estimating smooth structural change in cointegration models," Journal of Econometrics, Elsevier, vol. 196(1), pages 180-195.
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    5. James D. Hamilton, 2017. "Why You Should Never Use the Hodrick-Prescott Filter," NBER Working Papers 23429, National Bureau of Economic Research, Inc.
    6. Cai, Zongwu, 2007. "Trending time-varying coefficient time series models with serially correlated errors," Journal of Econometrics, Elsevier, vol. 136(1), pages 163-188, January.
    7. Feng, Guohua & Serletis, Apostolos, 2008. "Productivity trends in U.S. manufacturing: Evidence from the NQ and AIM cost functions," Journal of Econometrics, Elsevier, vol. 142(1), pages 281-311, January.
    8. Pesaran, M. Hashem & Yang, Cynthia Fan, 2020. "Econometric analysis of production networks with dominant units," Journal of Econometrics, Elsevier, vol. 219(2), pages 507-541.
    9. Peter C. B. Phillips & Sainan Jin, 2021. "Business Cycles, Trend Elimination, And The Hp Filter," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 62(2), pages 469-520, May.
    10. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    11. Chen, Jia & Gao, Jiti & Li, Degui, 2012. "Semiparametric trending panel data models with cross-sectional dependence," Journal of Econometrics, Elsevier, vol. 171(1), pages 71-85.
    12. Su, Liangjun & Jin, Sainan & Zhang, Yonghui, 2015. "Specification test for panel data models with interactive fixed effects," Journal of Econometrics, Elsevier, vol. 186(1), pages 222-244.
    13. Gao, Jiti, 2007. "Nonlinear time series: semiparametric and nonparametric methods," MPRA Paper 39563, University Library of Munich, Germany, revised 01 Sep 2007.
    14. Phillips, Peter C. B., 2001. "Trending time series and macroeconomic activity: Some present and future challenges," Journal of Econometrics, Elsevier, vol. 100(1), pages 21-27, January.
    15. Su, Liangjun & Jin, Sainan, 2012. "Sieve estimation of panel data models with cross section dependence," Journal of Econometrics, Elsevier, vol. 169(1), pages 34-47.
    16. Chen, Jia & Gao, Jiti & Li, Degui, 2012. "A New Diagnostic Test For Cross-Section Uncorrelatedness In Nonparametric Panel Data Models," Econometric Theory, Cambridge University Press, vol. 28(5), pages 1144-1163, October.
    17. Greene, William, 2005. "Reconsidering heterogeneity in panel data estimators of the stochastic frontier model," Journal of Econometrics, Elsevier, vol. 126(2), pages 269-303, June.
    18. Robinson, Peter M., 1997. "Large-sample inference for nonparametric regression with dependent errors," LSE Research Online Documents on Economics 302, London School of Economics and Political Science, LSE Library.
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    Citations

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    Cited by:

    1. Chaohua Dong & Jiti Gao & Oliver Linton & Bin peng, 2020. "On Time Trend of COVID-19: A Panel Data Study," Monash Econometrics and Business Statistics Working Papers 22/20, Monash University, Department of Econometrics and Business Statistics.
    2. Gao, Jiti & Liu, Fei & Peng, Bin & Yan, Yayi, 2023. "Binary response models for heterogeneous panel data with interactive fixed effects," Journal of Econometrics, Elsevier, vol. 235(2), pages 1654-1679.
    3. Chen, Zhihong & Xia, Huizhu, 2020. "Trend instrumental variable regression with an application to the US New Keynesian Phillips Curve," Economic Modelling, Elsevier, vol. 93(C), pages 595-604.

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    More about this item

    Keywords

    global mean sea level; nonparametric kernel estimation; nonstationarity.;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • Q54 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics - - - Climate; Natural Disasters and their Management; Global Warming

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