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Penalized Sieve Estimation and Inference of Semi-Nonparametric Dynamic Models: A Selective Review

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Abstract

In this selective review, we first provide some empirical examples that motivate the usefulness of semi-nonparametric techniques in modelling economic and financial time series. We describe popular classes of semi-nonparametric dynamic models and some temporal dependence properties. We then present penalized sieve extremum (PSE) estimation as a general method for semi-nonparametric models with cross-sectional, panel, time series, or spatial data. The method is especially powerful in estimating difficult ill-posed inverse problems such as semi-nonparametric mixtures or conditional moment restrictions. We review recent advances on inference and large sample properties of the PSE estimators, which include (1) consistency and convergence rates of the PSE estimator of the nonparametric part; (2) limiting distributions of plug-in PSE estimators of functionals that are either smooth (i.e., root-n estimable) or non-smooth (i.e., slower than root-n estimable); (3) simple criterion-based inference for plug-in PSE estimation of smooth or non-smooth functionals; and (4) root-n asymptotic normality of semiparametric two-step estimators and their consistent variance estimators. Examples from dynamic asset pricing, nonlinear spatial VAR, semiparametric GARCH, and copula-based multivariate financial models are used to illustrate the general results.

Suggested Citation

  • Xiaohong Chen, 2011. "Penalized Sieve Estimation and Inference of Semi-Nonparametric Dynamic Models: A Selective Review," Cowles Foundation Discussion Papers 1804, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:1804
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    References listed on IDEAS

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    1. S. Darolles & Y. Fan & J. P. Florens & E. Renault, 2011. "Nonparametric Instrumental Regression," Econometrica, Econometric Society, vol. 79(5), pages 1541-1565, September.
    2. repec:mtl:montec:05-2002 is not listed on IDEAS
    3. de Jong, Robert M., 2002. "A note on "Convergence rates and asymptotic normality for series estimators": uniform convergence rates," Journal of Econometrics, Elsevier, vol. 111(1), pages 1-9, November.
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    Cited by:

    1. James Wolter, 2013. "Separating the impact of macroeconomic variables and global frailty in event data," Economics Series Working Papers 667, University of Oxford, Department of Economics.
    2. Shujie Ma & Oliver Linton & Jiti Gao, 2017. "Estimation and inference in semiparametric quantile factor models," Monash Econometrics and Business Statistics Working Papers 8/17, Monash University, Department of Econometrics and Business Statistics.
    3. Xiaohong Chen & . . & Yixiao Sun, 2012. "Sieve inference on semi-nonparametric time series models," CeMMAP working papers CWP06/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    4. Shujie Ma & Oliver Linton & Jiti Gao, 2018. "Estimation in semiparametric quantile factor models," CeMMAP working papers CWP07/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    5. Jean-Jacques Forneron, 2019. "A Sieve-SMM Estimator for Dynamic Models," Papers 1902.01456, arXiv.org, revised Jan 2023.
    6. Semenova, Vira, 2023. "Debiased machine learning of set-identified linear models," Journal of Econometrics, Elsevier, vol. 235(2), pages 1725-1746.
    7. Ma, Shujie & Linton, Oliver & Gao, Jiti, 2021. "Estimation and inference in semiparametric quantile factor models," Journal of Econometrics, Elsevier, vol. 222(1), pages 295-323.
    8. Xiaohong Chen & . . & Yixiao Sun, 2012. "Sieve inference on semi-nonparametric time series models," CeMMAP working papers 06/12, Institute for Fiscal Studies.

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    More about this item

    Keywords

    Nonlinear time series; Temporal dependence; Tail dependence; Penalized sieve M estimation; Penalized sieve minimum distance; Semiparametric two-step; Nonlinear ill-posed inverse; Mixtures; Conditional moment restrictions; Nonparametric endogeneity; Dynamic asset pricing; Varying coefficient VAR; GARCH; Copulas; Value-at-risk;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C20 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - General

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