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Sieve Semiparametric Two-Step GMM under Weak Dependence

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Abstract
This paper considers semiparametric two-step GMM estimation and inference with weakly dependent data, where unknown nuisance functions are estimated via sieve extremum estimation in the first step. We show that although the asymptotic variance of the second-step GMM estimator may not have a closed form expression, it can be well approximated by sieve variances that have simple closed form expressions. We present consistent or robust variance estimation, Wald tests and Hansen's (1982) over-identification tests for the second step GMM that properly reflect the first-step estimated functions and the weak dependence of the data. Our sieve semiparametric two-step GMM inference procedures are shown to be numerically equivalent to the ones computed as if the first step were parametric. A new consistent random-perturbation estimator of the derivative of the expectation of the non-smooth moment function is also provided.

Suggested Citation

  • Xiaohong Chen & Zhipeng Liao, 2015. "Sieve Semiparametric Two-Step GMM under Weak Dependence," Cowles Foundation Discussion Papers 2012, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:2012
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    References listed on IDEAS

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    3. Victor Chernozhukov & Juan Carlos Escanciano & Hidehiko Ichimura & Whitney K. Newey & James M. Robins, 2022. "Locally Robust Semiparametric Estimation," Econometrica, Econometric Society, vol. 90(4), pages 1501-1535, July.
    4. Dong, Chaohua & Gao, Jiti & Linton, Oliver, 2023. "High dimensional semiparametric moment restriction models," Journal of Econometrics, Elsevier, vol. 232(2), pages 320-345.
    5. Hidehiko Ichimura & Whitney K. Newey, 2022. "The influence function of semiparametric estimators," Quantitative Economics, Econometric Society, vol. 13(1), pages 29-61, January.
    6. Jiafeng Chen & Xiaohong Chen & Elie Tamer, 2021. "Efficient Estimation in NPIV Models: A Comparison of Various Neural Networks-Based Estimators," Papers 2110.06763, arXiv.org, revised Oct 2022.
    7. de Castro, Luciano & Galvao, Antonio F. & Kaplan, David M. & Liu, Xin, 2019. "Smoothed GMM for quantile models," Journal of Econometrics, Elsevier, vol. 213(1), pages 121-144.
    8. Firpo, Sergio & Galvao, Antonio F. & Pinto, Cristine & Poirier, Alexandre & Sanroman, Graciela, 2022. "GMM quantile regression," Journal of Econometrics, Elsevier, vol. 230(2), pages 432-452.
    9. Francesco Bravo, 2022. "Misspecified semiparametric model selection with weakly dependent observations," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(4), pages 558-586, July.
    10. Chen, Jiafeng & Ritzwoller, David M., 2023. "Semiparametric estimation of long-term treatment effects," Journal of Econometrics, Elsevier, vol. 237(2).
    11. Zhao, Puying & Haziza, David & Wu, Changbao, 2020. "Survey weighted estimating equation inference with nuisance functionals," Journal of Econometrics, Elsevier, vol. 216(2), pages 516-536.
    12. Jean-Jacques Forneron, 2019. "A Sieve-SMM Estimator for Dynamic Models," Papers 1902.01456, arXiv.org, revised Jan 2023.
    13. Bang, Minji & Gao, Wayne Yuan & Postlewaite, Andrew & Sieg, Holger, 2023. "Using monotonicity restrictions to identify models with partially latent covariates," Journal of Econometrics, Elsevier, vol. 235(2), pages 892-921.
    14. Jean-Jacques Forneron, 2023. "Noisy, Non-Smooth, Non-Convex Estimation of Moment Condition Models," Papers 2301.07196, arXiv.org, revised Feb 2023.
    15. Xiaohong Chen & Yin Jia Jeff Qiu, 2016. "Methods for Nonparametric and Semiparametric Regressions with Endogeneity: A Gentle Guide," Annual Review of Economics, Annual Reviews, vol. 8(1), pages 259-290, October.
    16. Chen, Jiafeng & Chen, Xiaohong & Tamer, Elie, 2023. "Efficient estimation of average derivatives in NPIV models: Simulation comparisons of neural network estimators," Journal of Econometrics, Elsevier, vol. 235(2), pages 1848-1875.
    17. Chen, Xiaohong & Liu, Ying & Ma, Shujie & Zhang, Zheng, 2024. "Causal inference of general treatment effects using neural networks with a diverging number of confounders," Journal of Econometrics, Elsevier, vol. 238(1).
    18. Jiafeng Chen & Xiaohong Chen & Elie Tamer, 2021. "Efficient Estimation of Average Derivatives in NPIV Models: Simulation Comparisons of Neural Network Estimators," Cowles Foundation Discussion Papers 2319, Cowles Foundation for Research in Economics, Yale University.
    19. Ganesh Karapakula, 2023. "Stable Probability Weighting: Large-Sample and Finite-Sample Estimation and Inference Methods for Heterogeneous Causal Effects of Multivalued Treatments Under Limited Overlap," Papers 2301.05703, arXiv.org, revised Jan 2023.
    20. Chaohua Dong & Jiti Gao & Oliver Linton, 2017. "High dimensional semiparametric moment restriction models," Monash Econometrics and Business Statistics Working Papers 17/17, Monash University, Department of Econometrics and Business Statistics.
    21. Greg Lewis & Vasilis Syrgkanis, 2018. "Adversarial Generalized Method of Moments," Papers 1803.07164, arXiv.org, revised Apr 2018.

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    More about this item

    Keywords

    Sieve two-step GMM; Weakly dependent data; Auto-correlation robust inference; Semiparametric over-identification test; Numerical equivalence; Random perturbation derivative estimator;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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