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Methods for Nonparametric and Semiparametric Regressions with Endogeneity: a Gentle Guide

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Abstract
This paper reviews recent advances in estimation and inference for nonparametric and semiparametric models with endogeneity. It first describes methods of sieves and penalization for estimating unknown functions identified via conditional moment restrictions. Examples include nonparametric instrumental variables regression (NPIV), nonparametric quantile IV regression and many more semi-nonparametric structural models. Asymptotic properties of the sieve estimators and the sieve Wald, quasi-likelihood ratio (QLR) hypothesis tests of functionals with nonparametric endogeneity are presented. For sieve NPIV estimation, the rate-adaptive data-driven choices of sieve regularization parameters and the sieve score bootstrap uniform confidence bands are described. Finally, simple sieve variance estimation and over-identification test for semiparametric two-step GMM are reviewed. Monte Carlo examples are included.

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  • Xiaohong Chen & Yin Jia Qiu, 2016. "Methods for Nonparametric and Semiparametric Regressions with Endogeneity: a Gentle Guide," Cowles Foundation Discussion Papers 2032, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:2032
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    3. 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.
    4. Xin Geng & Carlos Martins-Filho & Feng Yao, 2015. "Estimation of a Partially Linear Regression in Triangular Systems," Working Papers 15-46, Department of Economics, West Virginia University.
    5. 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.
    6. Liu, Lin & Mukherjee, Rajarshi & Robins, James M., 2024. "Assumption-lean falsification tests of rate double-robustness of double-machine-learning estimators," Journal of Econometrics, Elsevier, vol. 240(2).
    7. Li, Mingyang & Jin, Man & Kumbhakar, Subal C., 2022. "Do subsidies increase firm productivity? Evidence from Chinese manufacturing enterprises," European Journal of Operational Research, Elsevier, vol. 303(1), pages 388-400.
    8. Berndt Jesenko & Christian Schlögl, 2021. "The effect of web of science subject categories on clustering: the case of data-driven methods in business and economic sciences," Scientometrics, Springer;Akadémiai Kiadó, vol. 126(8), pages 6785-6801, August.
    9. Giovanni Compiani, 2022. "Market counterfactuals and the specification of multiproduct demand: A nonparametric approach," Quantitative Economics, Econometric Society, vol. 13(2), pages 545-591, May.
    10. Wang, Ao, 2023. "Sieve BLP: A semi-nonparametric model of demand for differentiated products," Journal of Econometrics, Elsevier, vol. 235(2), pages 325-351.
    11. 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.

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    More about this item

    Keywords

    Conditional moment restrictions containing unknown functions; (Quantile) Instrumental variables; Linear and nonlinear functionals; Sieve minimum distance; Sieve GMM; Sieve Wald; QLR; Bootstrap; Semiparametric two-step GMM; Numerical equivalence;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • 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

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