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

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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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    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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