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

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  • Xiaohong Chen

    () (Department of Economics, Yale University, New Haven, Connecticut 06520)

  • Yin Jia Jeff Qiu

    () (Department of Economics, Yale University, New Haven, Connecticut 06520)

Abstract

This article 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 (NPIV) regression, nonparametric quantile IV regression, and many more semi/nonparametric structural models. Asymptotic properties of the sieve estimators and the sieve Wald, quasi-likelihood ratio 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 overidentification tests for the semiparametric two-step generalized method of moments are reviewed. Monte Carlo examples are also included.

Suggested Citation

  • 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.
  • Handle: RePEc:anr:reveco:v:8:y:2016:p:259-290
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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;

    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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