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.
Chen, Xiaohong and Qiu, Yin Jia, "Methods for Nonparametric and Semiparametric Regressions with Endogeneity: a Gentle Guide" (2016). Cowles Foundation Discussion Papers. 2476.