Empirical likelihood estimation of conditional moment restriction models with unknown functions

This paper proposes an empirical likelihood-based estimation method for conditional moment restriction models with unknown functions, which include several semiparametric models. Our estimator is called the sieve conditional empirical likelihood (SCEL) estimator, which is based on the methods of conditional empirical likelihood and sieves. We derive (i) the consistency and a convergence rate of the SCEL estimator for the whole parameter, and (ii) the asymptotic normality and efficiency of the SCEL estimator for the parametric component. As an illustrating example, we consider a partially linear regression model with nonparametric endogeneity and heteroskedasticity.