### Abstract

Consider the unconditional moment restriction ${E[m(y,v,w;\pi_{0})/f_{V|w} (v|w) s(w;\pi_{0})] = 0}$, where ${m(\cdot)}$ and ${s(\cdot)}$ are known vector-valued functions of data ${(y^\prime,v,w^\prime)^\prime}$. The smallest asymptotic variance that √n-consistent regular estimators of 0 can have is calculated when ${f_{V|w}(\cdot)}$ is only known to be a bounded, continuous, nonzero conditional density function. Our results show that plug-in kernel-based estimators of ${\pi_{0}}$ constructed from this type of moment restriction, such as Lewbel (1998, Econometrica 66, 105121) and Lewbel (2007, Journal of Econometrics 141, 777806), are semiparametric efficient.

Publication

**Econometric Theory**, (25), 3, pp. 847-855