EFFICIENCY BOUNDS FOR SEMIPARAMETRIC ESTIMATION OF INVERSE CONDITIONAL DENSITY-WEIGHTED FUNCTIONS

Consider the unconditional moment restriction E[m(y, v, w; pi(0))/f(V|w) (v|w) - s (w; pi(0))] = 0, where m (.) and s (.) are known vector-valued functions of data (y(T), v; w(T))(T). The smallest asymptotic variance that root n-consistent regular estimators of pi(0) can have is calculated when f(V|W) (.) is only Known to be a hounded, 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, 105-121) and Lewbel (2007, Journal of Econometrics 141, 777-806), are semiparametric efficient.