Published online by Cambridge University Press: 01 June 2009
Consider the unconditional moment restriction E[m(y, υ, w; π0)/fV|w (υ|w) −s (w; π0)] = 0, where m(·) and s(·) are known vector-valued functions of data (y┬, υ, w┬)┬. The smallest asymptotic variance that -consistent regular estimators of π0 can have is calculated when fV|w(·) is only known to be a bounded, continuous, nonzero conditional density function. Our results show that “plug-in” kernel-based estimators of π0 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.
We thank the co-editor Richard Smith, two anonymous referees, Francesco Bravo, Juan Carlos Escanciano, Javier Hidalgo, Kim Huynh, Oliver Linton, and Pravin Trivedi for many helpful comments, corrections, and suggestions. The usual disclaimers apply.