Efficiency bounds for semiparametric estimation of inverse conditional-density-weighted functions
Authors: D.T. Jacho-Chavez
Publication: Econometric Theory, (25), 3, pp. 847-855
DOI: 10.1017/S0266466609090732
Abstract
Consider the unconditional moment restriction $E[m(y,v,w;\pi_0) / f_{V\mid w}(v\mid w) \; s(w;\pi_0)] = 0$, where $m(\cdot)$ and $s(\cdot)$ are known vector-valued functions of data $(y^\prime,v,w^\prime)^\prime$. The smallest asymptotic variance that $\sqrt{n}$-consistent regular estimators of $0$ can have is calculated when $f_{V\mid w}(\cdot)$ 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.
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