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

Published online by Cambridge University Press:  01 June 2009

David T. Jacho-Chávez
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Abstract

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.

Type
Brief Report
Information
Econometric Theory , Volume 25 , Issue 3 , June 2009 , pp. 847 - 855
Copyright
Copyright © Cambridge University Press 2009

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Footnotes

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.

References

REFERENCES

Ai, Chunrong, & Chen, Xiaohong (2003) Efficient estimation of models with conditional moment restrictions containing unknown functions. Econometrica 71, 1795–1843.Google Scholar
Chamberlain, G. (1987) Asymptotic efficiency in estimation with conditional moment restrictions. Journal of Econometrics 34, 305–334.Google Scholar
Chamberlain, G. (1992) Efficiency bounds for semiparametric regression. Econometrica 60, 567–596.10.2307/2951584CrossRefGoogle Scholar
Hansen, L.P. (1982) Large sample properties of generalized methods of moments estimators. Econometrica 50, 1029–1054.CrossRefGoogle Scholar
Jacho-Chávez, D.T. (2006) Identification, estimation and efficiency of nonparametric and semiparametric models in microeconometrics. Ph.D. Dissertation, London School of Economics and Political Science.Google Scholar
Lewbel, A. (1998) Semiparametric latent variable model estimation with endogenous or mismeasured regressors. Econometrica 66, 105–121.10.2307/2998542Google Scholar
Lewbel, A. (2000) Semiparametric qualitative response model estimation with unknown heteroscedasticity or instrumental variables. Journal of Econometrics 97, 145–177.Google Scholar
Lewbel, A. (2007) Endogenous selection or treatment model estimation. Journal of Econometrics 141, 777–806.10.1016/j.jeconom.2006.11.004CrossRefGoogle Scholar
Magnac, T. & Maurin, E. (2007) Identification and information in monotone binary models. Journal of Econometrics 127, 76–104.Google Scholar
Newey, W.K. (1990) Semiparametric efficiency bounds. Journal of Applied Econometrics 5, 99–135.Google Scholar
Rothenberg, T.J. (1971) Identification in parametric models. Econometrica 39, 577–591.Google Scholar
Severini, T.A. & Tripathi, G. (2001) A simplified approach to computing efficiency bounds in semiparametric models. Journal of Econometrics 102, 23–66.CrossRefGoogle Scholar