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Efficient Semiparametric Estimation via Moment Restrictions

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  • Whitney K. Newey

Abstract

Conditional moment restrictions can be combined through GMM estimation to construct more efficient semiparametric estimators. This paper is about attainable efficiency for such estimators. We define and use a moment tangent set, the directions of departure from the truth allowed by the moments, to characterize when the semiparametric efficiency bound can be attained. The efficiency condition is that the moment tangent set equals the model tangent set. We apply these results to transformed, censored, and truncated regression models, e.g., finding that the conditional moment restrictions from Powell's (1986) censored regression quantile estimators can be combined to approximate efficiency when the disturbance is independent of regressors. Copyright The Econometric Society 2004.

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File URL: http://hdl.handle.net/10.1111/j.1468-0262.2004.00557.x
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Bibliographic Info

Article provided by Econometric Society in its journal Econometrica.

Volume (Year): 72 (2004)
Issue (Month): 6 (November)
Pages: 1877-1897

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Handle: RePEc:ecm:emetrp:v:72:y:2004:i:6:p:1877-1897

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Cited by:
  1. Bas Donkers & Marcia M Schafgans, 2005. "A method of moments estimator for semiparametric index models," STICERD - Econometrics Paper Series /2005/493, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  2. Chen, Songnian & Zhou, Xianbo, 2012. "Semiparametric estimation of a truncated regression model," Journal of Econometrics, Elsevier, vol. 167(2), pages 297-304.
  3. Komunjer, Ivana & Vuong, Quang, 2010. "Efficient estimation in dynamic conditional quantile models," Journal of Econometrics, Elsevier, vol. 157(2), pages 272-285, August.
  4. Manuel Arellano & Stéphane Bonhomme, 2009. "Identifying Distributional Characteristics In Random Coefficients Panel Data Models," Working Papers wp2009_0904, CEMFI.
  5. Cattaneo, Matias D. & Crump, Richard K. & Jansson, Michael, 2012. "Optimal inference for instrumental variables regression with non-Gaussian errors," Journal of Econometrics, Elsevier, vol. 167(1), pages 1-15.
  6. Chunrong Ai & Xiaohong Chen, 2009. "Semiparametric Efficiency Bound for Models of Sequential Moment Restrictions Containing Unknown Functions," Cowles Foundation Discussion Papers 1731, Cowles Foundation for Research in Economics, Yale University.
  7. David Kaplan & Yixiao Sun, 2013. "Smoothed Estimating Equations for Instrumental Variables Quantile Regression," Working Papers 1314, Department of Economics, University of Missouri.
  8. Marcelo Moreira, 2008. "A Maximum Likelihood Method for the Incidental Parameter Problem," NBER Working Papers 13787, National Bureau of Economic Research, Inc.
  9. Ai, Chunrong & Chen, Xiaohong, 2012. "The semiparametric efficiency bound for models of sequential moment restrictions containing unknown functions," Journal of Econometrics, Elsevier, vol. 170(2), pages 442-457.

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