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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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  • Whitney K. Newey, 2004. "Efficient Semiparametric Estimation via Moment Restrictions," Econometrica, Econometric Society, vol. 72(6), pages 1877-1897, November.
    • Handle: RePEc:ecm:emetrp:v:72:y:2004:i:6:p:1877-1897
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    File URL: http://hdl.handle.net/10.1111/j.1468-0262.2004.00557.x
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    Cited by:

    1. Kaplan, David M. & Sun, Yixiao, 2017. "Smoothed Estimating Equations For Instrumental Variables Quantile Regression," Econometric Theory, Cambridge University Press, vol. 33(1), pages 105-157, February.
    2. Christis Katsouris, 2023. "Quantile Time Series Regression Models Revisited," Papers 2308.06617, arXiv.org, revised Aug 2023.
    3. Huybrechts F. Bindele & Ash Abebe & Karlene N. Meyer, 2018. "General rank-based estimation for regression single index models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(5), pages 1115-1146, October.
    4. Chen, Songnian & Zhou, Xianbo, 2012. "Semiparametric estimation of a truncated regression model," Journal of Econometrics, Elsevier, vol. 167(2), pages 297-304.
    5. Manuel Arellano & Stéphane Bonhomme, 2012. "Identifying Distributional Characteristics in Random Coefficients Panel Data Models," Review of Economic Studies, Oxford University Press, vol. 79(3), pages 987-1020.
    6. Yingye Zheng & Tianxi Cai & Ziding Feng, 2006. "Application of the Time-Dependent ROC Curves for Prognostic Accuracy with Multiple Biomarkers," Biometrics, The International Biometric Society, vol. 62(1), pages 279-287, March.
    7. Daniel Ackerberg & Xiaohong Chen & Jinyong Hahn & Zhipeng Liao, 2014. "Asymptotic Efficiency of Semiparametric Two-step GMM," Review of Economic Studies, Oxford University Press, vol. 81(3), pages 919-943.
    8. Poirier, Alexandre, 2017. "Efficient estimation in models with independence restrictions," Journal of Econometrics, Elsevier, vol. 196(1), pages 1-22.
    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.
    10. Bustamante, M. Cecilia, 2016. "How Do Frictions Affect Corporate Investment? A Structural Approach," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 51(6), pages 1863-1895, December.
    11. Hans Fricke & Markus Frölich & Martin Huber & Michael Lechner, 2020. "Endogeneity and non‐response bias in treatment evaluation – nonparametric identification of causal effects by instruments," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 35(5), pages 481-504, August.
    12. Bas Donkers & Marcia M Schafgans, 2005. "A method of moments estimator for semiparametric index models," STICERD - Econometrics Paper Series 493, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    13. 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.
    14. de Castro, Luciano & Galvao, Antonio F. & Kaplan, David M. & Liu, Xin, 2019. "Smoothed GMM for quantile models," Journal of Econometrics, Elsevier, vol. 213(1), pages 121-144.
    15. Chen, Xiaohong & Linton, Oliver & Jacho-Chávez, David T., 2009. "An alternative way of computing efficient instrumental variable estimators," LSE Research Online Documents on Economics 58016, London School of Economics and Political Science, LSE Library.
    16. Aradillas-López, Andrés, 2021. "Computing semiparametric efficiency bounds in discrete choice models with strategic-interactions and rational expectations," Journal of Econometrics, Elsevier, vol. 221(1), pages 25-42.
    17. Chen, Songnian, 2010. "Root-N-consistent estimation of fixed-effect panel data transformation models with censoring," Journal of Econometrics, Elsevier, vol. 159(1), pages 222-234, November.
    18. Hui Li & Xiaogang Duan & Guosheng Yin, 2016. "Generalized Method of Moments for Additive Hazards Model with Clustered Dental Survival Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(4), pages 1124-1139, December.
    19. Li, Cheng & Jiang, Wenxin, 2016. "On oracle property and asymptotic validity of Bayesian generalized method of moments," Journal of Multivariate Analysis, Elsevier, vol. 145(C), pages 132-147.
    20. Frumento, Paolo & Bottai, Matteo, 2017. "An estimating equation for censored and truncated quantile regression," Computational Statistics & Data Analysis, Elsevier, vol. 113(C), pages 53-63.
    21. Komunjer, Ivana & Vuong, Quang, 2010. "Efficient estimation in dynamic conditional quantile models," Journal of Econometrics, Elsevier, vol. 157(2), pages 272-285, August.
    22. Hristache, Marian & Patilea, Valentin, 2021. "Equivalent models for observables under the assumption of missing at random," Econometrics and Statistics, Elsevier, vol. 20(C), pages 153-165.
    23. Marcelo Moreira, 2008. "A Maximum Likelihood Method for the Incidental Parameter Problem," NBER Working Papers 13787, National Bureau of Economic Research, Inc.

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