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Efficiency bounds for estimating linear functionals of nonparametric regression models with endogenous regressors

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  • Severini, Thomas A.
  • Tripathi, Gautam

Abstract

Let Y=μ∗(X)+ε, where μ∗ is unknown and E[ε|X]≠0 with positive probability but there exist instrumental variables W such that E[ε|W]=0 w.p.1. It is well known that such nonparametric regression models are generally “ill-posed” in the sense that the map from the data to μ∗ is not continuous. In this paper, we derive the efficiency bounds for estimating certain linear functionals of μ∗ without assuming μ∗ itself to be identified.

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  • Severini, Thomas A. & Tripathi, Gautam, 2012. "Efficiency bounds for estimating linear functionals of nonparametric regression models with endogenous regressors," Journal of Econometrics, Elsevier, vol. 170(2), pages 491-498.
    • Handle: RePEc:eee:econom:v:170:y:2012:i:2:p:491-498
    DOI: 10.1016/j.jeconom.2012.05.018
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    6. Hidehiko Ichimura & Whitney K. Newey, 2022. "The influence function of semiparametric estimators," Quantitative Economics, Econometric Society, vol. 13(1), pages 29-61, January.
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    8. Andrew Bennett & Nathan Kallus & Xiaojie Mao & Whitney Newey & Vasilis Syrgkanis & Masatoshi Uehara, 2023. "Source Condition Double Robust Inference on Functionals of Inverse Problems," Papers 2307.13793, arXiv.org.
    9. Santos, Andres, 2011. "Instrumental variable methods for recovering continuous linear functionals," Journal of Econometrics, Elsevier, vol. 161(2), pages 129-146, April.
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    18. V Chernozhukov & W K Newey & R Singh, 2023. "A simple and general debiased machine learning theorem with finite-sample guarantees," Biometrika, Biometrika Trust, vol. 110(1), pages 257-264.
    19. Juan Carlos Escanciano & Wei Li, 2013. "On the identification of structural linear functionals," CeMMAP working papers 48/13, Institute for Fiscal Studies.
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    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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