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Efficiency Bounds for Estimating Linear Functionals of Nonparametric Regression Models with Endogenous Regressors

Author

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  • Thomas A. Severini

    (Northwestern University)

  • Gautam Tripathi

    (University of Connecticut)

Abstract

Consider a nonparametric regression model Y=mu*(X) + e, where the explanatory variables X are endogenous and e satisfies the conditional moment restriction E[e|W]=0 w.p.1 for instrumental variables W. It is well known that in these models the structural parameter mu* is 'ill-posed' in the sense that the function mapping the data to mu* is not continuous. In this paper, we derive the efficiency bounds for estimating linear functionals E[p(X)mu*(X)] and int_{supp(X)}p(x)mu*(x)dx, where p is a known weight function and supp(X) the support of X, without assuming mu* to be well-posed or even identified.

Suggested Citation

  • Thomas A. Severini & Gautam Tripathi, 2007. "Efficiency Bounds for Estimating Linear Functionals of Nonparametric Regression Models with Endogenous Regressors," Working papers 2007-18, University of Connecticut, Department of Economics.
    • Handle: RePEc:uct:uconnp:2007-18
    Note: We thank Gary Chamberlain, Enno Mammen, Whitney Newey, and participants at several seminars for helpful suggestions and conversations. The first author also thanks the NSF for financial support.
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    References listed on IDEAS

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    Cited by:

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    4. Chen, Xiaohong & Pouzo, Demian & Powell, James L., 2019. "Penalized sieve GEL for weighted average derivatives of nonparametric quantile IV regressions," Journal of Econometrics, Elsevier, vol. 213(1), pages 30-53.
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    10. 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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    21. Escanciano, Juan Carlos, 2023. "Irregular identification of structural models with nonparametric unobserved heterogeneity," Journal of Econometrics, Elsevier, vol. 234(1), pages 106-127.
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    24. Zhang, Jeffrey & Li, Wei & Miao, Wang & Tchetgen Tchetgen, Eric, 2023. "Proximal causal inference without uniqueness assumptions," Statistics & Probability Letters, Elsevier, vol. 198(C).

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    More about this item

    Keywords

    Efficiency bounds; Linear functionals; Nonparametric regression; Endogenous regressors;
    All these keywords.

    JEL classification:

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

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