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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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    1. Bryan W. Brown & Whitney K. Newey, 1998. "Efficient Semiparametric Estimation of Expectations," Econometrica, Econometric Society, vol. 66(2), pages 453-464, March.
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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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