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Identification and shape restrictions in nonparametric instrumental variables estimation

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  • Freyberger, Joachim
  • Horowitz, Joel L.

Abstract

This paper is concerned with inference about an unidentified linear functional, L(g), where g satisfies Y=g(X)+U; E(U|W)=0. In much applied research, X and W are discrete, and W has fewer points of support than X. Consequently, L(g) is not identified nonparametrically and can have any value in (−∞,∞). This paper uses shape restrictions, such as monotonicity or convexity, to achieve interval identification of L(g). The paper shows that under shape restrictions, L(g) is contained in an interval whose bounds can be obtained by solving linear programming problems. Inference about L(g) can be carried out by using the bootstrap. An empirical application illustrates the usefulness of the method.

Suggested Citation

  • Freyberger, Joachim & Horowitz, Joel L., 2015. "Identification and shape restrictions in nonparametric instrumental variables estimation," Journal of Econometrics, Elsevier, vol. 189(1), pages 41-53.
  • Handle: RePEc:eee:econom:v:189:y:2015:i:1:p:41-53
    DOI: 10.1016/j.jeconom.2015.06.020
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    References listed on IDEAS

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    Cited by:

    1. Yu-Wei Hsieh & Xiaoxia Shi & Matthew Shum, 2017. "Inference on Estimators defined by Mathematical Programming," Papers 1709.09115, arXiv.org.
    2. repec:eee:ecolet:v:158:y:2017:i:c:p:84-87 is not listed on IDEAS
    3. repec:eee:econom:v:203:y:2018:i:2:p:316-327 is not listed on IDEAS

    More about this item

    Keywords

    Partial identification; Linear programming; Bootstrap;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation

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