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Identification and shape restrictions in nonparametric instrumental variables estimation

Author

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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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    Citations

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    Cited by:

    1. Pietro Tebaldi & Alexander Torgovitsky & Hanbin Yang, 2019. "Nonparametric Estimates of Demand in the California Health Insurance Exchange," NBER Working Papers 25827, National Bureau of Economic Research, Inc.
    2. Kamat, Vishal, 2019. "Identification with Latent Choice Sets," TSE Working Papers 19-1031, Toulouse School of Economics (TSE).
    3. repec:taf:emetrv:v:36:y:2017:i:6-9:p:988-1006 is not listed on IDEAS
    4. repec:eee:ecolet:v:158:y:2017:i:c:p:84-87 is not listed on IDEAS
    5. repec:kap:compec:v:53:y:2019:i:2:d:10.1007_s10614-017-9758-5 is not listed on IDEAS
    6. Lee, Y-Y. & Bhattacharya, D., 2018. "Applied Welfare Analysis for Discrete Choice with Interval-data on Income," Cambridge Working Papers in Economics 1882, Faculty of Economics, University of Cambridge.
    7. Timothy B. Armstrong & Michal Kolesár, 2018. "Sensitivity Analysis using Approximate Moment Condition Models," Cowles Foundation Discussion Papers 2158R, Cowles Foundation for Research in Economics, Yale University, revised Feb 2019.
    8. Yu-Wei Hsieh & Xiaoxia Shi & Matthew Shum, 2017. "Inference on Estimators defined by Mathematical Programming," Papers 1709.09115, arXiv.org.
    9. Bulat Gafarov, 2019. "Inference in high-dimensional set-identified affine models," Papers 1904.00111, arXiv.org.
    10. 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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