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Identification and Inference with Many Invalid Instruments

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  • Michal Kolesár
  • Raj Chetty
  • John N. Friedman
  • Edward L. Glaeser
  • Guido W. Imbens

Abstract

We analyze linear models with a single endogenous regressor in the presence of many instrumental variables. We weaken a key assumption typically made in this literature by allowing all the instruments to have direct effects on the outcome. We consider restrictions on these direct effects that allow for point identification of the effect of interest. The setup leads to new insights concerning the properties of conventional estimators, novel identification strategies, and new estimators to exploit those strategies. A key assumption underlying the main identification strategy is that the product of the direct effects of the instruments on the outcome and the effects of the instruments on the endogenous regressor has expectation zero. We argue in the context of two specific examples with a group structure that this assumption has substantive content.

Suggested Citation

  • Michal Kolesár & Raj Chetty & John N. Friedman & Edward L. Glaeser & Guido W. Imbens, 2011. "Identification and Inference with Many Invalid Instruments," NBER Working Papers 17519, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberwo:17519
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    Cited by:

    1. Matias D. Cattaneo & Michael Jansson & Whitney K. Newey, 2012. "Alternative Asymptotics and the Partially Linear Model with Many Regressors," CREATES Research Papers 2012-02, Department of Economics and Business Economics, Aarhus University.
    2. Hans (J.L.W.) van Kippersluis & Niels (C.A.) Rietveld, 2017. "Beyond Plausibly Exogenous," Tinbergen Institute Discussion Papers 17-096/V, Tinbergen Institute.
    3. Caner, Mehmet, 2014. "Near exogeneity and weak identification in generalized empirical likelihood estimators: Many moment asymptotics," Journal of Econometrics, Elsevier, vol. 182(2), pages 247-268.
    4. Frank Windmeijer & Helmut Farbmacher & Neil Davies & George Davey Smith, 2016. "On the Use of the Lasso for Instrumental Variables Estimation with Some Invalid Instruments," Bristol Economics Discussion Papers 16/674, Department of Economics, University of Bristol, UK, revised 08 Aug 2017.
    5. Joseph J. Doyle, Jr. & John A. Graves & Jonathan Gruber & Samuel Kleiner, 2012. "Do High-Cost Hospitals Deliver Better Care? Evidence from Ambulance Referral Patterns," NBER Working Papers 17936, National Bureau of Economic Research, Inc.
    6. Angrist, Joshua D., 2014. "The perils of peer effects," Labour Economics, Elsevier, vol. 30(C), pages 98-108.
    7. Michal Kolesár & Raj Chetty & John Friedman & Edward Glaeser & Guido W. Imbens, 2015. "Identification and Inference With Many Invalid Instruments," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(4), pages 474-484, October.
    8. Athanasouli, Daphne & Goujard, Antoine, 2015. "Corruption and management practices: Firm level evidence," Journal of Comparative Economics, Elsevier, vol. 43(4), pages 1014-1034.
    9. Clarke, Damian & Matta, Benjamín, 2017. "Practical Considerations for Questionable IVs," MPRA Paper 79991, University Library of Munich, Germany.
    10. repec:eee:econom:v:200:y:2017:i:2:p:207-222 is not listed on IDEAS
    11. Cameron McIntosh, 2014. "The presence of an error term does not preclude causal inference in regression: a comment on Krause (2012)," Quality & Quantity: International Journal of Methodology, Springer, vol. 48(1), pages 243-250, January.
    12. Anna Aizer & Joseph J. Doyle, 2015. "Juvenile Incarceration, Human Capital, and Future Crime: Evidence from Randomly Assigned Judges," The Quarterly Journal of Economics, Oxford University Press, vol. 130(2), pages 759-803.
    13. Markussen, Simen & Strøm, Marte, 2015. "The Effects of Motherhood," Memorandum 19/2015, Oslo University, Department of Economics.
    14. Ruoyao Shi & Zhipeng Liao, 2018. "An Averaging GMM Estimator Robust to Misspecification," Working Papers 201803, University of California at Riverside, Department of Economics.

    More about this item

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables
    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation
    • C36 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Instrumental Variables (IV) Estimation

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