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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.

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Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 17519.

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Date of creation: Oct 2011
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Handle: RePEc:nbr:nberwo:17519

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References

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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, School of Economics and Management, University of Aarhus.
  2. 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.
  3. Joshua Angrist, 2013. "The Perils of Peer Effects," NBER Working Papers 19774, National Bureau of Economic Research, Inc.
  4. Anna Aizer & Joseph J. Doyle, Jr., 2013. "Juvenile Incarceration, Human Capital and Future Crime: Evidence from Randomly-Assigned Judges," NBER Working Papers 19102, National Bureau of Economic Research, Inc.

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