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Identification and Inference with Many Invalid Instruments

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

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
Note: LS PE
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  7. Mehmet Caner, 2006. "Near Exogeneity and Weak Identification in Generlized Empirical Likelihood estimators : Fixed and Many Moment Asymptotics," Working Papers 212, University of Pittsburgh, Department of Economics, revised Jan 2006.
  8. Chao, John C. & Swanson, Norman R. & Hausman, Jerry A. & Newey, Whitney K. & Woutersen, Tiemen, 2012. "Asymptotic Distribution Of Jive In A Heteroskedastic Iv Regression With Many Instruments," Econometric Theory, Cambridge University Press, vol. 28(01), pages 42-86, February.
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  11. Eric Gautier & Alexandre Tsybakov, 2014. "High-dimensional instrumental variables regression and confidence sets," Working Papers hal-00591732, HAL.
  12. Kraay, Aart, 2008. "Instrumental variables regressions with honestly uncertain exclusion restrictions," Policy Research Working Paper Series 4632, The World Bank.
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  14. Richard A. Ashley., 2006. "Assessing the Credibility of Instrumental Variables Inference With Imperfect Instruments Via Sensitivity Analysis," Working Papers e06-9, Virginia Polytechnic Institute and State University, Department of Economics.
  15. Paul A. Bekker & Jan Ploeg, 2005. "Instrumental variable estimation based on grouped data," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 59(3), pages 239-267.
  16. Angrist, J D & Imbens, G W & Krueger, A B, 1999. "Jackknife Instrumental Variables Estimation," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 14(1), pages 57-67, Jan.-Feb..
  17. Phillips, Garry D A & Hale, C, 1977. "The Bias of Instrumental Variable Estimators of Simultaneous Equation Systems," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 18(1), pages 219-28, February.
  18. Chioda, Laura & Jansson, Michael, 2009. "Optimal Invariant Inference When The Number Of Instruments Is Large," Econometric Theory, Cambridge University Press, vol. 25(03), pages 793-805, June.
  19. Roland G. Fryer, 2011. "Financial Incentives and Student Achievement: Evidence from Randomized Trials," The Quarterly Journal of Economics, Oxford University Press, vol. 126(4), pages 1755-1798.
  20. Carlos A. Flores & Alfonso Flores-Lagunes, 2013. "Partial Identification of Local Average Treatment Effects With an Invalid Instrument," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(4), pages 534-545, October.
  21. T. W. Anderson & Naoto Kunitomo & Yukitoshi Matsushita, 2008. "On the Asymptotic Optimality of the LIML Estimator with Possibly Many Instruments," CIRJE F-Series CIRJE-F-542, CIRJE, Faculty of Economics, University of Tokyo.
  22. Bekker, Paul A, 1994. "Alternative Approximations to the Distributions of Instrumental Variable Estimators," Econometrica, Econometric Society, vol. 62(3), pages 657-81, May.
  23. Hahn, Jinyong, 2002. "Optimal Inference With Many Instruments," Econometric Theory, Cambridge University Press, vol. 18(01), pages 140-168, February.
  24. Anderson, T.W. & Kunitomo, Naoto & Matsushita, Yukitoshi, 2010. "On the asymptotic optimality of the LIML estimator with possibly many instruments," Journal of Econometrics, Elsevier, vol. 157(2), pages 191-204, August.
  25. Hasselt, Martijn van, 2010. "Many Instruments Asymptotic Approximations Under Nonnormal Error Distributions," Econometric Theory, Cambridge University Press, vol. 26(02), pages 633-645, April.
  26. Donald W. K. Andrews & Marcelo J. Moreira & James H. Stock, 2006. "Optimal Two-Sided Invariant Similar Tests for Instrumental Variables Regression," Econometrica, Econometric Society, vol. 74(3), pages 715-752, 05.
  27. Roland G. Fryer, Jr, 2010. "Financial Incentives and Student Achievement: Evidence from Randomized Trials," NBER Working Papers 15898, National Bureau of Economic Research, Inc.
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