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Robust, accurate confidence intervals with a weak instrument: quarter of birth and education


  • Guido W. Imbens
  • Paul R. Rosenbaum


An instrument or instrumental variable manipulates a treatment and affects the outcome only indirectly through its manipulation of the treatment. For instance, encouragement to exercise might increase cardiovascular fitness, but only indirectly to the extent that it increases exercise. If instrument levels are randomly assigned to individuals, then the instrument may permit consistent estimation of the effects caused by the treatment, even though the treatment assignment itself is far from random. For instance, one can conduct a randomized experiment assigning some subjects to 'encouragement to exercise' and others to 'no encouragement' but, for reasons of habit or taste, some subjects will not exercise when encouraged and others will exercise without encouragement; none-the-less, such an instrument aids in estimating the effect of exercise. Instruments that are weak, i.e. instruments that have only a slight effect on the treatment, present inferential problems. We evaluate a recent proposal for permutation inference with an instrumental variable in four ways: using Angrist and Krueger's data on the effects of education on earnings using quarter of birth as an instrument, following Bound, Jaeger and Baker in using simulated independent observations in place of the instrument in Angrist and Krueger's data, using entirely simulated data in which correct answers are known and finally using statistical theory to show that "only" permutation inferences maintain correct coverage rates. The permutation inferences perform well in both easy and hard cases, with weak instruments, as well as with long-tailed responses. Copyright 2005 Royal Statistical Society.

Suggested Citation

  • Guido W. Imbens & Paul R. Rosenbaum, 2005. "Robust, accurate confidence intervals with a weak instrument: quarter of birth and education," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 168(1), pages 109-126.
  • Handle: RePEc:bla:jorssa:v:168:y:2005:i:1:p:109-126

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    References listed on IDEAS

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    1. Chang, Pao-Li & Lee, Myoung-Jae, 2011. "The WTO trade effect," Journal of International Economics, Elsevier, vol. 85(1), pages 53-71, September.
    2. repec:bla:jorssa:v:180:y:2017:i:2:p:569-586 is not listed on IDEAS
    3. Andrews, Donald W.K. & Marmer, Vadim, 2008. "Exactly distribution-free inference in instrumental variables regression with possibly weak instruments," Journal of Econometrics, Elsevier, vol. 142(1), pages 183-200, January.
    4. Cabus, Sofie J. & De Witte, Kristof, 2011. "Does school time matter?—On the impact of compulsory education age on school dropout," Economics of Education Review, Elsevier, vol. 30(6), pages 1384-1398.
    5. Clemens, Jeffrey, 2017. "Pitfalls in the Development of Falsification Tests: An Illustration from the Recent Minimum Wage Literature," MPRA Paper 80154, University Library of Munich, Germany.
    6. Eduardo Fé & Mario Pezzino, 2015. "On The Local Causal Effects of Retirement on Human Capital," The School of Economics Discussion Paper Series 1508, Economics, The University of Manchester.
    7. Kasey S. Buckles & Daniel M. Hungerman, 2013. "Season of Birth and Later Outcomes: Old Questions, New Answers," The Review of Economics and Statistics, MIT Press, vol. 95(3), pages 711-724, July.
    8. Ganong, Peter & Jäger, Simon, 2014. "A Permutation Test and Estimation Alternatives for the Regression Kink Design," IZA Discussion Papers 8282, Institute for the Study of Labor (IZA).
    9. repec:hrv:faseco:34222894 is not listed on IDEAS
    10. David S. Abrams & Marianne Bertrand & Sendhil Mullainathan, 2012. "Do Judges Vary in Their Treatment of Race?," The Journal of Legal Studies, University of Chicago Press, vol. 41(2), pages 347-383.
    11. Bekker, Paul A. & Lawford, Steve, 2008. "Symmetry-based inference in an instrumental variable setting," Journal of Econometrics, Elsevier, vol. 142(1), pages 28-49, January.
    12. Rietveld, Cornelius A. & Webbink, Dinand, 2016. "On the genetic bias of the quarter of birth instrument," Economics & Human Biology, Elsevier, vol. 21(C), pages 137-146.
    13. David I. Stern, 2011. "From Correlation to Granger Causality," Crawford School Research Papers 1113, Crawford School of Public Policy, The Australian National University.

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