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Optimal Invariant Inference When The Number Of Instruments Is Large

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  • Chioda, Laura
  • Jansson, Michael

Abstract

This paper studies the asymptotic behavior of a Gaussian linear instrumental variables model in which the number of instruments diverges with the sample size. Asymptotic efficiency bounds are obtained for rotation invariant inference procedures and are shown to be attainable by procedures based on the limited information maximum likelihood estimator. The bounds are obtained by characterizing the limiting experiment associated with the model induced by the rotation invariance restriction.

Suggested Citation

  • Chioda, Laura & Jansson, Michael, 2009. "Optimal Invariant Inference When The Number Of Instruments Is Large," Econometric Theory, Cambridge University Press, vol. 25(3), pages 793-805, June.
    • Handle: RePEc:cup:etheor:v:25:y:2009:i:03:p:793-805_09
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    Cited by:

    1. Yukitoshi Matsushita & Taisuke Otsu, 2020. "Second-order refinements for t-ratios with many instruments," STICERD - Econometrics Paper Series 612, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    2. Bekker, Paul A. & Crudu, Federico, 2015. "Jackknife instrumental variable estimation with heteroskedasticity," Journal of Econometrics, Elsevier, vol. 185(2), pages 332-342.
    3. 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.
    4. Cattaneo, Matias D. & Crump, Richard K. & Jansson, Michael, 2012. "Optimal inference for instrumental variables regression with non-Gaussian errors," Journal of Econometrics, Elsevier, vol. 167(1), pages 1-15.
    5. Michal Kolesár, 2013. "Estimation in an Instrumental Variables Model With Treatment Effect Heterogeneity," Working Papers 2013-2, Princeton University. Economics Department..
    6. Marc Hallin & Marcelo Moreira J. & Alexei Onatski, 2013. "Group Invariance, Likelihood Ratio Tests, and the Incidental Parameter Problem in a High-Dimensional Linear Model," Working Papers ECARES ECARES 2013-04, ULB -- Universite Libre de Bruxelles.
    7. Kolesár, Michal, 2018. "Minimum distance approach to inference with many instruments," Journal of Econometrics, Elsevier, vol. 204(1), pages 86-100.
    8. Matsushita, Yukitoshi & Otsu, Taisuke, 2023. "Second-order refinements for t-ratios with many instruments," Journal of Econometrics, Elsevier, vol. 232(2), pages 346-366.
    9. Marcelo Moreira, 2008. "A Maximum Likelihood Method for the Incidental Parameter Problem," NBER Working Papers 13787, National Bureau of Economic Research, Inc.
    10. Matsushita, Yukitoshi & Otsu, Taisuke, 2023. "Second-order refinements for t-ratios with many instruments," LSE Research Online Documents on Economics 111065, London School of Economics and Political Science, LSE Library.
    11. Sølvsten, Mikkel, 2020. "Robust estimation with many instruments," Journal of Econometrics, Elsevier, vol. 214(2), pages 495-512.

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