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Regularization Based Anderson Rubin Tests for Many Instruments

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  • Marine Carrasco
  • Guy Tchuente

Abstract

This paper studies the asymptotic validity of the regularized Anderson Rubin (AR) tests in linear models with large number of instruments. The regularized AR tests use informationreduction methods to provide robust inference in instrumental variable (IV) estimation for data rich environments. We derive the asymptotic properties of the tests. Their asymptotic distribution depend on unknown nuisance parameters. A bootstrap method is used to obtain more reliable inference. The regularized tests are robust to many moment conditions in the sense that they are valid for both few and many instruments, and even for more instruments than the sample size. Our simulations show that the proposed AR tests work well and have better performance than competing AR tests when the number of instruments is very large. The usefulness of the regularized tests is shown by proposing confidence intervals for the Elasticity of Intertemporal Substitution (EIS).

Suggested Citation

  • Marine Carrasco & Guy Tchuente, 2016. "Regularization Based Anderson Rubin Tests for Many Instruments," Studies in Economics 1608, School of Economics, University of Kent.
    • Handle: RePEc:ukc:ukcedp:1608
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    References listed on IDEAS

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    1. Motohiro Yogo, 2004. "Estimating the Elasticity of Intertemporal Substitution When Instruments Are Weak," The Review of Economics and Statistics, MIT Press, vol. 86(3), pages 797-810, August.
    2. Marine Carrasco & Barbara Rossi, 2016. "In-Sample Inference and Forecasting in Misspecified Factor Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(3), pages 313-338, July.
    3. Carrasco, Marine & Tchuente, Guy, 2015. "Regularized LIML for many instruments," Journal of Econometrics, Elsevier, vol. 186(2), pages 427-442.
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    Cited by:

    1. Joel L. Horowitz, 2017. "Non-asymptotic inference in instrumental variables estimation," CeMMAP working papers CWP46/17, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    2. Marine Carrasco & Mohamed Doukali, 2022. "Testing overidentifying restrictions with many instruments and heteroscedasticity using regularised jackknife IV," The Econometrics Journal, Royal Economic Society, vol. 25(1), pages 71-97.
    3. Joel L. Horowitz, 2017. "Non-asymptotic inference in instrumental variables estimation," CeMMAP working papers 46/17, Institute for Fiscal Studies.
    4. Joel L. Horowitz, 2018. "Non-Asymptotic Inference in Instrumental Variables Estimation," Papers 1809.03600, arXiv.org.
    5. Horowitz, Joel L., 2021. "Bounding the difference between true and nominal rejection probabilities in tests of hypotheses about instrumental variables models," Journal of Econometrics, Elsevier, vol. 222(2), pages 1057-1082.
    6. Joel L. Horowitz, 2018. "Non-asymptotic inference in instrumental variables estimation," CeMMAP working papers CWP52/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.

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    Keywords

    Many weak instruments; AR test; Bootstrap; Factor Model;
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