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Weak-instrument-robust subvector inference in instrumental variables regression: A subvector Lagrange multiplier test and properties of subvector Anderson-Rubin confidence sets

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  • Malte Londschien
  • Peter Buhlmann

Abstract

We propose a weak-instrument-robust subvector Lagrange multiplier test for instrumental variables regression. We show that it is asymptotically size-correct under a technical condition. This is the first weak-instrument-robust subvector test for instrumental variables regression to recover the degrees of freedom of the commonly used non-weak-instrument-robust Wald test. Additionally, we provide a closed-form solution for subvector confidence sets obtained by inverting the subvector Anderson-Rubin test. We show that they are centered around a k-class estimator. Also, we show that the subvector confidence sets for single coefficients of the causal parameter are jointly bounded if and only if Anderson's likelihood-ratio test rejects the hypothesis that the first-stage regression parameter is of reduced rank, that is, that the causal parameter is not identified. Finally, we show that if a confidence set obtained by inverting the Anderson-Rubin test is bounded and nonempty, it is equal to a Wald-based confidence set with a data-dependent confidence level. We explicitly compute this Wald-based confidence test.

Suggested Citation

  • Malte Londschien & Peter Buhlmann, 2024. "Weak-instrument-robust subvector inference in instrumental variables regression: A subvector Lagrange multiplier test and properties of subvector Anderson-Rubin confidence sets," Papers 2407.15256, arXiv.org, revised Nov 2024.
    • Handle: RePEc:arx:papers:2407.15256
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    References listed on IDEAS

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    1. Cragg, John G. & Donald, Stephen G., 1997. "Inferring the rank of a matrix," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 223-250.
    2. Jean-Marie Dufour & Mohamed Taamouti, 2005. "Projection-Based Statistical Inference in Linear Structural Models with Possibly Weak Instruments," Econometrica, Econometric Society, vol. 73(4), pages 1351-1365, July.
    3. Patrik Guggenberger & Frank Kleibergen & Sophocles Mavroeidis & Linchun Chen, 2012. "On the Asymptotic Sizes of Subset Anderson–Rubin and Lagrange Multiplier Tests in Linear Instrumental Variables Regression," Econometrica, Econometric Society, vol. 80(6), pages 2649-2666, November.
    4. Kleibergen, Frank, 2021. "Efficient size correct subset inference in homoskedastic linear instrumental variables regression," Journal of Econometrics, Elsevier, vol. 221(1), pages 78-96.
    5. Kleibergen, Frank, 2007. "Generalizing weak instrument robust IV statistics towards multiple parameters, unrestricted covariance matrices and identification statistics," Journal of Econometrics, Elsevier, vol. 139(1), pages 181-216, July.
    6. Martin Emil Jakobsen & Jonas Peters, 2020. "Distributional robustness of K-class estimators and the PULSE," Papers 2005.03353, arXiv.org, revised Mar 2022.
    7. Hillier, Grant, 2009. "On The Conditional Likelihood Ratio Test For Several Parameters In Iv Regression," Econometric Theory, Cambridge University Press, vol. 25(2), pages 305-335, April.
    8. David Card, 1993. "Using Geographic Variation in College Proximity to Estimate the Return to Schooling," Working Papers 696, Princeton University, Department of Economics, Industrial Relations Section..
    9. Patrik Guggenberger & Frank Kleibergen & Sophocles Mavroeidis, 2019. "A more powerful subvector Anderson Rubin test in linear instrumental variables regression," Quantitative Economics, Econometric Society, vol. 10(2), pages 487-526, May.
    10. Marcelo J. Moreira, 2003. "A Conditional Likelihood Ratio Test for Structural Models," Econometrica, Econometric Society, vol. 71(4), pages 1027-1048, July.
    11. James H. Stock & Motohiro Yogo, 2002. "Testing for Weak Instruments in Linear IV Regression," NBER Technical Working Papers 0284, National Bureau of Economic Research, Inc.
    12. Martin Emil Jakobsen & Jonas Peters, 2022. "Distributional robustness of K-class estimators and the PULSE [The colonial origins of comparative development: An empirical investigation]," The Econometrics Journal, Royal Economic Society, vol. 25(2), pages 404-432.
    13. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
    14. Frank Kleibergen, 2002. "Pivotal Statistics for Testing Structural Parameters in Instrumental Variables Regression," Econometrica, Econometric Society, vol. 70(5), pages 1781-1803, September.
    15. Dominik Rothenhäusler & Nicolai Meinshausen & Peter Bühlmann & Jonas Peters, 2021. "Anchor regression: Heterogeneous data meet causality," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(2), pages 215-246, April.
    16. Morimune, Kimio, 1993. "A Derivation of the Limited Information Maximum Likelihood Estimator," Econometric Theory, Cambridge University Press, vol. 9(02), pages 315-316, April.
    17. Tomomi Tanaka & Colin F. Camerer & Quang Nguyen, 2010. "Risk and Time Preferences: Linking Experimental and Household Survey Data from Vietnam," American Economic Review, American Economic Association, vol. 100(1), pages 557-571, March.
    18. David Card, 1993. "Using Geographic Variation in College Proximity to Estimate the Return to Schooling," NBER Working Papers 4483, National Bureau of Economic Research, Inc.
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