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Robust Permutation Tests in Linear Instrumental Variables Regression

Purevdorj Tuvaandorj

arXiv 26 Nov 2021 · Econometrics · publishedJournal of the American Statistical Association (2024) · 3 citations (OpenAlex)

arXiv:2111.13774 · PDF · DOI · OpenAlex · Extracted main text

Abstract

This paper develops permutation versions of identification-robust tests in linear instrumental variables (IV) regression. Unlike the existing randomization and rank-based tests in which independence between the instruments and the error terms is assumed, the permutation Anderson- Rubin (AR), Lagrange Multiplier (LM) and Conditional Likelihood Ratio (CLR) tests are asymptotically similar and robust to conditional heteroskedasticity under standard exclusion restriction i.e. the orthogonality between the instruments and the error terms. Moreover, when the instruments are independent of the structural error term, the permutation AR tests are exact, hence robust to heavy tails. As such, these tests share the strengths of the rank-based tests and the wild bootstrap AR tests. Numerical illustrations corroborate the theoretical results.

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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Andrews, D. W. and Guggenberger, P (2019) Identification-and Singularity-Robust Inference for Moment Condition Models1.00093100%
2Andrews, D. W. K. and Marmer, V (2008) Exactly Distribution-Free Inference in Instrumental Variables Regression with Possibly Weak Instruments1.00073100%
3Moreira, M. J (2003) A Conditional Likelihood Ratio Test for Structural Models0.92843100%
4Andrews, D. W. K. and Soares, G (2007) Rank Tests for Instrumental Variables Regression with Weak Instruments0.87452100%
5Andrews, D. W. K. and Guggenberger, P (2019) Supplemental material to “Identification-and Singularity-Robust Inference for Moment Condition Models"0.81142100%
6Davidson, R. and MacKinnon, J. G (2012) Wild Bootstrap Tests for IV Regression0.81142100%
7DiCiccio, C. J. and Romano, J. P (2017) Robust Permutation Tests for Correlation and Regression Coefficients0.81142100%
8Imbens, G. W. and Rosenbaum, P. R (2005) Robust, Accurate Confidence Intervals with a Weak Instrument: Quarter of Birth and Education0.81142100%
9Lehmann, E. L. and Romano, J. P (2005) Testing Statistical Hypotheses0.81142100%
10Andrews, D. W. K., Cheng, X. and Guggenberger, P (2020) Generic Results for Establishing the Asymptotic Size of Confidence Sets and Tests0.73732100%

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Cited by, within the corpus

arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.

Citing paperIntensityMentionsSections
1Wild Bootstrap Inference for Instrumental Variables Regressions with Weak and Few Clusters0.40511
2A Robust Permutation Test for Subvector Inference in Linear Regressions0.40511
3Gradient Wild Bootstrap for Instrumental Variable Quantile Regressions with Weak and Few Clusters0.40511
4A Dimension-Agnostic Bootstrap Anderson-Rubin Test For Instrumental Variable Regressions0.40511
5Robust Inference with High-Dimensional Instruments0.40511
6Randomization Inference For the Always-Reporter Average Treatment Effect0.40511