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Robust Permutation Tests in Linear Instrumental Variables Regression

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  • Purevdorj Tuvaandorj

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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  • Purevdorj Tuvaandorj, 2021. "Robust Permutation Tests in Linear Instrumental Variables Regression," Papers 2111.13774, arXiv.org, revised Jun 2023.
    • Handle: RePEc:arx:papers:2111.13774
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    Cited by:

    1. Xavier D'Haultf{oe}uille & Purevdorj Tuvaandorj, 2022. "A Robust Permutation Test for Subvector Inference in Linear Regressions," Papers 2205.06713, arXiv.org, revised Sep 2023.

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