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This paper develops permutation versions of identification-robust tests inlinear instrumental variables (IV) regression. Unlike the existingrandomization and rank-based tests in which independence between theinstruments and the error terms is assumed, the permutation Anderson- Rubin(AR), Lagrange Multiplier (LM) and Conditional Likelihood Ratio (CLR) tests areasymptotically similar and robust to conditional heteroskedasticity understandard exclusion restriction i.e. the orthogonality between the instrumentsand the error terms. Moreover, when the instruments are independent of thestructural error term, the permutation AR tests are exact, hence robust toheavy tails. As such, these tests share the strengths of the rank-based testsand the wild bootstrap AR tests. Numerical illustrations corroborate thetheoretical results.

Robust Permutation Tests in Linear Instrumental Variables Regression