Robust Permutation Tests in Linear Instrumental Variables Regression

This article develops permutation versions of identification-robust tests in linear instrumental variables 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 heteroscedasticity under standard exclusion restriction, that is, 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. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.