Robust Permutation Tests in Linear Instrumental Variables Regression
本文在线性工具变量回归中开发了识别稳健检验的置换版本，在标准排除限制条件下，置换AR、LM和CLR检验渐近相似且对条件异方差稳健，当工具变量与结构误差项独立时，置换AR检验是精确的，对厚尾分布也稳健。
This paper 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 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.