Robust Permutation Tests in Linear Instrumental Variables Regression

TL;DR

This paper introduces permutation-based tests for linear IV regression that are robust to heteroskedasticity and heavy tails, providing more reliable inference under weaker assumptions.

Contribution

It develops permutation versions of AR, LM, and CLR tests that are asymptotically similar and exact under certain conditions, enhancing robustness in IV analysis.

Findings

Permutation tests are asymptotically similar to classical tests.

Permutation AR tests are exact under independence.

Numerical results support theoretical robustness.

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.