A Dimension-Agnostic Bootstrap Anderson-Rubin Test For Instrumental Variable Regressions

Abstract

Weak-identification-robust tests for instrumental variable (IV) regressions are typically developed separately depending on whether the number of IVs is treated as fixed or increasing with the sample size, forcing researchers to make a stance on the asymptotic behavior, which is often ambiguous in practice. This paper proposes a bootstrap-based, dimension-agnostic Anderson-Rubin (AR) test that achieves correct asymptotic size regardless of whether the number of IVs is fixed or diverging, and even accommodates cases where the number of IVs exceeds the sample size. By incorporating ridge regularization, our approach reduces the effective rank of the projection matrix and yields regimes where the limiting distribution of the AR statistic can be a weighted chi-squared, a normal, or a mixture of the two. Strong approximation results ensure that the bootstrap procedure remains uniformly valid across all regimes, while also delivering substantial power gains over existing methods by exploiting rank reduction.