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

2024-12-02

AI Summary

Conventional weak-identification-robust inference—particularly the Anderson–Rubin (AR) test—requires prespecifying the asymptotic regime of instrument dimensionality (fixed, diverging, or ultra-high), leading to ad hoc, path-dependent procedures and ambiguous dimensionality assumptions. Method: We propose a bootstrap-based AR test that dispenses with any asymptotic assumption on instrument dimension. Grounded in strong approximation theory, it uniformly handles fixed-, high-, and ultra-high-dimensional instruments. Contribution/Results: Our method achieves asymptotic size control uniformly over parameter spaces under both conventional and many-instrument asymptotics—the first such result for AR-type tests. It guarantees uniform Type I error control and exhibits robust statistical power against weak identification. Simulations demonstrate substantial gains in finite-sample performance over existing case-specific alternatives, especially in moderate-dimensional settings.

Technology Category

• Intelligent Robots: State Estimation
• Machine Learning: Adversarial Learning & Robustness
• Game Theory and Economic Paradigms: Mechanism Design

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

Weak-identification-robust Anderson-Rubin (AR) 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. These tests rely on distinct test statistics and critical values. To apply them, researchers are forced to take a stance on the asymptotic behavior of the number of IVs, which can be ambiguous when the number is moderate. In this paper, we propose a bootstrap-based, dimension-agnostic AR test. By deriving strong approximations for the test statistic and its bootstrap counterpart, we show that our new test has a correct asymptotic size regardless of whether the number of IVs is fixed or increasing -- allowing, but not requiring, the number of IVs to exceed the sample size. We also analyze the power properties of the proposed uniformly valid test under both fixed and increasing numbers of IVs.

Problem

• Develops a dimension-agnostic AR test for IV regressions
• Achieves correct asymptotic size regardless of IV count
• Accommodates cases where IVs exceed sample size

Innovation

• Bootstrap Anderson-Rubin test works with varying IV dimensions
• Ridge regularization reduces projection matrix effective rank
• Uniformly valid bootstrap across all asymptotic regimes