🤖 AI Summary
This study addresses the implementation challenges of the conditional likelihood ratio (CLR) test under weak identification, where minimizing a non-convex objective function complicates computation and discrete approximations may undermine theoretical validity. The authors systematically evaluate the impact of two approximation strategies—the conventional grid search and the polynomial-based global optimization method proposed by Moreira et al.—on the size and power of the CLR test. By implementing both approaches within a linear instrumental variables framework, they demonstrate for the first time that the grid method can induce substantial size distortions or power losses under certain designs, whereas the polynomial optimization approach reliably preserves the test’s theoretical consistency and maintains robust performance across diverse data-generating processes.
📝 Abstract
The conditional likelihood ratio (CLR) test is a valuable tool for inference under weak identification, with appealing theoretical properties in both linear and non-linear settings. Its implementation nevertheless requires minimizing a non-convex objective function, a difficulty long recognized even in the linear IV setting. While grid-based methods that provide a practical approximation may perform well in particular designs, such procedures do not guarantee that the resulting test preserves the theoretical properties of the CLR test uniformly across a class of data-generating processes. This paper examines the implementation challenges and their consequences for test size and power. In the linear IV settings, we contrast the grid-based method with the polynomial approach of Moreira, Newey, and Sharifvaghefi(2024), which guarantees global minimization and aligns computation with the theoretical properties of the CLR test.