A Heteroskedasticity-Robust Overidentifying Restriction Test with High-Dimensional Covariates

Area of Science:

• Econometrics
• Statistics

Background:

• High-dimensional instrumental variable (IV) models are crucial for causal inference in econometrics.
• Existing overidentifying restriction tests often fail when the number of covariates and instruments exceeds the sample size.

Purpose of the Study:

• To propose a novel overidentifying restriction test for high-dimensional linear IV models.
• To develop a test that accommodates more covariates and instruments than the sample size.
• To enhance the power and robustness of existing tests in challenging data scenarios.

Main Methods:

• The proposed test utilizes a maximum norm approach for high-dimensional parameters.
• A power-enhanced version is introduced, incorporating an asymptotically zero component.
• The test is designed to be scale-invariant and robust to heteroskedastic errors.

Main Results:

• The maximum norm test demonstrates higher theoretical power than the modified Cragg-Donald test for large-dimensional covariates.
• The power-enhanced test improves detection of extreme alternatives, particularly with numerous locally invalid instruments.
• The test's practical utility is validated through an empirical example on trade and economic growth.

Conclusions:

• The developed overidentifying restriction test is effective for high-dimensional IV models.
• The test provides a valuable tool for causal inference in econometrics with large datasets.
• The findings contribute to robust statistical inference in complex economic modeling.