Linear regression with weak exogeneity

• 成果类型: Article
• 署名作者: Mikusheva, Anna; Solvsten, Mikkel
• 署名单位: Massachusetts Institute of Technology (MIT); Aarhus University
• 刊物名称: QUANTITATIVE ECONOMICS
• ISSN/ISSBN: 1759-7323
• DOI: 10.3982/QE2622
• 发表日期: 2025
• 页码: 367-403
• 关键词: Time-series regression; weak exogeneity; many controls; feedback bias; OLS inconsistency; bias correction; valid inference; C13; C22

摘要

This paper studies linear time-series regressions with many regressors. Weak exogeneity is the most used identifying assumption in time series. Weak exogeneity requires the structural error to have zero conditional expectation given present and past regressor values, allowing errors to correlate with future regressor realizations. We show that weak exogeneity in time-series regressions with many controls may produce substantial biases and render the least squares (OLS) estimator inconsistent. The bias arises in settings with many regressors because the normalized OLS design matrix remains asymptotically random and correlates with the regression error when only weak (but not strict) exogeneity holds. This bias' magnitude increases with the number of regressors and their average autocorrelation. We propose an innovative approach to bias correction that yields a new estimator with improved properties relative to OLS. We establish consistency and conditional asymptotic Gaussianity of this new estimator and provide a method for inference.