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 the 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 even 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's magnitude increases with the number of regressors and their average autocorrelation. To address this issue, 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.

翻译：本文研究包含众多回归变量的线性时间序列回归问题。弱外生性是时间序列分析中最常用的识别假设，要求结构误差项在给定当前及过去回归变量值的条件下具有零条件期望，但允许误差项与未来回归变量实现值存在相关性。研究表明，在包含大量控制变量的时间序列回归中，弱外生性条件可能产生显著偏差，甚至导致最小二乘（OLS）估计量不一致。当仅满足弱外生性（而非严格外生性）时，众多回归变量情境下的偏差产生机理在于：归一化OLS设计矩阵保持渐近随机性，并与回归误差项产生相关性。该偏差的幅度随回归变量数量及其平均自相关性的增加而增大。针对此问题，我们提出创新的偏差校正方法，得到相较于OLS具有更优性质的新估计量。本文证明了新估计量的一致性与条件渐近高斯性，并给出相应的推断方法。