AI 中文总结
本文针对工具变量回归中异常值影响系数估计的问题，建立渐近理论改进常规启发式方法，提出含偏差校正的修剪2SLS、Hausman型检验及迭代方法，其不动点与Huber-skip M估计量渐近性质一致，模拟与实证示例验证了方法有效性。
AI 中文摘要
实证建模中一个常见问题是，估计的回归系数是否会受到少量异常观测值的影响。在工具变量回归的实际应用中，开展异常值稳健性检验的常规做法是运行普通两阶段最小二乘法（2SLS），并剔除标准化残差超出选定临界值的观测值，随后计算修剪后的2SLS并与原始全样本2SLS进行比较。本文旨在通过建立渐近理论来理解和改进上述启发式方法，具体有三项主要贡献：第一，即使在模型不含异常值的原假设下，修剪后的2SLS也有正概率剔除观测值；在此情况下，本文推导了修剪后2SLS的极限正态分布，其渐近方差为普通2SLS方差乘以相对效率膨胀因子，此外，本文为结构误差的方差估计量引入了偏差校正因子，否则该方差估计量会向下偏误。第二，本文构造了一种Hausman型检验，以形式化比较两种2SLS估计量的启发式方法。第三，修剪后的2SLS是一种两步方法，可迭代至达到不动点，该不动点被证明具有与Huber-skip M估计量相同的一阶渐近性质。本文的分析涉及一类新的经验过程，其理论在应用概率论中具有独立价值；模拟研究为该渐近理论提供了支持，对Acemoglu等人（2019）的实证示例也展示了所提方法的实用性。
英文摘要
A common concern in empirical modelling centres around whether estimated regression coefficients are affected by a small set of outlying observations. To conduct outlier robustness checks in practical applications of instrumental variables regressions, the common practice is to run ordinary two stage least squares (2SLS) and remove observations with standardised residuals beyond a chosen cut-off value. Subsequently, the trimmed 2SLS is computed and compared to the original full-sample 2SLS. This paper aims to understand and improve the above heuristic procedure by establishing an asymptotic theory. Specifically, there are three main contributions of the paper. First, the trimmed 2SLS has a positive probability of removing observations even under the null hypothesis where the model contains no outliers. Under this situation, we derive a limiting Normal distribution of the trimmed 2SLS with the asymptotic variance as the ordinary one multiplied by a relative efficiency inflator. Furthermore, a bias correction factor is introduced for the variance estimator of structural errors, which otherwise would be downward biased. Second, a Hausman-type test is constructed to formalize the heuristic procedure of comparing between the two 2SLS estimators. Third, the trimmed 2SLS is a two-step procedure, which can be iterated until a fixed point is reached. The fixed point is shown to have the same first order asymptotics as the Huber-skip M-estimator. Our analysis involves a new class of empirical processes, whose theory would be of independent interest in applied probability. Simulation studies lend support to the asymptotic theory. An empirical illustration to Acemoglu et al. (2019) shows the utility of the proposed method.
Comments76 pages, including appendices; 4 figures, 4 tables
