A Simple Robust Procedure in Instrumental Variables Regression
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工具变量回归中的简便稳健程序
- 研究问题
- 在工具变量回归中，按标准化残差阈值删除观测再估计的常用检查，会怎样影响渐近分布和方差估计，如何将比较正式化？
- 方法与思路
- 作者推导截尾两阶段最小二乘的渐近理论，修正误差方差估计，构造 Hausman 型检验，并研究重复截尾达到固定点的性质。
- 材料陈述的贡献
- 摘要称，无异常值时截尾仍可能删除观测，并需调整渐近方差；迭代固定点与 Huber-skip M 估计具有相同一阶渐近性质。
- 阅读关注点
- 应核对残差截尾规则、误差与工具变量条件、效率调整和方差修正公式，以及固定点存在性和 Hausman 型检验的原假设。
- 阅读边界
- 这是预印本，同行评审及期刊接收未核实。摘要未说明弱工具变量或污染分布下的保证，截尾不能仅凭名称被视为普遍稳健。
原文摘要
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.