Cross-Section Regression with Common Shocks
存在共同冲击的横截面回归AI 解读 ↓
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存在共同冲击的横截面回归
- 研究问题
- 横截面单位因共同冲击而相互依赖时，最小二乘估计何时仍然一致，通常的检验与置信区间又何时会出现严重失效？
- 方法与思路
- 作者在允许横截面依赖和个体异质性的框架下推导最小二乘概率极限与渐近分布，并将结果应用于一般及异质、函数型因子结构。
- 材料陈述的贡献
- 摘要给出一致性充要条件及重定心、缩放后的混合正态极限；被检验参数不满足一致性条件时，相关统计量在原假设下也发散。
- 阅读关注点
- 应核对共同冲击进入解释变量与误差的方式、一致性条件和重定心步骤，以及检验的缩放、方差估计与因子结构扩展。
- 阅读边界
- 摘要未列出具体一致性条件或方差估计要求；共同冲击是否无害须逐模型判断，不能据此认可任意横截面回归的常规推断。
原文摘要
This paper considers regression models for cross-section data that exhibit cross-section dependence due to common shocks, such as macroeconomic shocks. The paper analyzes the properties of least squares (LS) estimators in this context. The results of the paper allow for any form of cross-section dependence and heterogeneity across population units. The probability limits of the LS estimators are determined, and necessary and sufficient conditions are given for consistency. The asymptotic distributions of the estimators are found to be mixed normal after recentering and scaling. The t, Wald, and F statistics are found to have asymptotic standard normal, χ2, and scaled χ2 distributions, respectively, under the null hypothesis when the conditions required for consistency of the parameter under test hold. However, the absolute values of t, Wald, and F statistics are found to diverge to infinity under the null hypothesis when these conditions fail. Confidence intervals exhibit similarly dichotomous behavior. Hence, common shocks are found to be innocuous in some circumstances, but quite problematic in others. Models with factor structures for errors and regressors are considered. Using the general results, conditions are determined under which consistency of the LS estimators holds and fails in models with factor structures. The results are extended to cover heterogeneous and functional factor structures in which common factors have different impacts on different population units.