How to Detect Network Dependence in Latent Factor Models? A Bias-Corrected CD Test
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潜在因子模型中的网络依赖检测：偏误修正 CD 检验
- 研究问题
- 面板中的潜在共同因子被估计并剔除后，如何检验残差是否仍存在网络型截面依赖，避免标准 CD 检验在强因子下过度拒绝？
- 方法与思路
- 作者区分弱因子与强因子情形，为强因子提出偏误修正的 CD* 检验，并研究纯因子模型、含因子面板回归及误差序列相关情况。
- 材料陈述的贡献
- 摘要称因子强度小于二分之一时原 CD 检验仍有效，CD* 在零假设下渐近标准正态且对网络备择有功效，并展示模拟及美国房价应用。
- 阅读关注点
- 应核对因子强度的定义、偏误修正量与因子估计的关系、截面及时间维度的条件，以及序列相关和非高斯误差下的检验构造。
- 阅读边界
- 所据为 arXiv 预印本，不能据此确认同行评审或期刊接收；摘要未给完整渐近条件，模拟中的相对表现不能推广至所有网络结构。
原文摘要
In a recent paper Juodis and Reese (2022) (JR) show that the application of the CD test proposed by Pesaran (2004) to residuals from panels with latent factors results in over-rejection. They propose a randomized test statistic to correct for over-rejection, and add a screening component to achieve power. This paper considers the same problem but from a different perspective, and shows that the standard CD test remains valid if the latent factors are weak in the sense the strength is less than half. In the case where latent factors are strong, we propose a bias-corrected version, CD*, which is shown to be asymptotically standard normal under the null of error cross-sectional independence and have power against network type alternatives. This result is shown to hold for pure latent factor models as well as for panel regression models with latent factors. The case where the errors are serially correlated is also considered. Small sample properties of the CD* test are investigated by Monte Carlo experiments and are shown to have the correct size for strong and weak factors as well as for Gaussian and non-Gaussian errors. In contrast, it is found that JR's test tends to over-reject in the case of panels with non-Gaussian errors, and has low power against spatial network alternatives. In an empirical application, using the CD* test, it is shown that there remains spatial error dependence in a panel data model for real house price changes across 377 Metropolitan Statistical Areas in the U.S., even after the effects of latent factors are filtered out.