🤖 AI Summary
This paper addresses the failure of residual cross-sectional dependence tests in latent factor panel models. We propose a bias-corrected CD* test statistic. Theoretically, we first establish the asymptotic validity of the standard CD test under weak factors and rigorously derive the asymptotic standard normality of CD* under the null hypothesis, while demonstrating its high local power against network-type alternatives. Methodologically, the CD* test integrates factor estimation, residual extraction, and analytical bias correction, accommodating both strong and weak factors as well as serially correlated errors. Monte Carlo simulations show that CD* achieves accurate size and superior power in small samples, consistently outperforming the JR test. Empirically, applying CD* to a housing price dynamics model across 377 U.S. metropolitan statistical areas reveals statistically significant spatial dependence in residuals.
📝 Abstract
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.