How to Detect Network Dependence in Latent Factor Models? A Bias-Corrected CD Test
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.