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In a recent paper Juodis and Reese (2022) (JR) show that the application ofthe CD test proposed by Pesaran (2004) to residuals from panels with latentfactors results in over-rejection. They propose a randomized test statistic tocorrect for over-rejection, and add a screening component to achieve power.This paper considers the same problem but from a different perspective, andshows that the standard CD test remains valid if the latent factors are weak inthe sense the strength is less than half. In the case where latent factors arestrong, we propose a bias-corrected version, CD*, which is shown to beasymptotically standard normal under the null of error cross-sectionalindependence and have power against network type alternatives. This result isshown to hold for pure latent factor models as well as for panel regressionmodels with latent factors. The case where the errors are serially correlatedis also considered. Small sample properties of the CD* test are investigated byMonte Carlo experiments and are shown to have the correct size for strong andweak factors as well as for Gaussian and non-Gaussian errors. In contrast, itis found that JR's test tends to over-reject in the case of panels withnon-Gaussian errors, and has low power against spatial network alternatives. Inan empirical application, using the CD* test, it is shown that there remainsspatial error dependence in a panel data model for real house price changesacross 377 Metropolitan Statistical Areas in the U.S., even after the effectsof latent factors are filtered out.

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