Testing for Correlation between the Regressors and Factor Loadings in Heterogeneous Panels with Interactive Effects

G. Kapetanios, Laura Serlenga, Yongcheol Shin

Research output: Contribution to journalArticlepeer-review


A large literature on modelling cross-section dependence in panels has been developed through interactive effects. However, there are areas where research has not really caught on yet. One such area is the one concerned with whether the regressors are correlated with factor loadings or not. This is an important issue because if the regressors are uncorrelated with loadings, we can simply use the consistent two-way fixed effects (FE) estimator without employing any more sophisticated econometric methods such as the principal component
(PC) or the common correlated effects estimators. We explore this issue, which has received surprisingly little attention and propose a Hausman-type test to address the matter. Further, we develop two nonparametric variance estimators for the FE and PC estimators as well as their difference, that are robust to the presence of heteroscedasticity, autocorrelation and slope heterogeneity. Under the null hypothesis of no correlation between the regressors and loadings the proposed test follows the chi-squared distribution asymptotically. Monte Carlo simulation results confirm satisfactory size and power performance of the test even in small samples. Finally, we provide extensive empirical evidence in favour of uncorrelated factor loadings. In this situation, the FE estimator would provide a simple and robust estimation strategy which is invariant to nontrivial computational issues associated with the PC estimator.
Original languageEnglish
Pages (from-to)2611–2659
JournalEmpirical Economics
Early online date11 May 2023
Publication statusE-pub ahead of print - 11 May 2023

Bibliographical note

© The Author(s) 2023


  • Panel Data Model with Interactive Effects
  • Correlation between the Regressors and Factor Loadings
  • Robust Variance Estimators
  • Hausman-type Test

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