Cross-Section Bootstrap for CCE Regressions with General Unknown Factors

The Common Correlated Effects (CCE) approach enjoys considerable popularity for estimating factor-augmented panel data models. A key benefit is that by orthogonalizing the data on the available cross-section averages, the unobserved components are eliminated from the data, regardless of their order(s) of integration. This obviates the need for such knowledge, and makes CCE particularly attractive for macroeconomic applications, where the set of unobservables might contain both stationary and non-stationary variables. Despite of these benefits, it is often neglected that the pooled CCE (CCEP) estimator suffers from an asymptotic bias in TN−1→τ>0 panels, which too is common in macroeconomic research. This bias is highly disruptive for inference but cannot generally be remedied with analytical corrections. As such, we establish in this paper the validity of the cross-section bootstrap under general unknown factors for TN−1→τ<∞ as (N,T)→∞. We show that the scheme replicates the distribution of the CCE estimators, leading to a straightforward bias-correction, and confidence intervals that enable asymptotically valid inference for τ<∞. This significantly broadens the applicability of the CCEP method. We in addition explore the case where idiosyncratics serve as another source of non-stationarity. Simulation experiments show that our theoretical predictions translate well to finite samples, and that the methodology outperforms alternative bias-corrections and estimators. The method is finally demonstrated with a gravity trade application based on the dataset of Serlenga and Shin (2007).