Bootstrap inference for group factor models

Andreou et al. (2019) have proposed a test for common factors based on canonical correlations between factors estimated separately from each group. We propose a simple bootstrap test that avoids the need to estimate the bias and variance of the canonical correlations explicitly and provide high-level conditions for its validity. We verify these conditions for a wild bootstrap scheme similar to the one proposed in Gonçalves and Perron (2014). Simulation experiments show that this bootstrap approach leads to null rejection rates closer to the nominal level in all of our designs compared to the asymptotic framework.