Bootstrapping factor models with cross sectional dependence

Abstract

We consider bootstrap methods for factor-augmented regressions with cross sectional dependence among idiosyncratic errors. This is important to capture the bias of the OLS estimator derived recently by Gonçalves and Perron (2014). We first show that a common approach of resampling cross sectional vectors over time is invalid in this context because it induces a zero bias. We then propose the cross-sectional dependent (CSD) bootstrap where bootstrap samples are obtained by taking a random vector and multiplying it by the square root of a consistent estimator of the covariance matrix of the idiosyncratic errors. We show that if the covariance matrix estimator is consistent in the spectral norm, then the CSD bootstrap is consistent, and we verify this condition for the thresholding estimator of Bickel and Levina (2008). Finally, we apply our new bootstrap procedure to forecasting inflation using convenience yields as recently explored by Gospodinov and Ng (2013).