Bootstrapping factor-augmented regression models

This paper proposes and theoretically justifies bootstrap methods for regressions where some of the regressors are factors estimated from a large panel of data. We derive our results under the assumption that T / N → c , where 0 ≤ c < ∞ ( N  and T  are the cross-sectional and the time series dimensions, respectively), thus allowing for the possibility that the factor estimation error enters the limiting distribution of the OLS estimator as an asymptotic bias term (as was recently discussed by Ludvigson and Ng (2011)). We consider general residual-based bootstrap methods and provide a set of high-level conditions on the bootstrap residuals and on the idiosyncratic errors such that the bootstrap distribution of a rotated OLS estimator is consistent. We subsequently verify these conditions for a simple wild bootstrap residual-based procedure.