Abstract: The main contribution of this paper is to propose and theoretically justify 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 $\sqrt{T}/N \rightarrow c$, where $0\leq c < \infty$ ($N$ and $T$ are the cross-sectional and the time series dimensions, respectively) thus allowing for the possibility that factors estimation error enters the limiting distribution of the OLS estimator. 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 the OLS estimator is consistent. We subsequently verify these conditions for a simple wild bootstrap residual-based procedure.