Before revision:  We first show that the pairs bootstrap that samples cross-sectional units with replacement does not approximate well the limiting distribution of the penalized estimator. We then propose a wild residual bootstrap procedure and show that it is asymptotically valid for approximating the distribution of the penalized estimator.
After revision:  We propose a wild residual bootstrap procedure and show that it is asymptotically valid for approximating the distribution of the penalized estimator.