Before revision:  We justify this procedure under N, T \to \infty asymptotics where we allow T to be much smaller than N. As part of our theoretical arguments, we develop new simultaneous anti-concentration inequalities for the MAX and the QLR statistics. Monte Carlo results indicate that our confidence sets have adequate coverage and are informative. We illustrate the practical relevance of our confidence sets in two applications .
After revision:  We justify this procedure under N, T \to \infty asymptotics using tools from high-dimensional statistics, some of which we extend or develop in this paper. We provide an empirical application as well as Monte Carlo evidence that the confidence set has adequate coverage in finite samples .