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This is a very interesting paper. However, one point to note is that it seems to assume an autocorrelation of 1 between baseline outcomes and follow-up outcomes when doing its simulation exercises. For many economic variables the autocorrelation is much lower, and so achieving such strong balance on baseline is no guarantee that balance will be as good at follow-up if there is no treatment effect - and so the power gains from baseline balance are much lower. My AEJ-Applied paper with Miriam Bruhn shows this for the case of pairwise matching and re-randomization, where the gains over pure randomization are much lower for outcomes like profits and consumption (low autocorrelation) than they are for test scores (high autocorrelation). I would think the same would be true for this method.