In a Vox column describing their findings, they report that the policy did work, after all. A couple of the main conclusions:
[T]he average household increased its weekly expenditures on non-durable goods by 3.5% after receipt of the rebate. The impact is highest in the week where the rebate is received (not reported) with weekly spending increasing by almost 6% on average during the first week. We find no impact on spending in the few weeks prior to the receipt of the rebate.Interesting - economic theory would imply that households should change their consumption when they get the news of the stimulus, rather than waiting for the check actually arriving. This suggests that households are either myopic, or that credit constraints are binding.
[O]ur estimates imply that the receipt of the tax rebates directly raised nondurable PCE by 2.4% in the second quarter of 2008 and will raise it by 4.1% in the third quarter.Update (8/20): Macroblog (hooray, it's back) weighs in.