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It has been shown in previous work that bootstrapping the J test for nonnested linear regression models dramatically improves its finite-sample performance. We provide evidence that a more sophisticated bootstrap procedure, which we call the fast double bootstrap, produces a very substantial further improvement in cases where the ordinary bootstrap does not work as well as it might. This FDB procedure is only about twice as expensive as the usual single bootstrap.doi:10.1081/etc-120015384 fatcat:3qwbozyz6zdolpwpm6w53zxnn4