In an attempt to predict a peak in the US economy using a classical statistical decision methodology and a Bayesian methodology and using the 1996 revised composite leading economic indicators (CLI), it is learned that the Bayesian models have generally outperformed the classical statistical ones and, among the Bayesian models, the two using two and three consecutive CLI growth rates are superior in reliability and in accuracy. These two models, however, failed to correctly predict the 2001 recession. In investigating the reasons behind their failures, we learned that: (1) if the concurrent data for the economic structure of 1983–1999 are used for the prediction, they have also been able to predict the 2001 recession correctly, but their overall reliability is not as strong as before; (2) given the overwhelming weight of the monetary policy tools in the CLI-1996 design and the combination of the economic and political events in the year 2000, the less than expected effectiveness of the monetary policy since 2001 has contributed to this failure; and (3) a possible structural change in the US economy since 2000 has also contributed to this prediction failure.