We estimate a medium-scale model with and without rule-of-thumb consumers over the pre- Volcker and the Great Moderation periods, allowing for indeterminacy. Passive monetary policy and sunspot fluctuations characterize the pre-Volcker period for both models. The estimated fraction of rule-of-thumb consumers is low, such that the models are empirically almost equivalent. In both subsamples, the two models yield very similar impulse response functions, variance and historical decompositions. We conclude that rule-of-thumb consumers are irrelevant to explain aggregate U.S. business cycle fluctuations.