Does habit formation always increase the agents' desire to smooth consumption?

In the literature, habit formation has been often introduced to enhance the agents' desire to smooth consumption over time. This characteristic was found particularly useful in solving the equity premium puzzle and in matching several stylized facts in growth, and business cycles theory as, for example, the high persistence in the U.S. output volatility. In this paper we propose a definition of habit formation, which is ``general'' relative to the assumptions on the intensity, persistence, and lag structure, and we unveil two mechanisms which point to the opposite direction: habits may reduce the desire of smoothing consumption over time and then may potentially decrease the power of a model in explaining the previously mentioned facts. More precisely, we propose a complete taxonomy of the rich dynamics which may emerge in an AK model with external addictive habits for all the feasible combinations of the intensity, persistence and lag structure characterizing their formation and we point out to the region in the parameters' space coherent with less smoothing in consumption. An economic explanation of these mechanisms is suggested and the robustness of our results in the case of internal habits verified. Finally and crucially habit formation always reduces the desire of consumption smoothing once the model is calibrated to match the average U.S. output and utility growth rates observed in the data.