Consumption habits in a New Keynesian business cycle model

Consumption habits have become an integral component in new Keynesian models. However, consumption habits can be modeled in a host of different ways and this diversity is reflected in the literature. I examine whether different approaches to modeling consumption habits have important implications for business cycle behavior. Using a standard New Keynesian business cycle model, I show that, to a first-order log-approximation, the consumption Euler equation associated with the additive functional form for habit formation encompasses the multiplicative function form. Empirically, I show that whether consumption habits are internal or external has little effect on the model's business cycle characteristics