⁷We neglect an uninteresting constant term. will also include any higher-order terms that are discarded in the process of the log-linearization, including terms that reflect the precautionary motive. Note, however, that the excess smoothness of aggregate consumption cannot be explained by a precautionary saving motive in a model without habits (Ludvigson and Michaelides (2001)). See Michaelides (2002) for a careful numerical examination of a model with both habits and a precautionary motive. Unfortunately, that paper does not examine the accuracy of the approximation (3) in the presence of uncertainty, and we are not aware of any other paper that does so. But Carroll and Slacalek (2007) show that the random walk implication of the model without habits survives largely intact for simulated aggregate data for an economy populated by households facing both idiosyncratic and aggregate risk; this suggests that the log-linearized approximation is likely to be plausible.