An Exact Analysis of Precautionary Consumption Growth

While macro models increasingly incorporate substantial risk, the theoretical knowledge about the effect of uncertainty on consumption growth consists of intuitions from the second order log-linearized Euler equation. I show that the derivation of the log-linearized Euler equation is flawed in that it does not consist in linearizing an Euler equation but in linearizing an ad-hoc mathematical identity. I prove exactly that uncertainty raises consumption growth and makes consumption depart from a random walk. I also prove that this precautionary consumption growth is decreasing in assets, and in transitory and permanent income when income is a transitory-permanent process.