Consumption Does Not Evolve as a Random Walk Around Small Income Shocks

While Hall (1978) argues that the solution for consumption of a life-cycle model with uncertainty and isoelastic preferences evolves as a random walk in first order approximation around small income shocks, I show that it does not. First, I explain that the solution for consumption departs from a random walk because of precautionary behavior. A prudent household facing uncertainty allocates more of its resources to the uncertain future, raising its future consumption growth to an extent that depends on its current variables. This precautionary component of consumption growth does not disappear in first order approximation around small realized income shocks because it relates to the magnitude of the uncertainty ex-ante, not to the magnitude of the realized shocks ex-post. Second, I account for the previous literature that finds consumption to evolve approximately as a random walk: I show that there is an element of circular reasoning in the derivation of a random walk expression. Third, I assess the importance of the correlation of assets, total income and transitory income with subsequent consumption growth in a calibrated life-cycle model. I find all correlations to be highly significant. ∗Economics Department, European University Institute, Via dei Roccettini 9, 50014 San Domenico di Fiesole, Italy; [email protected]. ’Indeed, when Hall first presented the paper deriving and testing the random-walk result, one prominent macroeconomist told him that he must have been on drugs when he wrote the paper.’ David Romer, Advanced Macroeconomics, 4th Edition, April 2011, p375