a href"https:cms.hoover.orgresearchstochastic-implications-life-cycle-permanent-income-hypothesis-theory-and-evidence" hreflang"en"Stochastic Implications of the Life Cycle-Permanent Income Hypothesis: Theory and Evidencea

Optimization of the part of consumers is shown to imply that the marginal utility of consumption evolves according to a random walk with trend. To a reasonable approximation, consumption itself should evolve in the same way. In particular, no variable apart from current consumption should be of any value in predicting future consumption.