Precautionary saving and the marginal propensity to consume out of permanent income

The budget constraint requires that, eventually, consumption must adjust fully to any permanent shock to income. Intuition suggests that, knowing this, optimizing agents will fully adjust their spending immediately upon experiencing a permanent shock. However, this paper shows that if consumers are impatient and are subject to transitory as well as permanent shocks, the optimal marginal propensity to consume out of permanent shocks (the MPCP) is strictly less than one, because buffer-stock savers have a target wealth-to-permanent-income ratio; a positive shock to permanent income moves the ratio below its target, temporarily boosting saving.