The profession has been longing for closed-form solutions to consumption functions under uncertainty and borrowing constraints. This paper proposes an analytical approach to solving buffer-stock saving models with both idiosyncratic and aggregate uncertainties. It is shown analytically that an individual’s optimal consumption plan under uncertainty follows the rule of thumb: Consumption is proportional to a target wealth with the marginal propensity to consume depending on the state of the macroeconomy. The method is applied to addressing two long- standing puzzles: the "excess smoothness" and "excess sensitivity" of consumption with respect to income changes. Some of my findings sharply contradict the conventional wisdom.
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Paper provided by Federal Reserve Bank of St. Louis in its series Working Papers with number
2009-026.
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