The permanent-income hypothesis (PIH) of Milton Friedman (1957) states that the agent saves in anticipation of possible future declines in labor income (John Y. Campbell, 1987). He also saves for precautionary reasons, and dissaves because of impatience. To justify the PIH in an intertemporal optimization framework, it has been conventional to assume both (i) quadratic utility, to turn off precautionary motives (Hall, 1978), and (ii) equality between the subjective discount rate and the interest rate, in order to rule out dissavings for lack of patience. Neither assumption is plausible. Much work on consumption in the past decade has focused on individual's precautionary savings motives and liquidity constraints. Impatience is a standard result in heterogeneous agents general-equilibrium incomplete-markets models, generally known as Bewley models. This paper shows that the PIH is in any case the optimal rule, in a Bewley model, in which each agent solves the precautionary-savings model of Caballero (1990, 1991). In addition to the demand for savings for a "rainy day," Caballero's model also predicts a constant precautionary- savings demand and constant dissavings due to impatience. In equilibrium, I show that these two forces must cancel each other. As a result, the agent behaves in accordance with the PIH.
Wang, Neng. "Caballero Meets Bewley: The Permanent-Income Hypothesis in General Equilibrium." American Economic Review 93, no. 3 (June 2003): 927-36.
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