Life-Cycle/Permanent Income Hypothesis and Precautionary Savings:Theoretical Implication and Empirical Problems(in Japanese)

How do people determine their levels of consumption? This question has attracted much attention; not only is it important in its own right, but it is also related to economic trends and macroeconomic policies. The life cycle/permanent income hypothesis has been regarded as the most important theory on consumption decisions. In this paper, the recent development of the theoretical studies on the life cycle/permanent income hypothesis is surveyed since the well-known article of Hall (1978). The survey focuses on the study about precautionary savings. The structure of this paper is as follows. In Section 1, the outline and background of the permanent income hypothesis by Friedman (1956) are presented. Briefly explained is the difference between the studies before Hall (1978) and these after his. In Section 2, the proper definition of the permanent income hypothesis, introduced by Flavin (1981), is presented. This definition is derived from the intertemporal budget constraint of an infinitely lived household. Some discussions are shown over that the definition is the mathematical formulation of Hicks (1946)'s definition of income, and that there are some difficulties to extend it to the case when future wages and interest rates are not certain. If a household determines his current level of consumption according to the permanent income hypothesis, consumption follows a random walk. In Section 3, so-called "certainty equivalence model" is presented, where a rational household decides his current consumption equal to his permanent income. Some arguments about this model are shown over why the government debt become neutral, that the marginal propensity to consume is less than unity in case of the temporal income hike, and why people have precautionary motives for savings. In Section 4, two empirical findings -"excess sensitivity" and "excess smoothness"- are discussed, both of which contradict the certainty equivalence model. In the framework of this model, since consumption follows a random walk, the following two conclusion can be reached: (1) no information available at period t except the current level of consumption, ct, helps predict the future consumption, ct+1; and (2) the variance of consumption is equal to that of the permanent income. Flavin (1981) tested the former conclusion and found the fact that current income, xt, is positively correlated with future consumption. This phenomenon is referred to as "excess sensitivity of consumption." On the other hand, Deaton (1987) tested the latter conclusion and found another fact that the variance of consumption is strictly less than that of the permanent income. This phenomenon is known as "excess smoothness of consumption." In Section 5, some extensions of the certainty equivalence model are reviewed. These extensions are intended in order to relax the specific assumptions of the certainty equivalence model and to solve the two problems of excess sensitivity and excess smoothness. By introducing the extensions, such as (1) preference shock, (2) durables, (3) habit formation, (4) liquidity constraint, and (5) income fluctuation generated by multivariate process, significant changes are made in the stochastic process of consumption. Some extensions can explain either excess sensitivity or excess smoothness, but none can explain both. Section 6 focuses on precautionary savings. In Section 6.1, the intuition of precautionary motives for saving is presented. A household has a precautionary motive of saving if the third derivative of his instantaneous utility function, u´´´(c), is positive. In Section 6.2, the work of Kimball (1990) on "prudence" is reviewed, which measures the strength of the precautionary saving motive. His theory of precautionary savings is mathematically analogous to the Arrow-Pratt theory of risk aversion. Kimball measures the absolute prudence by u´´´(c)/u´´(c), and shows that precautionary saving is larger as the value of absolute prudence is larger. Sections 6.3 and 6.4 review Caballero (1990), which studies the optimal consumption-saving decision of an infinitely living household with constant absolute risk aversion (CARA) utility. In case of homoscedastic labor income, the stochastic process of consumption follows a martingale with drift. On the other hand, in case of the certainty equivalence model, the process of consumption follows a pure martingale process (without drift). The drift term is a result of precautionary motive for saving. If labor income is heteroscedastic, the current increase in uncertainty of the future labor income causes the increase in future consumption. Thus, precautionary savings might explain either excess sensitivity or excess smoothness, if there is the correlation between labor income itself and its uncertainty. In Section 6.5, the "incomplete adjustment" of consumption is introduced to Caballero (1990)'s model in order to approximate the behavior of households with non-separable preference such as durables and habits. The "incomplete adjustment" means that the actual consumption differs from the optimal one. Even if the consumption plan is adjusted incompletely, a positive correlation exists between the uncertainty of income and the difference between current and future consumption. Section 6.6 reviews the "buffer stock" theory of saving, propounded by Carroll (1992, 1997). For simplicity, the constant relative risk aversion utility function is assumed. In this case, current consumption, ct, becomes strict positive and concave function of the current non-human wealth, Wt. (it includes current labor income). As Wt converges to zero, ct converges to zero. These properties of the consumption function is interpreted as follows; a household regards its non-human wealth as a "buffer" for labor income fluctuation and chooses consumption so as to keep his non-human wealth to an appropriate level. A linear approximation of this "buffer stock" model explains both excess sensitivity and excess smoothness at the same time, if the marginal propensity to consume toward the increase of human wealth is very small. Section 6.7 surveys some empirical studies of precautionary savings and shows that many of them suffer serious misspecifications. In particular, Dynan (1993) derived her regression equation from a second-order approximation of the Euler equation, but this regression equation neglects the possibility that the variance of consumption is endogenous and correlated with non-human wealth. Such a misspecification creates a serious bias in the estimation. Keywords : life cycle/permanent income hypothesis, precautionary saving, excess sensitivity, excess smoothness, buffer stock theory of saving.