Risk Premiums and the Life Cycle Hypothesis
How does the consumer react to uncertainty in his future inconme receipts from human and nonhuman wealth? In answering this question, it is helpful to replace his stochastic life cycle problem with a certaintyequivalent problem in which expectations of future income receipts are adjusted by the subtraction of risk premiums, as a manifestation of risk aversion on the part of the individual. A recent paper by Keizo Nagatani utilizes this idea. B1v supposing the consumer to maximize a lifetime utility function subject to an intertemporal budget constraint in which incomes are replaced by their certaintv equivalents, he shows that with the unfolding of his y-ears, the individual's planned consumption at anv' future date will shift up or down. Thus suppose the consumer is now aged v years and is planning consumption for age t>v. Then Cv(t) will in general differ from Ct(t). However, the risk premiums on uncertain future inconme (from hunman wealth) that Nagatani uses are arbitrarily imposed, or exogenotus to the maximizing problem. This seems wrong. Such premiiiums should reflect not onl the variability of future incomes, but also the individual's reaction to such variability; or in other words, the nature of his intertemporal utility function. Further, there is a prior question of uniqueness; are the risk premliums in each period uniquely defined? To see that this might prove potentially troublesome, imagine a decision problem:
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