Academic journal article Economic Inquiry

Time Preference and Life Cycle Consumption with Endogenous Survival

Academic journal article Economic Inquiry

Time Preference and Life Cycle Consumption with Endogenous Survival

Article excerpt

I. INTRODUCTION

Economic theory has traditionally regarded preferences as given. As a result, there is little guidance for economists on how to formulate intertemporal preferences. The standard approach, derived from Samuelson (1937), is to assume time-separable preferences with a constant rate of time preference. The purpose of this article is to provide a structural theory of intertemporal utility in which the dynamic specification and the rate of time preference are endogenous.

We assume that individuals maximize their longevity--expected life span. Incorporating physical and economic constraints allows us to replace the metaphysical concept of a utility function with the observable concept of a health function. Intertemporal preference is accordingly viewed as the manifestation of whatever design of allocating consumption over time as an input to the health function maximizes expected survival time.

The assumption of maximization of expected life span is consistent with an evolutionary perspective. In line with a growing body of literature, we may view preferences as the end product of natural selection: Subject to physiological constraints, preferences that survive maximize some measure of fitness. Fitness is typically operationalized as number of offspring raised. For instance, Maynard Smith (1982) considers maximization of expected offspring the individual's objective. We adopt the similar but simpler objective of expected life span maximization to focus more directly on time preference issues. We believe that the expected life span objective is a good working approximation for the expected offspring objective,t Even beyond the point where individuals are fertile, they can help increase the fitness of their descendants. In particular, because fitness for humans is as much or more based on mental strength than on physical strength, the elderly can maintain an important role as grandparents. So as people live longer, they can expect to have more and fitter descendants, ceteris paribus. (2)

An alternative evolutionary perspective motivating expected life span maximization is related to cultural learning. Children learn from their parents' generation how to live; the lifestyles that lead to increased life expectancy are more likely to be imitated (either by direct parental guidance or the children's choice). Alternatively, focus on expected life span as a primary goal may be reasonable in modeling subsistence economies, explaining the underlying impediments to development in them. Becker et al. (2001), for instance, emphasize life span considerations to explain that convergence in welfare among countries, though difficult to detect in terms of gross national products, can be observed clearly when longevity improvements are taken into account.

The impact of longevity considerations or survival on intertemporal choice has not received much attention in the literature. Yaari (1965) allows the rate of time preference to vary based on the probability of death; this probability, however, is exogenous. (3) Rogers (1994) applies an idea in Hansson and Stuart (1990)--where the marginal rate of substitution in preferences is set equal to the marginal rate of substitution in "fitness" to an intertemporal context. His article has a role for bequests and specific implications for how an individual's time preference varies with age. However, it takes a time-additive utility specification as given. Becker and Mulligan (1997) have provided a basic theory of time preference, which is not survival based. They assume that individuals may invest to increase their appreciation of the future, thus endogenously affecting their rates of time preference. As in Rogers, a drawback of the Becker and Mulligan formulation is that it assumes the additively separable intertemporal utility form.

Our theoretical approach derives an intertemporal utility specification that sheds a preliminary theoretical light on debates concerning expected utility, time consistency, separability of consumption decisions, the difference between risk aversion and intertemporal substitution, the effect of health on life-cycle choices, and the factors governing time preference. …

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