Age Clienteles Induced by Liquidity Constraints

Abstract

Lifetime consumption-portfolio rules are analyzed for individuals with nonmarketable income. Future income for which liquidity constraints are not binding is effectively and is capitalized, while other income is not capitalized. If the age-income profile is humped, then, for a given level of marketable wealth, relative risk aversion to gambles in marketable wealth is low for the middle-aged and high for the retired, in the special case of isoelastic utility. The existence of these clienteles suggests that equilibrium security prices are determined, in part, by the distribution of wealth over age groups in the economy. The existence of nonmarketable income has profound and puzzling consequences for an individual's consumption/portfolio choice. Consequently a model of lifetime policies in the presence of liquidity constraints provides a wealth of opportunities to explain interesting phenomena. The desirability of an elegant model is even greater when income from human capital is systematically related to age. With a realistic age profile of nonmarketable income one can provide intuition for behaviors that are common within age cohorts. Unfortunately the analysis of optimal policies, as in Samuelson (1969), is difficult after liquidity constraints are introduced. Portfolio choice is not separable from the consumption choice, and the propensity to consume is not independent of wealth, even when preferences are time-additive and exhibit constant relative risk aversion to gambles in consumption (CRRA). One must work considerably harder to understand the implications of a model once nonmarketable income is added. Yet it is this complexity that makes the model rich in behavioral implications. This paper analyses an individual's lifetime problem in the presence of liquidity constraints. A finite length of life is assumed and optimal choices are described as functions of lifetime patterns of income. In particular, when income patterns used in numerical solutions of the lifetime problem mimic (cross sectional) age-income profiles and CRRA utility is assumed, the elderly are relatively risk averse in their portfolio choice, the middle-aged are risk tolerant and the young adults are in the middle range. Furthermore, the marginal propensity to consume from wealth is a bowl-shaped function of age; in some circumstances young adults optimally consume all of their income upon receipt. The specification of liquidity constraints in a model of consumption/portfolio