An essay on the Life Cycle: Characterizing intertemporal behavior with uncertainty,human capital,taxes, durables,imperfect capital markets,and non-separable preferences

This paper formulates a general characterization of a household's portfolio choice and savings behavior in an environment with uncertain future interest rates, prices, wages, and factors influencing tastes. Savings may be invested in three types of assets: financial assets; human capital, which is non-tradable; and consumer durables, in which investment may be partially irreversible. Risk-return relations determine the optimal allocation of resources across assets at a point in time. The optimal intertemporal allocation of resources is determined by a restriction on the planned growth rate for the marginal utility of after-tax wealth, where growth rates depend on rates of time preference and measures of long-term riskless rates of interest. Given special assumptions, this marginal utility follows a martingale process as a consequence of optimizing behavior. Pricing formulae are developed for evaluating shifts in uncertain future income, wage, and price profiles. The relations characterizing portfolio and savings behavior presented here do not rely on particular distributional assumptions; they account for all forms of uncertainty including wage uncertainty induced by human capital investment; they allow for the non-marketability of assets; and the main results apply for very general functional form assumptions for preferences. In later sections, results are extended to incorporate income taxes and to account for a wide variety of imperfections in asset markets.