The optimal savings and investment decisions of households along the life cycle were a central issue in Chapter 5. There, savings decisions were made under various forms of risks.However, we restricted our analysis to three period models owing to the limitations of the numerical all-in-one solution we used. In this chapter we want to take a different approach. Applying the dynamic programming techniques learned so far allows us to separate decision-making at different stages of the life cycle into small sub-problems and therefore increase the number of periods we want to look at enormously. This enables us to take amuchmore detailed look at how life-cycle labour supply, savings, and portfolio choice decisions are made in the presence of earnings, investment, and longevity risk. Unlike in Chapter 9, the models we study here are partial equilibrium models. Hence, all prices as well as government policies are exogenous and do not react to changes in household behaviour. This chapter is split into two parts. The first part focuses on labour supply and savings decisions in the presence of labour-productivity and longevity risk. Insurance markets against these risks are missing, such that households will try to self-insure using the only savings vehicle available, a risk-free asset. This model is a quite standard workhorse model in macroeconomics and a straightforward general equilibrium extension exists, the overlapping generations model, which we study in Chapter 11. In the second part of the chapter, we slightly change our viewpoint and look upon the problem of life-cycle decision-making from a financial economics perspective. We therefore exclude laboursupply decisions, but focus on the optimal portfolio choice of households along the life cycle, when various forms of investment vehicles like bonds, stocks, annuities, and retirement accounts are available. This section is devoted to analysing consumption and savings behaviour when households face uncertainty about future earnings and the length of their life span. We study how households can use precautionary savings in a risk-free asset as a means to selfinsure against the risks they face. While in our baseline model we assume that agents always work full-time, we relax this assumption later on by considering a model with endogenous labour supply as well as a model with a labour-force participation decision of second earners within a family context.
Asset Market Participation and Portfolio Choice Over the Life-Cycle
