RDP 2006-06: Ageing, Retirement and Savings: A General Equilibrium Analysis 2. Related Literature

Our work relates to two strands of the literature. One of these focuses on the impact of changes in fertility (baby ‘booms’ and/or ‘busts’) on key aspects of the economy.^[5] The other strand concentrates on the economic effects of increased longevity. We discuss some central features of both of these strands in turn.

The standard workhorse for economic questions related to demographic changes is the OLG model, which distinguishes between individuals according to their stage of life. At the heart of the OLG model is the life-cycle hypothesis, which states that individuals prefer to smooth consumption over their lifetime. This implies that saving rates will typically be low early in life when income is low, rise as individuals move through their peak earning years, then decline and become negative in retirement as people draw down on accumulated assets.

Poterba (2004) offers a simple starting point for understanding the effect that changes in fertility rates have on the economy.^[6] In this model, when the baby boom generation retires and goes to sell their assets to the smaller subsequent generation, the price of the asset falls. Hence the baby boom generation experiences a lower return on their asset holdings in their retirement years than do previous and subsequent generations.

While Poterba's model highlights an important link between asset prices or rates of return and the age structure of the population, it ignores several relevant complications. For example, we might think that optimising behaviour, a variable supply of capital, bequests, portfolio choices over risky assets, borrowing constraints, international capital flows, endogenous retirement, and pension schemes (to name a few) might be important in determining the relationship between fertility rates and the economy. A number of studies have incorporated some of these factors into stylised models to explore the effects of changes in fertility on asset markets.

Abel (2003) relaxes simple assumptions about capital supply and bequests. He shows that, in an OLG model where the supply of capital is variable, a baby boom reduces the rate of return relative to what it would have been in a steady state with a constant birth rate. He shows that those born into a baby boom cohort experience less attractive returns on their capital than those born at other times. When individuals are allowed to leave bequests, the basic results still hold, although these are sensitive to the specification of the bequest motive. Bohn (2006) presents a dynastic OLG model where bequests are endogenous. He shows that ageing can reduce bequests, which works to stabilise the capital-to-labour ratio and hence the rate of return.

Yoo (1997) also experiments with a variable capital supply. He calibrates an OLG model with inelastic labour supply and exogenous retirement in which consumers live for 55 periods and work for 45. He finds that a rise in the fertility rate, followed by a decline, initially raises and then lowers asset prices. The effects are sensitive to whether or not capital is in fixed supply. The price of the asset rises 35 per cent when capital is in fixed supply and 15 per cent when the supply is variable.

Brooks (2002) augments a four-period OLG economy with a portfolio decision over risky and riskless assets. The four generations alive at any one time are children, young workers, old workers and retirees. Agents supply labour inelastically and retire in their last period. The model is calibrated so that older individuals prefer to hold less of the risky asset. A simulated baby boom affects the equilibrium level of both risky and riskless asset returns, but the returns on the risky asset change by half as much as the riskless return. Overall, baby boomers earn returns on retirement savings about 100 basis points below current returns, but in terms of lifetime utility they are slightly better off than other cohorts. This reflects the fact that, by short-selling the riskless asset, baby-boom workers are able to supply capital as well as labour. This offsets the movement that would otherwise occur in relative factor prices if the strategy of short-selling the riskless asset were not available. Constantinides, Donaldson and Mehra (2002) show that imposing borrowing constraints on the young magnifies the effect that fertility changes have on capital markets by preventing these kinds of short-selling strategies.

Geanakoplos, Magill and Quinzii (2002) also incorporate a portfolio decision over a risky and riskless asset. They study a calibrated three-period OLG endowment economy to investigate the relationship between fertility changes and the equity market. The main finding is that actual equity market movements in the United States are two to three times larger than their demographic model can explain.

Börsch-Supan, Ludwig and Winter (2003) use a multi-country OLG model to study the effects of ageing on international capital flows. Their long-term demographic projections for several world regions suggest that capital flows from fast-ageing countries to the rest of the world are likely to be substantial. While factors of production could move to mitigate some of the effects of ageing, closed economy analyses remain valid precisely because ageing is a global phenomenon.^[7]

A second strand of the ageing literature has studied the economic impacts of rising life expectancy. Kotlikoff (1989) uses a general equilibrium model with exogenous retirement to investigate the effect of rising life expectancy on key macroeconomic variables such as output per capita and capital intensity. He finds that proportional increases in the age of retirement and the age of death raise capital intensity and output per capita.

Recently, Bloom et al (2004) have studied the effects of increases in longevity on optimal retirement and saving decisions in a partial equilibrium model. Retirement is motivated by an increasing disutility from work throughout life, which is interpreted as capturing individuals' age-specific health status. They show that increases in longevity reduce saving rates and result in a less-than-proportional increase in the retirement age. These results are driven by the wealth effect from compound interest: a higher lifespan means that individuals' savings earn the same rate of interest for longer. This increases lifetime income and raises consumption of both market goods and leisure. However, these results might not necessarily hold in a general equilibrium setting where the return to capital is endogenous.

Kotlikoff, Smetters and Walliser (2001) investigate different scenarios for life expectancy in an elaborate version of the Auerbach and Kotlikoff (1987) model which includes intragenerational heterogeneity. The authors study the potential of ageing-related capital deepening to lessen ageing-related fiscal pressure in the US, and investigate the fiscal implications of a number of demographic changes including alternative life expectancy scenarios. They find that the need to save for longer retirement stimulates capital accumulation. However, this additional capital increases labour demand and leaves the capital-to-labour ratio unchanged in the long run.

Finally, it is worth noting that calibrated general equilibrium studies can be a valuable tool for assessing the effects of ageing on the macroeconomy. This is because of the difficulties suffered by empirical studies in this area. Regardless of whether macro- or microeconomic data are used, the empirical findings appear to be sensitive to both the definition of demographic variables and the specification of the econometric model. For example, Bergantino (1998) finds that the age structure of the population has a significant effect on post-war equity price fluctuations in the US, while Poterba (2001) finds very limited support for this kind of relationship.^[8]

Footnotes

Economic variables also affect demographic variables. See Zhang and Zhang (2005) and the references therein for models in which demographic variables are to some extent endogenously determined. [5]

Poterba's model assumes (among other things) two generations, constant saving rates, and an asset in fixed supply. [6]

See also Börsch-Supan (2005), which examines how different speeds of ageing in different regions affect trade and factor movements. [7]

For an overview of the empirical literature, see Miles (1999), Poterba (2004) and the references therein. [8]