4.2  The impact of ageing on optimal national saving

The size of the response of optimal saving is determined by the degree of consumption smoothing. The higher the degree of consumption smoothing, the more that any temporary fluctuations in income from a demographic shock are absorbed into saving. The degree of consumption smoothing is, as described above, determined by the elasticities of substitution in consumption and production and, in this model, by the responsiveness of the interest rate (the return to saving) to changes in foreign liabilities.

The case of a zero interest rate premium, with the highest possible degree of consumption smoothing, implies the biggest response of optimal saving. This is illustrated in Figure 11 by the prominent hump shape for the λ=0 case. In this case, optimal saving rises by nearly 4 percentage points of GDP. However, this is probably only a hypothetical case because, as discussed in the Section 3.1, the assumption of a zero interest rate premium is very unlikely to be met in practice.

Figure 11 - Percentage point change in national savings from the initial steady state

In the base case optimal saving rises by about one half of one percentage point for the first six years and then falls steadily over the next thirty years by a total of eight percentage points. The pattern is more extreme for the low fertility scenario. In that case saving falls by about 20% over the next thirty years and then rises by at least 40% over the following fifty years to a point that is about 25% above its current level by 2080. As mentioned above the low fertility scenario implies fertility levels equal to the lowest-fertility countries in the OECD. The simulation of a smaller elasticity of substitution in consumption (from 0.66 to 0.33) shows a slightly larger hump response in optimal saving than in the base case (see Table 7).

These results have implications for the change in savings needed to achieve any given target growth in living standards. For the base case parameter values, substantial growth of living standards can be achieved with no increase in current saving. In the unlikely case of a zero endogenous interest rate premium, or where the elasticity of substitution in consumption is very low, the conclusion is less clear. In those cases the results show that an increase in the current national saving rate of several percentage points for perhaps the twenty years would be required to optimise the growth of living standards. The growth of living standards in those cases is nevertheless substantial.

Calculations not shown here suggest that if saving and investment rates remained at their current levels indefinitely, living standards would be at least maintained over the next 50 years provided labour productivity growth is greater than 0.28%, given base case demographics. That is, the cost of ageing would be 0.28% in terms of lost productivity growth. Recall from Table 6 that the corresponding figure for the optimal consumption path is 0.24% (under base case demographics). This implies that the cost of not optimising (that is, not smoothing consumption), but instead maintaining current saving and investment rates, is only 0.04% per annum in productivity growth – for example, a reduction from 1.5% p.a. to 1.46% p.a. An alternative way of describing the cost of maintaining current saving and investment rates, instead of following the optimal path, is to say that living standards would be, on average, 1.8% lower over the next 50 years, compared with living standards along the optimal path. It is emphasised that this 1.8% figure is not a cumulative figure like the 0.04% productivity growth figure – rather it is the average difference in levels of consumption per person at any time. Both of these numbers are small; they indicate that savings and investment would not have to change dramatically to attain optimal levels.

4.3  Comparison of the consumption profiles of successive cohorts

So far this paper has concentrated on aggregate consumption. Much of the policy debate over population ageing is, however, concerned with how the costs of population ageing are shared among generations (Auerbach, Baker, Kotlikoff and Walliser 1995). Questions about sharing among generations require a more disaggregated approach.

This section compares the welfare of different generations by examining the lifetime consumption paths of successive birth cohorts. A birth cohort is a group of people born in a given year. A cohort consumption path shows a cohort’s consumption as it moves through its life cycle. The consumption path of the year 2000 birth cohort, for instance, is constructed from the consumption levels of 0-year-olds in the year 2000, the consumption levels of 1-year-olds in 2001, the consumption levels of 2-year-olds in 2002, and so on. The requisite data on age-specific consumption is not produced by the Ramsey-Solow model, which provides only average consumption across all age-sex-groups, in equivalent person terms, C/P. However, age-specific consumption levels can be calculated from the C/P’s by using the age-sex specific consumption weights shown in Equation 1 (the ’s).

Note that these consumption paths do not reflect age-specific income profiles. It is not, in fact, possible to calculate age-specific income profiles from the model, since the model contains no measures of age-specific income comparable to the age-specific consumption weights.

Consumption paths for males under the base case scenario are presented in Figure 12. The cohorts are 30 years—approximately one generation—apart. The horizontal axis shows age and the vertical axis shows annual per capita consumption. Upward kinks appears when each cohort moves from youth to the working ages, and from the working ages to old age. The figure clearly shows how, despite the ageing shock, each cohort achieves consumption levels substantially higher than the cohort born 30 years earlier. From the time it is born, for instance, the 2061 cohort has an annual consumption at least twice as high as the 2001 cohort.

Figure 12 - Consumption paths of selected birth cohorts

Consumption levels for later cohorts are nevertheless lower than they would have been in the absence of an ageing shock. This is illustrated in Figure 13. The figure shows the extent to which the ageing shock reduces cohorts’ consumption below the level they would have attained without the shock. It shows, for instance, that by the time the 2000 cohort is aged 75, its consumption levels are only about 86% as high as they would have been without the shock. For the cohorts chosen, the later a cohort is born the greater the proportional reduction in its consumption. Although this is not shown on the graph, when the system finally reaches the steady state, consumption is 84% lower at every age with the ageing shock than it would have been without the shock.

Figure 13 - The ratio between consumption with the ageing shock and consumption without the ageing shock, for selected birth cohorts

Figures 12 and 13 combined indicate that the ageing shock causes later generations to forgo more consumption than earlier generations, but that, even with the shock, later generations still enjoy consumption levels substantially higher than earlier ones.