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The Actuary The magazine of the Institute & Faculty of Actuaries
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The impact of demographic change

A few years ago many actuaries were happy with the idea that problems
which demographic change cause to unfunded pay-as-you-go (paygo) pen-
sion and social security arrangements would not apply to the same extent
to funded pensions arrangements that amounts saved or invested by and on behalf of elderly people would mean that their claim to a share of the economy’s output would be comparatively unaffected by demographic change. Others gave more emphasis to the argument that it would affect funded pension arrangements as well as paygo systems, by adjusting the returns to labour and capital.
Actuarial tools on their own are insufficient fully to explore how any such interactions might work they are properly the realm of economics. A recent paper by Professor David Miles of Imperial College, London entitled ‘Modelling the impact of demographic change upon the economy’ (published in The Economic Journal, January 1999) aims to investigate this. This paper describes a model of the UK economy over the period 1960 to 2060, where individuals decide in each year of their working life how much labour to contribute and how much of their earnings to save, given certain desires to balance work and leisure and to save to provide for their retirement.
Construction and design
How is this model constructed? It uses a technique introduced by economists about ten years ago called an overlapping generations model. This was first introduced in work by Auerbach and Kotlikoff in 1987, but Professor Miles’s current work differs mainly by allowing technological change (in effect real growth in the economy), which manifests itself by falling periods spent working over the period of the projection. The model is solved iteratively, with a starting guess for the key variable of the rate of return, which then determines other variables in the model. This enables the ‘dynamic programming problem’ to be solved, ie each cohort in each year chooses the optimal combination of leisure and labour, consumption and saving, which in turn implies different amounts saved and different amounts of labour supplied, giving a revised set of interest rates. This process is repeated until equilibrium is reached it is, perhaps, fortunate that the model did converge, as no comment is made on possible divergent results.
Clearly, such a model is crucially dependent on a number of assumptions. Key assumptions included:
– a flat-rate state pension set, in the first case for the UK, at 20% of average earnings;
– no uncertainty for rational agents deciding their preferred mix of leisure and labour, consumption and saving, with children having no effect on this choice;
– a closed economy assumption, enabling the equation of domestic capital stock and domestic saving;
– the productivity of labour at various ages (this peaks in the early 40s);
– that individuals aim to equate their (discounted) income and (discounted) consumption over their working lives ie they aim to leave no bequests; and
– a few technical parameters, including the form of the utility function, and the factors affecting the choice between consumption now and consumption later and between leisure and consumption in any period.
Sensitivity analyses were performed which did not affect the overall pattern of results. The central values of the assumptions used gave sensible results for key economic indicators such as savings rate, capital formation and total wealth stock. The most crucial assumption is that of certainty for agents and rationality of agents.

Demographic shifts
The key results were that demographic shifts could well lead to shifts in savings and investment returns over the next 60 years. Wealth stocks would tend to rise with the proportion of the population who are in their 50s and 60s, who have the largest wealth stocks according to the model. However, the saving rate falls, as these people move from saving while working to dis-saving during retirement the effect is quite pronounced, as the fall is from around 14% in the 1990s to around 6% in 2040. The effect on investment returns is a fall from a return of around 4.6% to around 4.2% over the period from the 1990s to the 2030s. This implies that funded pension schemes as well as unfunded schemes will be affected by demographic change, although the effect on funded schemes will be less. As Professor Miles says:
(T)here may well be substantial swings in private savings rates over the next 50 years saving in the longer term is likely to fall well below recent levels as the proportion of the population aged over 65 rises the impact of this upon rates of return on capital may be relatively muted because a lower savings rate (which other things equal would lower the path of the capital labour ratio) is likely to be offset by a smaller workforce (which obviously works in the opposite direction).
In addition, the model was used to investigate the situation where the paygo state pension was phased out. As might have been expected, the savings rate did not fall to the same extent, and the fall in rates of return was more pronounced and went on for longer. The model was also used for other European countries, which were assumed to have a state pension with a higher replacement ratio and faster real growth. Broadly similar results (falling investment returns driven by demographics) were found.
This paper offers a view on the issue of funded versus unfunded pension schemes, rooted in economic techniques not often used by actuaries. The interaction of the labour market and savings as affected by demographic shift have effects beyond pensions, but they are crucial to pensions, both funded and paygo.

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