Europe's ageing population is creating a pensions crisis. Maintaining the continent's pay-as-you-go systems, whereby state benefits to retirees are paid out of contributions from current workers, will consume an ultimately intolerable proportion of national incomes.

In Italy, spending on the pay-as-you-go system as a share of gross domestic product is expected to peak at 15.8 per cent in 2032. In Germany, forecasts indicate a similar peak, although these projections do not take into account that this year and next, pensions will be increased, not in line with average net earnings, but only by the rate of inflation.

In France, where the population decline will be less pronounced, state-funded pensions are expected to rise to 16 per cent of GDP in 2040, according to a recent study commissioned by Mr Lionel Jospin, the French prime minister.

By contrast, in Britain, where state retirement benefits are much less generous, public pension costs are expected to reach only 6 per cent of GDP in 2030.

For the continental economies, the burden of their pay-as-you-go systems is unsustainable. How can Europe avert this looming crisis? Many governments' first response has been to look for new sources of financing.

One approach is to widen the group of people required to contribute, for example, by including the self-employed. However, forcing more people into the system increases the numbers who will claim benefits from it in future. It also means reducing the chances of creating a voluntary, privately-funded system.

Another possible remedy is general taxation. But the trouble here is that tax financing weakens the links between contributions and benefits in the pension system. It would also require a significant shift from the generous continental European pension levels to the parsimonious Anglo-Saxon system. No one is going to vote for that.

In Germany, an "ecological tax" has been introduced to raise funds. However, the measure is merely an increase in the oil tax and a new tax on electricity; it is not a levy on carbon dioxide emissions and global warming. Moreover, the tax damages productivity and hurts the competitiveness of energy-intensive industries if it is applied unilaterally by one country. The German way out has been to allow exemptions for the very industries that are the worst polluters.

A more promising way forward would be to raise the statutory and the effective retirement age. The existing systems put an implicit tax on labour prior to retirement. Doing away with this distorting incentive to retire early would reduce expenditures and increase receipts into the pension system. Another realistic remedy is to allow greater immigration. Young immigrants expand the workforce, and incoming workers with high skills raise productivity.

But while any of the above measures may ease the pressure on the pay-as-you-go system, none offers a full solution. The root of the problem is the implicit public debt - that is, the unfunded future obligations. A mechanism must be established to prevent an excessive rise of this implicit debt, and this requires linking benefits to contributions, with some smoothing between the periods.

There are two ways of doing this. One is to compensate for greater life expectancy by reducing the value of retirees' monthly state pension. The other is to retain full entitlements for those nearest to retirement, but progressively lower them for younger workers by age group.

Either course of action means reducing the pension level relative to the working income for future generations.

Smaller pensions hardly represent an appealing political message - and that brings us back to the problem of feasibility. A better solution is to introduce an element of private provision, which gives a higher rate of return and can provide old age insurance more cheaply.

There is a further complication: reducing benefits provided by the pay-as-you-go system to encourage greater private provision can be taken only so far before pensioners' incomes fall to a level at which minimum welfare payments become payable.

Governments cannot expect people to contribute to a state-run pension system for 45 years of their working life and then give them only the same monthly benefits as welfare recipients.

Pension reform is thus linked to reform of the welfare state as a whole. In short, there are no easy answers.

The writer is president of the Kiel Institute of World Economics and a member of the German Council of Economic Advisers