At a recent presentation in Brussels a European Commission representative asserted that the costs of ageing implied huge problems of sustainability and a rising burden on the – smaller – working population in the future. Based on the analysis in a recent major report on the sustainability of public finances, he stated that, if policies remain unchanged, pension payments will rise by 2.3 percentage points of GDP across the EU by 2060. Adding in health care costs raises the figure to 4 ½ percentage points (from a starting level of age-related spending of 23% of GDP). His message: ‘be afraid, be very afraid’ – and change course.

An obvious question is whether such an increase, €2.50 for every €100 of spending in the economy, spread over a fifty year period, is really such a big deal, given the talk of a demographic crisis. Also, preparations are already being made across Europe to raise effective retirement ages and make other policy changes. There is a more fundamental issue, though: the official somehow ‘forgot’ to mention a simple fact. GDP will be far higher in 2060 than it is now. Against that background, the (small) shift in the distribution of national income pales into insignificance.

To see this, let’s go through a simple illustration, using small numbers – if you prefer, you can multiply everything by a million, and imagine you are in the Netherlands – in which the shift in national income towards pensioners is actually much larger than projected in the Commission’s scenario.

In our economy – let’s call it Ageia – there are 16 people. In 2010, 3 of them are children, 3 are pensioners, and 6 of the 10 people of working age have a job. The old-age dependency ratio, the number of pensioners divided by the number of workers, is 0.5.

In 2060 the population structure is 3 children, 6 pensioners and 7 people of working age. Let us suppose that 5 of these 7 have a job (This means that – as envisaged in the EU’s Lisbon Strategy – the employment rate, the share of the working age population that has a job, increases from 60% to just over 70%.) The old-age dependency ratio rises dramatically to 1.2.

Let GDP in 2010 be 160 Ageian dollars. So per capita income is $10.

If labour productivity grows at 1.5% every year then output per worker over 50 years more than doubles (to be precise it rises by 2.105). Labour input is reduced by a factor of 0.833 (5/6) because there are only five instead of six workers.

So GDP (at constant prices) in 2060 is approx. $280 (that’s 160 X 2.105 X 0.833) and so the average income of our 16 Ageians in 2060 is $17.5.

Notice that we have doubled the number of pensioners in our economy. The old-age dependency ratio has more than doubled and the labour force has fallen by almost 20%. We have also kept the number of dependent children constant, rather than assuming a decline as might be more realistic. The rate of productivity growth is conservative, at least on past experience in the EU. (Hourly productivity growth has been faster this decade up to the crisis. Of course it may be lower in the future, but even if just 1% productivity growth is assumed this would still raise output per worker by around two thirds over the fifty year period, such is the power of compound interest.)

In short, this is a very drastic demographic scenario. But we see that Ageians’ average incomes increase by three-quarters over the period, despite a ‘crippling’ demographic crisis.

If we assume further that Ageians have a social norm such that those who work have double the income of non-workers (including children), then in 2010 the non-workers have an income of approx. $7.3 and workers $14.6. In 2060 non-workers have $13.3 and workers $26.6. We can easily calculate pensioners’ share of national income. In 2010 it is 3/22 = 13.6% and in 2060 is 6/21 = 28.5%.

There is thus a massive rise in the share of national income going to pensions in Ageia. Recall that the European Commission actually estimates this shift for Europe at about 2.3 percentage points of GDP, whereas in poor Ageia it is almost 15 percentage points! Yet both workers and pensioners have far higher real living standards in 2060 than in 2010. And there has been no change in the relative position of each worker to each retiree.

Are you scared now?

An additional simple, but important, point that can be made using this illustration is that these calculations are fundamentally the same whatever the pension system, in Ageia or any other economy. In particular, it is irrelevant whether it is pay-as-you go or capital funded. Whatever the system, 6 workers support 3 pensioners in 2010 and 5 workers have to support 6 pensioners in 2060. Current workers cannot, collectively, ‘save’ for their retirement via saving in funded schemes because the goods they want to consume in, say, 2060 have to be produced in (or marginally before) that year, and there are only five workers to do that work.

There are two possible caveats to this: one is that, in an open economy, current income can be invested via a funded scheme in other countries with a different demographic pattern meaning that in future workers in those countries will deliver goods and services for future retirees in the home country. However in many countries, notably in China, demographic trends are not that different from Europe’s. The other possibility is that the increased saving raises the rate of productivity growth, and so GDP grows faster, enabling more to be distributed in 2060. This may seem obvious, but is in fact far from certain. Without going into a detailed discussion, it depends centrally on whether investment is assumed to be driven more by demand or by the cost of finance. In fact if firms’ investment decisions are driven by demand expectations, it is perfectly possible for a rise in desired savings for retirement to depress, rather than raise, the rate of investment, as Keynes pointed out more than seventy years ago.

The messages for policymakers are clear. Don’t panic about pensions. Don’t rush into funded schemes as a panacea. Do try and get, and keep, more people in employment. And do try and raise the rate of productivity growth.

Oh, and sometimes a bit of simple maths can help one face the future. Happy New year to all readers!

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