It is by now well known that the main hope for developed societies subject to rapid population ageing who wish to maintain their relative standard of living lies in increasing their collective productivity more rapidly than they increase their dependency ratio via-a-vis the older age groups. Now in the comments thread on the recent ‘Reform is a Dirty Word‘ post I ventured to say that I found it obvious that at some stage we would reach a point where the rate of population ageing was going to outstrip the rate of productivity increase (in which case relative income per capita would inevitaby start to fall). David, unsurprisingly, asked me why I thought this to be the case. I was not happy with the response I offered (which was essentially some ‘rigmarole’ about the biology of ageing which is coming in a separate post), and since that time I have been scratching my head trying to find a simple way to get this point across. Perhaps I now have one.
All you need to get to grips with what follows is a basic understanding of geometry and a vague interest in football.
We are all aware that the demographic transition can be conceptualised as a process of pyramidal transformation. This transformation is brought about by a continuous process of age structure change, and this age structure change is in turn produced by a steady decline in fertility and a steady increase in life expectancy.
Essentially, in high-fertility low-life-expectancy societies, the pyramid has a very thick base (rather like this one for Mali). As the transition advances and countries pass through their ‘demographic dividend’ growth-spurt, the pyramid starts to be transformed (as can be seen here for Turkey). Later, as populations age even further, you get the high-elderly-dependency pyramid (Japan is a pretty clear case of this).
Now so far I hope there is not really anything controversial being said. The next analytic tool we need is the simple geometric idea of ‘centre of mass‘ (or, if you prefer, centroid). And what we need to be clear about is the fact that as societies transit, from having a pyramid structure like Mali to having one like Japan, the centre of mass moves steadily up the pyramid.
The Value Pyramid
Now, side-by-side with the transition process there is a development process. Most societies with the ‘Mali-type’ population pyramid, are agricultural societies, which means that the majority of their population work in agriculture, and the majority of their GDP comes from the agricultural sector. This process can now be seen at work in India, where some 60% of the population still participate in the agricultural sector, while some 30% of GDP is produced there. India is, of course, already well into the transition, and if we were to go back twenty years we would undoubtedly find a far higher share of the population working in agriculture and a majority of GDP being produced there.
Then, as societies develop, there is a steady movement in economic activity up this value pyramid. Again, as we can see in China and Turkey, this begins with a shift into low value industry. Then the balance changes into a higher value industry profile, and eventually we get the dominance of a services (or knowledge industry) sector.
So what we can see is that alongside the population pyramid there is a value pyramid. The value pyramid also to some extent inverts as economic activities move up the value chain. The two pyramids are related, but as we should be able to see immediately from the Indian example, the correspondance is far from being one-to-one. In fact the centre of mass of the value pyramid moves in a way which is somehow related to the movement of the centre of mass in the population one, but it is precisely this ‘somehow’ which remains to be determined. In essence my proposal is that if we could perform the mapping operation between the two pyramids we would have a much clearer idea about the productivity dynamics of ageing populations.
OK, I said we needed football. I mention football, since professional footballers have a more-or-less undisputed age productivity profile. Young footballers are below their peak, whilst older ones are already past it. If we take the club which is so dear to my very own heart (BarÃ§a), it is easy to see that Leo Messi has his best years out there in front of him, that Ronaldinho Gaucho is more or less in his prime, and that Lilian Thuram while still being a very good player (and has experience which to some extent compensates for his loss of speed), is now well past his ‘optimum performance’. All of these factors can be readily seen in little details like salaries and transfer values.
Now populations (collectively) are not so different from footballers in this respect. The centre of mass moves up the pyramid and productivity and collective performance rise (in a way which is also reflected by movement of the centre of gravity up the value pyramid). But when you think of this on a theoretical (and consequently rather abstract) level it is also clear that the ‘Thuram effect’ will mean that at some point in the process the directional movements of the centres of mass in the two pyramids will start to diverge, in that in societies which have a certain proportion of the economically active population who have passed their peak, the centre of mass will strat to drift down again. I am not saying where this point lies – that is a question for empirical research – I am simply trying to demonstrate that theoretically such a point *must* exist. After this point has been passed any society whose centre of mass continues to rise will experience declining per-capita incomes.
Obviously this ‘proof’ is extremely simplified. It is, after all, written for a blog. Clearly it needs to be modified and extended by taking account of the fact that there is more than one country in the global economy, and that values are thus relative to values being generated in other countries simultaneously as reflected in the level of global prices.
A second issue is that the model is static, in that the vaue pyramid does not, in fact, simply shift across a pre-exisiting space, but rather is subject to a constant process of evolution: that is, the apex of the value pyramid is constantly moving upwards, in a way which means that the relative values of all the points below are constantly changing. I think this makes the whole thing much more difficult to model, but does not change the substance of the argument. At some given moment in time one group of developing countries will be moving nearer to the centre of mass of the value pyramid in just the same measure as another group of older developed economies will be moving upwards and away from it.