The United Nations Population Division recently released its latest set of projections for the world’s population, the 2010 Revision. The headline of the press release accompanying the projections was “World Population to Reach 10 Billion by 2100 if Fertility in all Countries Converges to Replacement Level”. The publication of these projections generated a lot of heat and concern about how our planet could cope with such large numbers.

But is this reaction reasonable? Underlying the UN’s projections is an implicit assumption that life is generally getting better because if it was getting worse we would get nowhere near 10 billion. This is rarely acknowledged.

What I find amazing is that while many people know how many people there are on Earth most people are usually stumped when asked how big the world is. But how is it possible to claim that there are or will be too many people when one does not know how big the planet is? Somehow 10 billion people is just too many, no matter how big the world is.

There are a number of new features of these latest UN projections compared to previous sets of provisions. The first is that the projections go out as far as 2100. The second is that the UN has assumed in its central projection that fertility rates will, over the long term, tend to be around replacement level. And the third is that new probabilistic methods have been used to project mortality and fertility rates.

Before looking at more detail at these novel aspects it is worth bearing in mind that the UN’s projections are precisely that: projections and not forecasts. The UN is, at one level, simply showing what the population of the world and individual countries would be based on certain sets of assumptions. The UN is not saying that this is what will actually happen.

However, as it must have been very clear that publishing a projected population of 10 billion by 2100 would capture the headlines, the choice of assumptions is absolutely critical not only to determining the results of the projections but also to how the projections will be used and, unfortunately, misused.

Horror was expressed by the projected population sizes of a number of countries, mainly in sub-Saharan Africa. For example, Niger’s population is projected to increase from 15.5 million in 2010 to 139.2 million in 2100. However, the population of Niger is unlikely to get to anywhere near this size. If it had a problem feeding them, couples would have fewer children and more people would migrate.

Another point to note is that the starting population for the 2010 Revision is 13 million lower than projected in the previous projection (the 2008 revision) yet the UN ends up projecting a high future population. While this is not necessarily inconsistent, especially as 13 million out of a global population of some 7 billion is a small error, some further explanation of why there was this difference been the actual and expected population would have been useful. Was it as a result of differences in fertility or mortality? Were the projections for some countries particularly less accurate than those for others? To give its statisticians their due the UN must use, in many cases, deficient and out-of-date data on for its projections, so some differences between projected and actual results are to be expected.

Previously the UN projected populations out only as far as 2050. A number of years ago it did produce ultra-long projections to 2300 but these were given even less credence than the shorter term projections. Making population projections for more than a couple of decades ahead is subject to increasingly large funnels of doubt over the validity of the assumptions for such a long period of time. Fertility, mortality and migration (which does not affect global population but affects populations at a national level) are not exogenous variables but respond to, and in turn influence, changes in the political, economic, social and cultural environment. And who would be confident enough to project these for at most a few years?

The most contentious of the new features is the assumption that fertility rates in the central projection will tend to the replacement level of around 2.1 children per women (although more in countries with higher than normal ratios of boys to girls at birth).

Countries currently with fertility rates below replacement level are expected to see an increase in fertility rates up to replacement level while those with higher fertility rates are assumed to see a reduction in their fertility rates, initially to below replacement level followed by a recovery to replacement level.

In some countries, for example Malawi, the fertility rates are currently significantly above replacement level and past changes have been so small that even by the end of the projection period in 2100 these countries are still assumed to have a fertility rate in excess of replacement level. On the other hand the UN’s model assumes that by 2100 the fertility rate in Afghanistan will be 1.88 while in New Zealand it will be 2.10 and in the UK 2.08. The rates for these three countries are currently 6.62, 2.14 and 1.83 respectively. These projected fertility rates are consistent with the assumptions underlying the model but they really do need to be clearly understood before the results of the projections are used to set or influence policy decisions such as increased funding of population control programs around the world.

It may seem at first sight unlikely that Afghanistan’s fertility rate could be lower than New Zealand’s. However, 30 or 40 years ago it might have been considered equally unlikely that South Korea’s fertility rate would be lower than the UK’s.

The theory underpinning part of the UN’s fertility assumptions is the “demographic transition” according to which fertility rates will, sooner or later, fall in response to reductions in mortality rates. However, the demographic transition does not determine how long the transition will take nor what the eventual level of fertility rates will be. Assuming that over the long term fertility rates will tend to be around the replacement rate is possibly a victory of hope over experience.

Those countries which have gone through the demographic transition have ended up with fertility rates significantly below the replacement rate. While in recent years there has been some increase in these rates this seems to be the effect of increases in fertility at older ages and this is unlikely on its own to bring the rates up to replacement level.

Possibly the UN is assuming that governments will not want fertility rates in their countries to remain below replacement level for too long and will introduce policies or seek to change cultural norms to encourage women to have more children. If so, then governments need more effective measures than those that have been tried to date as these have had relatively little impact. What impact they have had may simply have been an acceleration of child-bearing rather than an overall increase in fertility. Also, it is unlikely that in the face of the handwringing over the results of the UN’s current projections that many governments will be brave enough to try and introduce those measures which would be necessary to achieve levels of fertility consistent with the UN’s assumptions.

The third novel feature of the UN’s projections was the use of probabilistic models in projecting the future country and global populations. The previous projections had used a central fertility assumption that all countries would tend towards a fertility rate of 1.85, even if there was not enough time to get there by 2050. To show the effect of higher or lower fertility rates on the future population of the world, the UN produced projections assuming alternative long term fertility rates of 1.35 and 2.35 i.e. half a child fewer or half a child more. However, there was no way of knowing how likely these alternative fertility rates were compared to the central assumption.

The 2010 Revision used a new approach to demonstrating uncertainty and this is to be commended. The future path of fertility rates are projected by running the model 100,000 times (scenarios) with the future fertility rates in each scenario dependent on a random, within certain limits, choice of the fertility rate. These limits are based on the current fertility rates, the path taken by historic fertility rates and the long term trend towards the replacement level. This type of approach is able to provide alternative sets of future fertility rates with a certain level of likelihood. However, these alternatives are still dependent on the initial assumptions used to generate the scenarios. They give a much better idea of the range of possible outcomes but do not reduce the concern over the appropriateness of the assumption that the average long term fertility rate will be the replacement level.

The UN continues to do a good job of projecting national and global populations and these are probably the best sets of projections available. Care though has to be taken when using the results and if one feels that the central fertility assumption is too high then the UN has provided results assuming a lower long term fertility rate which can be used instead.

Dermot Grenham is an actuary in London.

Dermot Grenham is chief actuary for the social security, demography and overseas pensions team of the Government’s Actuary Department in the UK. He has held various financial reporting...