I came across a mention of a report that pointed to falling world population and that it listed a load of countries who will experience negative growth. I thought this interesting enough to want to know more, but nothing appeared in my usual sources of information. Here I go find out; this may include finding out why my regular news services decided this was a non-event.
I suspect the trigger event was source [1] a piece of Pew research for the UN. That paper says that by 2100, the world’s population is projected to reach approximately 10.9 billion, with annual growth of less than 0.1% — a steep decline from the current rate.
Current growth is between 1 and 2% a year and has been so since about 1950, during which time we have gone—globally—from 2.5 to 7.7 billion of us. Looking at the top graph, the predicted upper limit (plus half a child in reproduction) is pretty close to linear and adds another billion every 10.5 years. The lower bound, a child less across the world, has us peaking in 2055. In between is a variety of predictions in somethng akin to a normal distibution.
As with the study of covid-19, we are learning about non-linear systems of the class that are that are chaotic when we look hard at the detail. Thus a study that breaks the global population into nation states produces predictions that Europe will slow in growth to a reproduction rate below two, balanced by immigration. In the same model, Africa produces a surplus of people, as do parts of Asia; India passes China as the most populous nation. Religions correlate with growth, too. We could so easily attend to these issues; in my opinion we continue to fail to create models for what we deem success as a society that allows us to have a decreasing population. Inevitably, without migration, any decrease in population means the average age rises (quite rapidly, potentially) which has consequences for care, for tax, pensionable age and so on. That doesn't mean we cannot do this; it doesn't mean we cannot change attitudes to migration, temporary or permanent; it doesn't automatically mean an end to economic growth, though I continue to think that too many, perhaps all, economic models are based on that assumption. Reduction does not mean collapse.
I've inserted a graph I made that shows the growth rate per year that associates with the predicted low and high population growth. This is more complicated than gradient, this is the 'compound interest figure'. You can see the post-war boom and that both curves see future growth going below 0.5% per year. I say we need growth very close to zero and I'd prefer a negative growth. Indeed, since so many will disagree or simply not care to act, we might well assume that it is only the nations that are prepared to address the issue that are able to affect any change at all, which pushes us steadily to a position where some countries have burgeoning growth. Let us not confuse growth with absolute population, a country could have a high population that is set to decline towards a desired population density level. Those nations with low or negative growth will then have what the crowded and expanding nations will view as the very space they 'need' (because they continue to deny that they are themselves the problem, so 'expansion of population' becomes a perception for expansion in other senses too). That requires the acting nations to educate outside their own borders and to have an enlightened attitude to migration—imagine accepting only incomers that are skilled so as to benefit the less expansive society. Imagine also the desperation among the crowded nations as each individual continues that irrational urge to procreate; we need the education that encourages us not to do that. In turn, we seem to have learned that education, especially of females, is key. I still say that religions have a significant part to play and it is the competitive push to expand belief systems (I disagree at a fundamental level) that we need to also change. Indeed. onme could turn that around and suggest that the educated attitude that says one wants fewer or no children might well collide with religions that say versions of the opposite (some to many), reaching a point where the religion itself loses support. There are parallels in disease propagation; for survival, the infecting agent must adapt; so too with religions.
Enough soap-box; lets inspect the predictive models, especially that explained in [1].
Do not misunderstand: a fall in growth rate predicted does not mean a fall iin population. That is confusing gradient with position. Current fertility is 2.5 (births per woman) and is predicted to fall to 1.9 by 2100. Since 1.9 is less than two, that means a slow decline in population, but from a very large figure. Decrease in fertility inevitably raises the median age (24 in 1950, 31 in 2020, 42 in 2100). This pushes the over-80 population from 146 million in 2020 to 881 million in 2100. As you would expect, a falling population means relatively few young people, so there will be more over 65s than under 15s as soon as 2073. I say that is a curious choice of age groups, implying a refusal to recognise that pensionable age will rise and will be matched by increased time in compulsory education.
Projections show greater growth (than elsewhere) of population in Africa, notably sub-Saharan Africa. I wonder how they are going to feed themselves. By 2100, declining populations are foreseen in Europe and Latin America, but North America is assumed to continue to welcome migrants as the primary driver of continued population growth. Conversely, we should expect that some regions shrink without compensating migration and the modellers think this will apply to Latin America and the Caribbean, so that they have very old populations, such that by 2100 the median age in the US will be 45, while Argentina, Mexico and Brazil are expected to be 47, 49 and 51 respectively. Meanwhile Colombia will have moved from 16 in 1965 to 52 in 2100, and Albania will have reached 61 by this measure.
I've put a link to the full data at [3], but I found that confusing, mostly since I expected it to be a longer report. What I wanted to see was detail about the assumptions. That should be found in 'data sources' but again I didn't find what I expected, only some general descriptions of the basis for the assumptions.
I went looking to see if there is any study of economic growth models in a declining population. At last, I found one at [6], from which this Fig1 is taken. The focus of this paper: what happens to economic growth if population growth is negative? There are some interesting points made: growth of an economy might well depend on the growth of knowledge, but there has been a general assumption that this depends on the magnitude of population, that more people means more knowledge, when surely that is a bit like saying 'more' is the same as 'more copies of the same thing'. Could we perhaps assume that knowledge would grow with a constant population? I think we should, since non-expanding universities can be assumed to make non-negative progress. So then the issue becomes whether growth of knowledge is greater than the reduction in people. Or can be encouraged into being so.
The modelling I found and read falls so very easily into the trap of assuming that once established, the same assumptions apply indefinitely, leading to an empty planet. That is silly; I'm only saying that the previous model of perpetual growth of population needs to change. A good model, in my view, would show that there is a balance of factors leading to a relatively stable population, possibly oscillating, that balances resources against numbers while also balancing what we might call fairness and general happiness — quality of life for all. One of the matters that the economists generate is to wonder about competing ideologies (what they call competition of ideas). What we need is a model that allows the population to reduce to some 'better' value, not one that must necessarily run until we have no people remaining.
We have confused optimal fertility with maximum fertility or, perhaps simply confusing optimal as to whom it applies, a family, a larger group like a tribe of some description, or a nation. We need to think at a large scale, that of nation or species. I have always thought that optimal fertility in my lifetime ought to be below equilibrium fertility, but not by an awful lot. Maximum children at replacement value, by which I mean two kids is the most you should have; I've come across arguments for trading quota, but that seems to me (i) close to counting children as an expression of wealth and (ii) likely to encourage population expansion. On the other hand, it would push the rich into being those bearing the costs of progeny. Do please think on this for yourself; I find I soon reach positions I wish to retract from, such that in general quota trading should not be permitted.
Economists say People obtain utility from consumption and from having descendants [6] Being me, I immediately wish to query the underlying assumptions here. Those as posed imply time devoted to fertility (devoted to offspring) and this could be constant or variable, growing or not. A reducing fertility rate might be balanced by greater devotion to the offspring one has, partly since in some sense the future of that offspring is somehow more reliable than it was. But we can imagine positions in which 'family' could b a social grouping that included lesser or zero biological relationships, more like village or tribe.
From fairly late on in [6]: The transition dynamics lead to an important economic point, summarised in Figure 9.
The social planner would like the economy to have a much higher fertility rate and converge to the “expanding cosmos” steady state, with positive population growth and positive economic growth: both the number of people and the amount of income per person would rise exponentially forever. In contrast, the equilibrium allocation will simply move the economy steadily to the right, to higher values of x, along the lower line: there will be a constant negative rate of population growth, so knowledge per person, x, will rise as the number of people declines.
Figure 9: The bottom line in the figure shows the transition dynamics for the equilibrium allocation while the curved lines show the dynamics for the optimal allocation. An economy governed by the equilibrium dynamics can get trapped in the Empty Planet outcome if it waits too long to switch to the optimal allocation. In this example, that would occur if knowledge per person, x, rises above about 1990.
At any point in time, society may adopt better institutions, such as a fertility subsidy, that move the economy to the optimal allocation. If this occurs at x = 100 or x = 400 or x = 1600 (i.e. where the growth rate of At is 1% or 0.25% or 0.0625%), then the economy will eventually transition to the high steady state and exhibit exponential growth forever. However — and this is the surprising point — if the economy delays adopting good institutions for too long, eventually knowledge per person x will rise above the jump point (around 1990 in the figure). Once this happens, the optimal regime changes. Adopting good institutions that deliver the optimal allocation will involve negative population growth, albeit at a higher rate than the equilibrium. This means that knowledge per person will continue to grow — not because of large increases in knowledge but rather because of declines in the number of people — and the economy will converge to the low steady state. Population will decline, knowledge will remain below an upper bound, and income per person will stagnate. This is the Empty Planet outcome. The surprise is that if society waits too long to adopt good institutions, the optimal allocation switches from one of sustained exponential growth in population, knowledge, and living standards to one of stagnation and an empty planet.
This reduces the modelling to two states, too many people or too few. Endogenizing fertility leads to an additional subtlety. When the equilibrium fertility rate is negative, the optimal allocation features two stable steady states. If the economy the optimal allocation soon enough, it converges to the Expanding Cosmos. But if the economy waits too long to switch, even the optimal allocation can be trapped by the Empty Planet outcome. ¹
This is not in any way an obligatory result: we could so easily adapt and survive differently, thanks to, for example, a change in automation, which could quite easily produce growth in living standards while also giving us a decreasing population. We might change our health for better or worse, so that the mortality rate changes—it is that relative to the fertility rate that determines growth, after all.
I will continue to look for discussion of this topic.
DJS 20200716-9
top pic from BDA
² ³ ⁴ ⁵ ⁶ ⁷ ⁸ ⁹ footnote spares
[2] https://www.un.org/en/sections/issues-depth/population/
[3] https://population.un.org/wpp/ the full 2019 report.
[4] https://ourworldindata.org/future-population-growth
[5] https://www.livemint.com/news/india/how-declining-populations-kill-economic-growth-11579162625168.html one of several similar articles, all referring to [6]
[6] https://web.stanford.edu/~chadj/emptyplanet.pdf Charles I Jones, The End of Economic Growth? Unintended Consequences of a Declining Population
Somne wtf moments:
• With endogenous fertility, there is no unique criterion for social welfare.
• a larger population generates more nonrival ideas, raising everyone’s income
1 Endogenous In econometrics, endogeneity broadly refers to situations in which an explanatory variable is correlated with the error term. The distinction between endogenous and exogenous variables originated in simultaneous equations models, where one separates variables whose values are determined by the model from variables which are predetermined; ignoring simultaneity in the estimation leads to biased estimates as it violates the exogeneity assumption of the Gauss–Markov theorem. Antonym: exogenous. If your doctor says your sickness is endogenous, he means that whatever's wrong with you went wrong inside your body, and wasn't caused by anything you can catch, like a virus. Endogenous is a fancy term for anything that originates internally. Various sites.
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