Andrey Korotayev

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We would like to stress that in no way are we claiming that the literacy growth is the only factor causing the demographic transition. Important roles were also played here by such factors as, for example, the development of medical care and social security subsystems. These variables, together with literacy, can be regarded as different parameters of one integrative variable, the human capital development index. These variables are connected with demographic dynamics in a way rather similar to the one described above for literacy. At the beginning of the demographic transition, the development of the social security subsystem correlates rather closely with the decline of mortality rates, as both are caused by essentially the same proximate factor – the GDP per capita growth. However, during the second phase, social security development produces quite a strong independent effect on fertility rates through the elimination of one of the main traditional incentives for the maximization of the number of children in the family.

The influence of the development of medical care on demographic dynamics shows even closer parallels with the effect produced by literacy growth. Note first of all that the development of modern medical care is connected in the most direct way with the development of the education subsystem. On the other hand, during the first phase of the demographic transition, the development of medical care acts as one of the most important factors in decreasing mortality. In the meantime, when the need to decrease fertility rates reaches critical levels, it is the medical care subsystem that develops more and more effective family planning technologies. It is remarkable that this need arises as a result of the decrease in mortality rates, which could not reach critically low levels without the medical care subsystem being sufficiently developed. Hence, when the need to decrease fertility rates reaches critical levels, those in need, almost by definition, find the medical care subsystem sufficiently developed to satisfy this need quite rapidly and effectively.

Let us recollect that the pattern of literacy's impact on demographic dynamics has an almost identical shape: the maximum values of population growth rates cannot be reached without a certain level of economic development, which cannot be achieved without literacy rates reaching substantial levels. Hence, again almost by definition, the fact that the system reached the maximum level of population growth rates implies that literacy – especially of females – had attained such a level that its negative impact on fertility rates would cause population growth rates to start to decline. On the other hand, the level of development of both medical care and social security subsystems displays a very strong correlation with literacy (see Korotayev, Malkov, and Khaltourina 2006a: Chapter 7). Thus, literacy rate turns out to be a very strong predictor of the development of both medical care and social security subsystems.

Note that in reality, as well as in our model, both the decline of mortality at the beginning of the demographic transition (which caused a demographic explosion) and the decline of fertility during its second phase (causing a dramatic decrease of population growth rates) were ultimately produced by essentially the same factor (human capital growth); there is therefore no need for us to include mortality and fertility as separate variables in our model. On the other hand, literacy has turned out to be a rather sensitive indicator of the development level of human capital, which has made it possible to avoid including its other parameters as separate variables in extended macromodels (for more detail see Korotayev, Malkov, and Khaltourina 2006a: Chapter 7).

Model (0.20)-(0.14)-(0.21) describes mathematically the divergence from the blow-up regime not only for world population and literacy dynamics, but also for world economic dynamics. However, this model does not describe the slowdown of the World System's economic growth observed after 1973. According to the model, the relative rate of world GDP growth should have continued to increase even after the World System began to diverge from the blow-up regime, though more and more slowly. In reality, however, after 1973 we observe not just a decline in the speed with which the world GDP rate grows – we observe a decline in the world GDP growth rate itself (see, e.g., Maddison 2001). It appears that model (0.20)-(0.14)-(0.21) would describe the recent world economic dynamics if the (1 – l) multiplier were added not only to its first equation, but also to the second (0.14). This multiplier might have the following sense: the literate population is more inclined to direct a larger share of its GDP to resource restoration and to prefer resource economizing strategies than is the illiterate one, which, on the one hand, paves the way toward a sustainable-development trajectory, but, on the other hand, slows down the economic growth rate (cp., e.g., Liuri 2005).

Note that development, according to this scenario, does not invalidate Kremer's technological growth equation (0.12). Thus, the modified model does imply that the World System's divergence from the blow-up regime would stabilize the world population, the world GDP, and some other World-System development indicators (e.g., urbanization and literacy as a result of saturation, i.e., the achievement of the ultimate possible level); technological growth, however, will continue, though in exponential rather than hyperbolic form.

Due to the continuation of technological growth, the ending of growth in the world's GDP will not entail a cessation of growth in the standard of living of the world's population. A continuing rise in the world's standard of living is most likely to be achieved due to the so-called "Nordhaus effect" (Nordhaus 1997). The essence of this effect can be spelled out as follows: imagine that you are going to buy a new computer and plan to spend $1000 on this. Now imagine what computer you would have been able to buy with the same $1000 five years ago. Of course, the computer that you will be able to buy with $1000 now will be much better, much more effective, much more productive etc. than the computer that you could have bought with the same $1000 five years ago. However, open a current World Bank handbook and you will see that the present-day $1000, in terms of purchasing power parity (PPP), constitutes a significantly smaller sum than did the $1000 of five years ago. The point is that traditional measures of economic growth (above all, the GDP as measured in international PPP dollars) reflect less and less the actual growth of the standard of living (especially in more developed countries). Imagine a firm that in 2001 produced 1 million computers and sold them at $1000 a piece, in 2006 the same firm produced 1 million 100 thousand new, much more effective computers, but still sells them (due to increasing competition) at $1000 a piece (let us also imagine that the firm has managed to reduce production costs and thus increased both its profits and employees' salaries). How will this affect GDP, both in the country in which the firm operates, and in the world as a whole? In fact, the effect is most likely to be exactly zero. In 2006 the firm produces computers for a total price of 1100 million 2006 international PPP dollars. However, the World Bank will recalculate this sum into 2001 international PPP dollars and will find out that 1100 million 2006 international PPP dollars equal just 1000 million 2001 international PPP dollars. Thus, technological progress sufficient to raise the level of life of a significant number of people will in no way affect the World Bank GDP statistics, according to which it will appear that the above-mentioned technological advance has led to GDP increase at neither the country nor the world level.

The point is that the traditional GDP measures of production growth work really well when they are connected with the growth of consumption of scarce resources (including labor resources); however, if the production growth takes place without an increase in the consumption of scarce resources, it may well go undetected. The modified macromodel predicts such a situation when the World System's divergence from the blow-up regime will have resulted in the cessation of the resource-consuming World GDP production in its traditional measures, accompanied by the transition to exponential (in place of hyperbolic) growth of technology through which an increasing standard of living will be achieved without the growth of scarce-resource consumption.

Because the macrodynamics of the World System's development obey a set of rather simple laws having extremely simple mathematical descriptions, the macroproportions between the main indicators of that development can be described rather accurately with the following series of approximations:

N ~ S ~ l ~ u,

G ~ L ~ U ~ N2 ~ S2 ~ l2 ~ u2 ~ SN ~ etc.,

where (let us recollect) N is the world population; S is per capita surplus produced, at the given level of the World System’s technological development, over the "hungry survival" level m that is necessary for simple (with zero growth) demographic reproduction; l is world literacy, the proportion of literate people among the adult (> 14 year old) population of the world; u is world urbanization, the proportion of the world population living in cities; G is the world GDP; L is the literate population of the world; and U is the urban population of the world. Yes, for the era of hyperbolic growth the absolute rate of growth of N (but, incidentally, also of S, l and u) in the long-run is described rather accurately28 as kN2 (Kapitza 1992, 1999); yet, with a comparable degree of accuracy it can be described as k2SN, k3S2 or (apparently with a somehow smaller precision) as k4G, k5L, k6U, k7l2, k8u2, etc.

It appears important to stress that the present-day decrease of the World System's growth rates differs radically from the decreases that inhered in oscillations of the past. This is not merely part of a new oscillation; rather, it is a phase transition to a new development regime that differs radically from the one typical of all previous history. Note, first of all, that all previous cases of reduction of world population growth took place against the background of catastrophic declines in the standard of living, and were caused mainly by increases in mortality as a result of various cataclysms – wars, famines, epidemics; and that after the end of such calamities the population, having restored its numbers in a relatively rapid way, returned to the earlier hyperbolic trajectory. In sharp contrast, the present day decline of the world population's growth rate takes place against the background of rapid economic growth and is produced by a radically different cause – the decline of fertility rates that is occurring precisely because rising standards of living for the majority of the World System's population have meant the growth of education, health care (including various methods and means of family planning), social security, etc. Decrease in the rate of growth of literacy and urbanization was not infrequent in the earlier epochs either; but in those epochs it was connected with economic decline, whereas now it takes place against the contrary background of rapid economic growth, and is connected to the closeness of the saturation level. Earlier declines, we might say, reflected a deficit of economic resources, whereas the present one reflects their abundance.

It appears necessary to stress that the models discussed above have been designed to describe long-term ("millennial") trends, whereas when we analyze social macrodynamics at shorter ("secular") time scales we also have to take into account its cyclical (as well as stochastic) components; it is these components that will be the main task of the present part of our Introduction to Social Macrodynamics. To begin with, the actual dynamics typical for agrarian political-demographic cycles are usually the opposite of those that are theoretically described by "millennial" models and actually observed at the millennial scale. For example, as we shall see below, during agrarian political-demographic cycles the population normally grew much faster than technology, which naturally resulted in Malthusian dynamics: population growth was accompanied not by increase, but by decrease of per capita production, usually leading to political-demographic collapse and the start of a new cycle.

In Chapter 1, we shall review available mathematical models of political-demographic cycles. In Chapter 2, we shall consider in more detail political-demographic cycles in China, where long-term population dynamics have been recorded more thoroughly than elsewhere. In Chapter 3 we shall present our own model of pre-Industrial political-demographic cycles. Finally, in Chapter 4 we shall consider the interaction between long-term trends and cyclical dynamics.

1 This book is a translation of an amended and enlarged version of the second part of the following monograph originally published in Russian: Коротаев, А. В., А. С. Малков и Д. А. Хал­турина. Законы истории: Математическое моделирование исторических макропроцессов (Демография. Экономика. Войны). М.: УРСС, 2005.

2 To be exact, the equation proposed by von Foerster and his colleagues looked as follows: . However, as has been shown by von Hoerner (1975) and Kapitza (1992, 1999), it can be written more succinctly as .

3 Of course, von Foerster and his colleagues did not imply that the world population on that day could actually become infinite. The real implication was that the world population growth pattern that was followed for many centuries prior to 1960 was about to come to an end and be transformed into a radically different pattern. Note that this prediction began to be fulfilled only in a few years after the "Doomsday" paper was published (see, e.g., Korotayev, Malkov, and Khaltourina 2006a: Chapter 1).

4 Note that the value of coefficient k (equivalent to parameter С in equation (1)) used by us is a bit different from the one used by von Foerster.

5 Thomlinson 1975; Durand 1977; McEvedy and Jones 1978; Biraben 1980; Haub 1995; Modelski 2003; UN Population Division 2006; U.S. Bureau of the Census 2006.

6 Thomlinson 1975; McEvedy and Jones 1978; Biraben 1980; Modelski 2003; UN Population Division 2006; U.S. Bureau of the Census 2006.

7 Thomlinson 1975; McEvedy and Jones 1978; Biraben 1980; Maddison 2001; Modelski 2003; U.S. Bureau of the Census 2006.

8 350 million (McEvedy and Jones 1978), 374 million (Biraben 1980).

9 The second characteristic (p, standing for "probability") is a measure of the correlation's statistical significance. A bit counterintuitively, the lower the value of p, the higher the statistical significance of the respective correlation. This is because p indicates the probability that the observed correlation could be accounted solely by chance. Thus, p = 0.99 indicates an extremely low statistical significance, as it means that there are 99 chances out of 100 that the observed correlation is the result of a coincidence, and, thus, we can be quite confident that there is no systematic relationship (at least, of the kind that we study) between the two respective variables. On the other hand, p = 1 × 10-16 indicates an extremely high statistical significance for the correlation, as it means that there is only one chance out of 10000000000000000 that the observed correlation is the result of pure coincidence (in fact, a correlation is usually considered as statistically significant with p < 0.05).

10 In fact, with slightly different parameters (С = 164890.45; t0 = 2014) the fit (R2) between the dynamics generated by von Foerster's equation and the macrovariation of world population for CE 1000 – 1970 as estimated by McEvedy and Jones (1978) and the U.S. Bureau of the Census (2006) reaches 0.9992 (99.92%), whereas for 500 BCE – 1970 CE this fit increases to 0.9993 (99.93%) (with the following parameters: С = 171042.78; t0 = 2016).

11 Note that after the 1960s, world population deviated from the hyperbolic pattern more and more; at present it definitely is no longer hyperbolic (see, e.g., Korotayev, Malkov, and Khaltourina 2006a: Chapter 1).

12 In fact, Kremer asserts the presence of this pattern since 1 million BCE; Kapitza, since 4 million BCE! We, however, are not prepared to accept these claims, because it is far from clear even who constituted the "world population" in, say, 1 million BCE, let alone how their number could have been empirically estimated.

13 Note that at that time these economies were exclusively foraging (though quite intensive in a few areas of the world [see, e.g., Grinin 2003b]).

14 Or 57.671 million according to a later re-evaluation by Bielenstein (1987: 14).

15 Due to the separation of the census registration from the tax assessment conducted in the first half of the 18th century, the Chinese population in 1800 had no substantive reason for avoiding the census registration. Therefore, the Chinese census data for this time are particularly reliable (e.g., Durand 1960: 238; see also Chapter 2 of this book).

16 Due to the first scientific estimation of the Egyptian population performed by the members of the scientific mission that accompanied Napoleon to Egypt (Jomard 1818).

17 With a notable exception of China (Durand 1960; see also below Chapter 2).

18 Whereas the answers to the questions regarding the quadratic hyperbolic growth of the world GDP might not have been quite clear even for those readers who know the hyperbolic demographic models.

19 In addition to this, the absolute growth rate is proportional to the population itself – with a given relative growth rate a larger population will increase more in absolute numbers than a smaller one.

20 Kremer uses the following symbols to denote respective variables: Y – output, p – population, A – the level of technology, etc.; while describing Kremer's models we will employ the symbols (closer to the Kapitza's [1992, 1999]) used in our model, naturally without distorting the sense of Kremer's equations.

21 "This implication flows naturally from the nonrivalry of technology… The cost of inventing a new technology is independent of the number of people who use it. Thus, holding constant the share of resources devoted to research, an increase in population leads to an increase in technological change" (Kremer 1993: 681).

22 Note that "the growth rate of technology" means here the relative growth rate (i.e., the level to which technology will grow in a given unit of time in proportion to the level observed at the beginning of this period).

23 In Economic Anthropology it is usually denoted as "Boserupian" (see, e.g., Boserup 1965; Lee 1986).

24 Kremer did not test this hypothesis empirically in a direct way. Note, however, that our own empirical test of this hypothesis has supported it (see below Appendix 1).

25 Thus we arrive, on a theoretical basis, at the differential equation discovered empirically by von Hoerner (1975) and Kapitza (1992, 1999).

26 Since literacy appeared, almost all of the Earth's literate population has lived within the World System; hence, the literate population of the Earth and the literate population of the World System have been almost perfectly synonymous.

27 On the ground, the saturation effect means, for example, that raising literacy from 98 to 100 per cent of the adult population would require much more time and effort than would raising it from 50 to 52 per cent.

28 However, for u the fit of this description appears to be smaller than for the rest of variables.

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