Which Countries Generate Kondratieff Waves in Global GDP Growth Rate Dynamics in the Contemporary World?

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- Korotayev, Andrey - подписаться на статьи автора
- Bilyuga, Stanislav E. - подписаться на статьи автора
- Shishkina, Alisa R. - подписаться на статьи автора
Журнал: Journal of Globalization Studies. Volume 11, Number 1 / May 2020 - подписаться на статьи журнала

DOI: https://doi.org/10.30884/jogs/2020.01.03

It is shown that the Kondratieff wave dynamics in the growth rates of global GDP is generated now by the developing countries, while in the previous era the Kondratieff dynamics was generated primarily by the most economically developed countries of the First World. We re-visit the question of the presence of the Kondratieff waves in the world GDP dynamics. We find that, though in the post 1960 series they are quite visible at the global level, they are hardly visible in the GDP growth rates of the economically developed countries where the Kondratieff wave component (still detectable with special techniques) is almost entirely overwhelmed by the secular trend towards the decline of the GDP growth rates. After analyzing how much this trend is connected with the decline of the population growth rates and the decline of the share of investments in GDP, we move to the analysis of the Kondratieff waves in the GDP growth rates of the developing countries where they turn out to be much more pronounced and visible, which allows us to conclude that in the present the K-waves are generated by the Third World. We also show that in the developing countries a pronounced Kondratieff wave dynamics is accompanied by an overall upward trend (that stands in a sharp contrast with the pronounced downward trend observed in the developed economies). Finally, we analyze Kondratieff waves in the efficiency of investments as well as demographic characteristics of the developing countries, which allows us to forecast that the GDP growth rates in the developing countries are likely to also step on the downward secular trend starting with the sixth Kondratieff wave.

Keywords: Kondratieff waves, developing countries, developed countries, economic growth, global dynamics, GDP.

Andrey V. Korotayev, National Research University Higher School of Economics more

Stanislav E. Bilyuga, Lomonosov Moscow State University, Moscow  more

Alisa R. Shishkina, National Research University Higher School of Economics more

1. Introduction

A Russian economist writing in the 1920s, Nikolai Kondratieff observed that the historical record of some economic indicators then available to him appeared to indicate a cyclic regularity of phases of gradual increases in values of respective indicators followed by the phases of decline (Kondratieff 1922: ch. 5; 1925, 1926, 1928a, 1928b, 1935, 1979, 1984, 1998, 2002, 2004). The period of these apparent oscillations seemed to him to be around 50 years. This pattern was found by him with respect to such indicators as prices, interest rates, foreign trade, coal and pig iron production for some major Western economies (first of all Britain, France, and the United States), whereas the long waves in pig iron and coal production were claimed to be detected since the 1870s for the world level as well.

Kondratieff himself identified the following long waves and their phases (see Table 1).

Table 1

Long waves and their phases identified by Kondratieff

Long Wave Number	Long Wave Phase	Dates of the Beginning	Dates of the End
The First	A: upswing	The end of the 1780s or beginning of the 1790s	1810–1817
	B: downswing	1810–1817	1844–1851
The Second	A: upswing	1844–1851	1870–1875
	B: downswing	1870–1875	1890–1896
The Third	A: upswing	1890–1896	1914–1920
	B: downswing	1914–1920

The subsequent students of Kondratieff cycles identified additionally the following long waves in the post-World War I period (see Table 2).

Table 2

‘Post-Kondratieff’ long waves and their phases

Long wave number	Long wave phase	Dates of the beginning	Dates of the end
The Third	A: upswing	1890–1896	1914–1920
	B: downswing	1914–1928/29	1939–1950
The Fourth	A: upswing	1939–1950	1968–1977
	B: downswing	1968–1974	1984–1991
The Fifth	A: upswing	1984–1991	2007–2008
	B: downswing	2007–2008	?

Sources: Mandel 1980; Dickson 1983; van Duijn 1983: 155; Wallerstein 1984; Goldstein 1988: 67; Modelski and Thompson 1996; Pantin and Lapkin 2006: 283–285, 315; Ayres 2006; Linstone 2006: Fig. 1; Tausch 2006: 101–104; Thompson 2007: table 5; Jourdon 2008: 1040–1043; Korotayev and Grinin 2012a, 2012b; Korotayev and Tsirel 2010a, 2010b, 2010c; Korotayev, Zinkina et al. 2011a; Lynch 2004; Akaev, Sadovnichy, and Korotayev 2010; Akaev, Fomin et al. 2011; Akaev, Grinberg et al. 2012, Akaev, Korotayev et al. 2017; Grinin, Korotayev, and Tsirel 2011, Grinin, Korotayev, and Tausch 2016.

Nowadays, Kondratieff wave theory has a rather peculiar status in the academic world. On the one hand, it has numerous supporters (see, e.g., Phillips 2016, 2018; Phillips and Linstone 2016; Berry and Elliott 2016; Nefiodow 2016; Norkus 2016; Thompson 2016; Tausch 2016; Gallegati 2016; Gallegati et al. 2017; Grinin, Korotayev, and Tausch 2016; Grinin, L., Grinin, A., Korotayev 2017; Devezas et al. 2017; Modis 2017; Sokolov et al. 2017; Akaev, Korotayev et al. 2017; Coccia 2018). On the other hand, it is rejected by the majority of mainstream economists (see, e.g., Garvy 1943; Rothbard 1984; Zarnowitz 1985; Mankiw 1989; 2008: 740; 2015: 420; Block and Rockwell 2007: 166–169; Focacci 2017) and even by some world-system scholars (e.g., Morineau 1984; Plys 2012, 2014).

This is connected with the fact that many economists have failed to detect Kondratieff waves in many important economic indicators, including GDP growth rates, for the majority of modern developed economies (see, e.g. Van Ewijk 1982; Metz 1998, 2006; Diebolt and Doliger 2006, 2008; Diebolt 2012, 2014).

In this article we will argue that this might be connected with the point that in the present epoch, Kondratieff waves in the global GDP dynamics are generated by the developing (rather than developed) economies. We will re-visit the question of the presence of the Kondratieff waves in the world GDP dynamics. We will see that although in the post 1960 series they are quite visible at the global level, they are hardly visible in the GDP growth rates of the economically developed countries where the Kondratieff wave component is almost entirely overwhelmed by the secular trend towards the decline of the GDP growth rates. After analyzing how much this trend is connected with the decline of the population growth rates and the decline of the share of investments in GDP, we will move to the analysis of the Kondratieff waves in the GDP growth rates of the developing countries where they appear to be much more pronounced and visible, which will allow us to conclude that in the present epoch the K-waves are generated by the Third World. We will also show that in the developing countries pronounced Kondratieff wave dynamics is accompanied by an overall upward trend (that stands in a sharp contrast with the pronounced downward trend found in the developed economies). Finally, we analyze Kondratieff waves in the efficiency of investments as well as demographic characteristics of the developing countries, which will allow us to forecast that the GDP growth rates in the developing countries are also likely step on the downward secular trend starting with the sixth Kondratieff wave.

2. Kondratieff Waves in the Global GDP Dynamics

To begin with, let us consider the dynamics of GDP growth at the level of the World System as a whole. The general dynamics of annual growth rates of world GDP for 1945–2014 looks as follows (see Fig. 1a):

Note that we are dealing precisely with the Fourth and Fifth Kondratieff waves identified by the students of K-cycles (see Table 2 above). Special attention should be paid to the fact that the peak of the current Kondratieff wave was noticeably lower than the previous peak, whereas previously the peak of every next wave always turned out to be higher than the peak of the previous cycle (see, e.g., Korotayev and Tsirel 2010a, 2010b, 2010c; Korotayev and Grinin 2012a, 2012b; Korotayev, Khaltourina et al. 2010; Grinin, Korotayev, and Tausch 2016). This serves as an additional confirmation of the fact that in the 1970s, most of the global macrotrends that had been observed during the preceding centuries and millennia were reversed (see, e.g., Korotayev and Bogevolnov 2010; Korotayev 2015a; Korotayev, Goldstone, and Zinkina 2015; Korotayev 2020). However, an appreciable part of the academic community continues to ignore this fact, maintaining faith in the continuous ‘acceleration of the pace of historical development’ and refusing to see that since the early 1970s the pace of historical development is no longer accelerating, but rather slowing down (cf. Modis 2002, 2020).

3. Are There Kondratieff Waves in the GDP Growth Rates of the Most Economically Developed Countries?

This slowdown is particularly evident for the group of the most economically developed countries (see Fig. 2):

As can be clearly seen in Fig. 2, over the last decades, the linear downward trend in the rate of GDP growth has been dominant in economically developed countries (accounting for 40 per cent of all the variation of the GDP growth rates). Moreover, even the upswing phase of the fifth Kondratieff wave only slowed down this trend, but did not stop it completely.

Thus, unlike for the world GDP growth rates, the K-waves in the developed economies' GDP growth rates are not directly visible in Fig. 2. However, they can still be seen quite clearly if we apply the very technique widely used by Kondratieff in order to detect long waves in the dynamics of economic indicators, that is, to plot not the indicator dynamics directly, but rather the dynamics of deviations from the secular trend smoothed by means of a nine-year moving average (e.g., Kondratieff 1979: 626) (see Fig. 3).

After the application of this procedure, one can see in Fig. 3 quite clearly the end of the upswing of the fourth Kondratieff wave, its downswing, as well as the upswing and downswing of the present, fifth, K-wave (consisting in its turn of two Kuznets swings [see Korotayev and Tsirel 2010a, 2010b, 2010c]).

Of course, the first explanation that comes to mind in this case is to explain the slowdown in GDP growth rates in developed countries by the reduction in population growth rates, as it was quite real in the years under consideration (see Fig. 4):

Source: World Bank 2019: NY.GDP.MKTP.KD.ZG

After 1973 in economically developed countries there was observed a pronounced tendency toward deceleration of not only GDP but also of the GDP per capita growth rates, which shows that it is impossible to explain the slowdown in the GDP growth rates of developed countries first of all by the deceleration in their population growth rates. At the same time, it should be noted that the Kondratieff wave component is still visible here, but in an extremely blurred form (especially when compared with the dynamics of this indicator for developing countries, see below). Actually, this dynamics during the downswing phase of the fourth Kondratieff wave was manifested in the fall of per capita GDP growth rates in developed countries significantly below the downward trend line with the return within the fifth K-wave back to the downward trend line during the fifth K-wave upswing. However, to make the K-waves in the GDP per capita growth rate dynamics clearly visible one should apply again the technique widely used by Kondratieff in order to detect long waves in the dynamics of economic indicators, that is, to plot not the indicator dynamics directly, but rather the dynamics of deviations from the secular trend smoothed by means of a nine-year moving average (e.g., Kondratieff 1979: 626) (see Fig. 6).

Again, after the application of the above specified procedure, one can see in Fig. 6 quite clearly the end of the upswing of the fourth Kondratieff waves, its downswing, as well as the upswing and downswing of the present, the fifth K-wave (consisting again in its turn of two Kuznets swings [see Korotayev and Tsirel 2010a, 2010b, 2010c]).

In this regard, the dynamics of the share of investments in the GDP in the first world countries turn out to be of considerable interest (see Fig. 7):

This diagram clearly demonstrates that the steady decline in the economic growth rates of the first world countries in recent decades is not coincidental, while allowing to identify one of the most important factors of this decline – a no less systematic decline in the share of investments in the GDP of economically most developed countries. During the period under consideration, some systematic growth was observed only at its start, up to the year of the inflection of global trends, 1973.³ Starting from 1973 and up to the present time, a systematic decrease of this indicator was observed in the first world countries. In its dynamics, however, there was a pronounced cyclical component corresponding to Juglar cycles.⁴ In general, in the phase of the rise of these cycles in the Western economies there was an increase in the share of GDP spent on investment, whereas at the recession and depression phases this indicator decreased. However, since 1973, at the peak of each new Juglar cycle, the value of this indicator turned out to be much lower than at the peak of the previous cycle, and during the recession this indicator fell every time below the level of the previous recession, which created a systematic downward trend for the share of investments in GDP in the high-income OECD countries, confidently observed after 1973.

4. Kondratieff Waves in the GDP Growth Rates of the Developing Countries

At the same time, the developing countries demonstrate a very different dynamics. Let us begin its analysis by examining the dynamics of GDP in the developing countries (see Fig. 8):

As we can see, the dynamics of the annual growth rates of developing countries, actually demonstrates the most significant differences in comparison to those of highly developed countries. Here we are dealing with the wave component predominating in the expressed absence of any downward trend (and a pronounced upward trend as well). Thus, the Kondratieff wave dynamics in the growth rates of global GDP in the last decades of the Great Convergence is generated precisely by the developing countries, while in the previous era of the Great Divergence it was generated primarily by the most economically developed countries of the First World (see, e.g., Korotayev and Tsirel 2010а, 2010b, 2010c; Grinin, Korotayev, and Tsirel 2011; Grinin and Korotayev 2012, 2014b).

It appears appropriate to recollect at this point that in the nineteenth century, northwestern Europe witnessed the birth of capital-intensive and fossil-fuel based manufacturing. Spreading throughout Europe and the United States, these changes triggered an explosive growth of the gap in per capita incomes between the First and Third World that became known as the Great Divergence (see, e.g., Pomeranz 2000; Goldstone 2008, 2012; Clark 2008; Allen 2011; Sadovnichiy et al. 2014; Malkov et al. 2010a; Korotayev, Malkov et al. 2010; Korotayev 2014, 2015а; Grinin and Korotayev 2014a, 2015; Korotayev, Goldstone, and Zinkina 2015). In the twentieth century, the Great Divergence peaked before the First World War and continued until the early 1970s, then, after two decades of indeterminate fluctuations, in the late 1980s it was alternated by the Great Convergence since the majority of the Third World countries reached economic growth rates that far exceeded those of most First World countries (e.g., Sala-i-Martin 2006; Korotayev and Khaltourina 2009; Spence 2011; Derviş 2012; Grinin and Korotayev 2014a, 2015; Akaev 2015; Malkov et al. 2010a, 2010b; Korotayev 2013, 2014, 2015a, 2015b; Malkov and Korotayev 2014; Korotayev, Andreev et al. 2014; Korotayev, Zinkina et al. 2011a, 2011b, 2012; Korotayev and de Munck 2013, 2014; Korotayev and Zinkina 2014b; Zinkina et al. 2014).

It is also noteworthy that, unlike the highly developed countries, during the peak of the fifth Kondratieff wave, the developing countries advanced in terms of their GDP growth rates to the peak level of the fourth K-cycle.

It seems appropriate to compare GDP growth rates in the developed and developing countries (see Fig. 9):

As one can see, at the end of the 1960s and the beginning of the 1970s, the GDP growth rates in developing countries were already somewhat ahead of those in the developed countries. However, given the fact that in those years in the developing countries the population growth rate reached its maximum (see Fig. 10) and was significantly higher than in the developed countries, the gap between the developed and developing countries in GDP per capita continued to grow,⁵ and therefore the Great Divergence continued. In the 1990s, the GDP growth rates in the developing countries again rose markedly above those in the developed countries, but most of the developing countries had by then achieved a very marked decline in the birth rate, so everything was happening against the background of a fast decline in population growth rates in the developing countries.

Thus, in the 1990s, the developing countries began to overtake the developed ones not only in terms of GDP growth rates, but also as regards the GDP per capita growth rates, the gap between them began to narrow more and more, and the Great Convergence replaced the Great Divergence era. The processes of the Great Convergence have intensified significantly since 2000, when the GDP growth rates of the developing countries already outpaced significantly those in the developed countries against the background of the continuing decline in the population growth rates of developing countries, as a result of which, as we shall see below, at the peak of the fifth Kondratieff wave these countries in terms of GDP per capita growth even managed to significantly outperform the peak of the fourth K-wave (see Fig. 11).

Fig. 11. Dynamics of annual per capita GDP growth rates (% per year)
in developing countries, 1961–2014

Source: World Bank 2019.

As one can see, at the peak of the fifth Kondratieff wave the developing countries in sharp contrast to the developed countries were really able not only to achieve very high values that were obtained at the peak of the preceding wave, but even to noticeably outperform the previous peak.

In the light of the above said, it seems appropriate to consider the dynamics of the investment share in the GDP of the developing countries in comparison with this indicator for the developed countries (see Fig. 12).

As one can see, in the 1960s, there was still a very significant gap between the developed and developing countries in the share of investment in GDP (in favor of the developing countries), which undoubtedly contributed to the continuation of the Great Convergence. By the mid-1970s, these shares were equal, and in the 1990s, the share of the developing countries began to noticeably exceed the share of the developed ones, and in the 2000s the gap between the developing and developed countries (in favor of the former) reached enormous proportions, which also significantly contributed to the development of the processes of the Great Convergence.

5. Kondratieff Waves in the Global Investment Efficiency

Let us consider also the dynamics of such an important macroeconomic indicator as the efficiency of investments (calculated as how many dollars of GDP growth are produced by one dollar of investment). One should keep in mind that in the global dynamics of this indicator, the Kondratieff cyclic component is again very clearly traced. In a predictable manner, in the upward phases of K-waves, the global efficiency of investments increases while in the downward phases it decreases (see Fig. 13).

At the same time, a closer examination reveals that the developing and not the developed countries are the real generator of Kondratieff cyclical component in the modern world. Indeed, in the dynamics of the developed countries, a downward trend predominates: if in the early 1960s every dollar of investment gave 25 cents of GDP growth, by now this indicator has fallen almost fivefold. At the same time, Kondratieff cyclical component in the dynamics of economically developed countries is barely visible (see Fig. 14).

Fig. 15. Dynamics of investment efficiency in the economies of the developing countries, 1965–2014

Source: authors' calculations based on the World Bank data (2017).

As we see, Kondratieff wave component is expressed incomparably clearer when applied to economically developed countries. In the era of the Great Convergence, these are the developing and not the developed countries that act as the main drivers of the Kondratieff wave dynamics. At the same time, the following point attracts attention: at the peak of the fifth (current) Kondratieff wave, the developing countries have failed to reach the level of investment efficiency that they had at the peak of the previous (fourth) Kondratieff wave. This suggests that the majority of the middle income countries are likely to experience in the forthcoming decades a slowdown in economic growth rates that could be similar to the one that has been observed for the economically developed countries for several decades since the early 1970s. In this regard, the trajectory of the decline in GDP growth rates of economically developed countries observed in recent years and presented above in Fig. 2 may well be considered as ‘memories of the future’ for the middle income countries.

6. Why Can We Expect the Developing Countries to Step on the Downward Secular Trend Starting with the Sixth Kondratieff wave?

Particular attention should be paid to the following point: at the peak of the current (fifth) Kondratieff wave, the developing countries managed, despite a noticeable reduction in the macroeconomic efficiency of investments, to reach the growth rates of per capita GDP exceeding those at the peak of the previous (fourth) Kondratieff wave, mostly due to the two following points:

1) It was the peak of the fifth Kondratieff wave when the developing countries received the maximum of their demographic bonus.⁶ As we could see above, at the upswing phase of the fifth Kondratieff wave, the rapid acceleration of GDP growth rates in developing countries (see Fig. 8 above) was accompanied by a very rapid (by one third in just two decades) decline in population growth rates, resulting in a particularly strong increase in per capita GDP growth during this period. However, this issue can be looked from different perspectives. Why was the reduction in the population growth rates in the developing countries at the upswing phase of the fifth Kondratieff wave quite naturally accompanied by such an impressive acceleration in GDP growth rates per capita? The fact is that the abovementioned decline in population growth rates was due to a very rapid reduction in the birth rate, since most developing countries at that time were in the midst of the second phase of their demographic transition. This led to a marked improvement (from an economic point of view) in the structure of the population of developing countries. Indeed, during the period in question, in developing countries, the number of underage children per a working age adult decreased very significantly, but in the same period, the population did not get aged to such an extent as to ‘compensate’ the decrease in the number of underage dependents per worker by the number of the old age dependents on him/her. As a result, during the entire upswing phase of the fifth Kondratieff wave in the developing countries there was a significant increase in the share of working age population in the general population and, consequently, a significant reduction in the number of dependents per worker, which operated as a significant factor that increased the rate of growth of GDP per capita in these countries.

However, as shown in Fig. 17, by now the majority of economically developing countries are already finishing to receive their demographic bonus. The fertility rate in many of them (China, Iran, Thailand, etc.) has already dropped significantly below the replacement level, and any further substantial fertility rate decreases are not likely there, so the potential for reducing the demographic burden by decreasing the share of dependents of younger ages in the total number the population in this case has been already exhausted. On the other hand, the population aging here begins to manifest itself more and more, the proportion of dependents of older age in the total population begins to grow at an ever-increasing rate, which ceases to be compensated by a decrease in the share of dependents of younger ages. This means that the total number of dependents per worker increases. The demographic bonus is replaced by a demographic onus (see, e.g., Ogawa, Kondo, and Matsukura 2005; Park and Shin 2015; Goldstone 2015). If in the upward phase of the fifth Kondratieff wave the demographic processes in developing countries (through the mechanisms of the demographic bonus) contributed to the acceleration of GDP per capita growth, then in the coming decades, in economically developing countries, the same processes (through the mechanisms of the demographic onus) would contribute to a slowdown in rates of per capita GDP growth.

2) As Fig. 15 indicates, the developing countries (unlike the developed ones) succeeded in raising the efficiency of investments at the upswing phase of the fifth Kondratieff wave. However, at the peak of the fifth wave they failed to surpass the level of efficiency that they reached at the peak of the fourth wave. The fact that they were able to exceed the growth rates of GDP per capita of the fourth wave at the peak of the fifth wave is connected not only with the demographic bonus at the time, but also with the fact that a tremendous increase (almost twofold!) occurred between the peak of the fourth and the peak of the fifth K-waves in the share of investment in the GDP of these countries (see Fig. 10 above). The lack of growth in investment efficiency at the peak of the fifth K-wave relative to the Fourth one was more than compensated by the growth in the volume of these investments. However, there is no reason to expect a similar increase in the share of investment in the GDP of developing countries at the peak of the sixth Kondratieff wave. Rather, one should expect a decline in this share; in particular, this refers to the share of investment in the GDP of the major modern locomotive of developing countries – China (see, e.g. Grinin et al. 2014).

Thus, there are grounds to assume that developing countries at the peak of the fifth Kondratieff wave achieved record-high growth rates of GDP per capita, which at the peak of the sixth K-wave they are unlikely to surpass.⁷

7. Conclusion

Hence, the Kondratieff wave dynamics in the growth rates of global GDP in the recent Great Convergence decades is generated precisely by the developing countries, while in the previous era of the Great Divergence the Kondratieff dynamics was generated primarily by the most economically developed countries of the First World. At the same time, in sharp contrast to the developed countries, the developing states at the peak of the fifth Kondratieff wave not only achieved very high growth rates of GDP per capita attested at the peak of the preceding wave, but even significantly exceeded them. It is also shown that the dynamics of the share of investments in GDP played an important role in the processes of transformation of the Great Divergence into the Great Convergence. Back in the 1960s, there was a very significant gap in the share of investment in GDP between the developed and developing countries in favor of the developed countries, which undoubtedly contributed to the continuation of the process of the Great Convergence. By the mid-1970s, these shares became equal. In the 1990s, the share of developing countries began to noticeably exceed the share of developed countries, so in the 2000s the gap between the developing and developed countries (in favor of developing ones) had reached enormous proportions, which appears to be tightly connected with the process of transferring the role of a generator of K-waves in the global GDP growth rate dynamics from the developed to developing countries.

NOTE

^* The study was implemented with support of the Russian Science Foundation (Project No. 20-61-46004).

¹ For Kondratieff waves/long cycles see also, e.g., Schumpeter 1939; Rostow 1975; Mensch 1979; Marchetti and Nakicenovic 1979; Mandel 1980; Marchetti 1980, 1983, 1986; Volland 1987; Berry 2000; Modelski 2001; Devezas, Linstone, and Santos, 2005; Devezas 2006; Dator 2006; de Groot and Frances 2008, 2012; Grinin, Devezas, and Korotayev 2012, 2015; Korotayev, Zinkina and Bogevolnov 2011; Sadovnichiy et al. 2012; Linstone and Devezas 2012; Grinin, Korotayev, and Malkov 2013; Grinin, Korotayev, and Bondarenko 2015; Wilenius and Casti 2014; Phillips and Linstone 2016.  

² Even without any additional smoothing.

³ For more information about this global trend inflection, see, for example, Korotayev, Malkov et al. 2010; Korotayev and Bogevolnov 2010; Sadovnichiy et al. 2014; Malkov and Korotayev 2014; Akaev, Korotayev, and Malkov 2014; Korotayev 2020.

⁴ For more information about these cycles, see, for example: Juglar 1862; Tugan-Baranovskiy 2008 [1913]; Schumpeter 1939; Grinin, Korotayev, and Malkov 2010a, 2010b; Grinin and Korotayev 2009, 2012; Grinin, Korotayev, and Malkov 2010b; Grinin and Korotayev 2015b.

⁵ See for example: Barro 1991; Mankiw et al. 1992; Quah 1996; Sala-i-Martin 1996; Acemoglu 2009; Korotayev, Malkov et al. 2010; Malkov, Bogevolnov et al. 2010; Sadovnichiy et al. 2014.

⁶ For a demographic bonus, see, for example: Bloom and Williamson 1998; Bloom and Sachs 1998; Bloom, Canning, and Malaney 2000; Bloom and Canning 2001, 2008; Bloom, Canning, and Sevilla 2003; Bloom et al. 2007a, 2007b; Mason 2001, 2007; Hawksworth and Cookson 2008: 7–10; Lee and Mason 2006, 2011.

⁷ This, of course, is applicable to most developing countries (and to the ‘developing countries’ aggregate as a whole). At the same time, it is obvious that some developing countries should reach the GDP growth rates per capita at the peak of the Sixth K-wave significantly exceeding those reached by them at the peak of the Fifth wave. This is particularly true for the least developed countries that are still far enough from the end of the demographic transition, and which will receive their main demographic bonus just at the upward phase of the sixth K-wave (if, of course, they will soon be able to accelerate the rate of decline birth rate [see, e.g. Vassiliev et al. 2014; Zinkina and Korotayev 2013а, 2013b, 2014a, 2014b; Korotayev and Zinkina 2012, 2014a, 2014c, 2015]).

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