Population-Control-Policies and their Implications for Economic Growth in China
Bachelor’s Thesis supervised by the Department of Economics at the University of Zurich Prof. Dr. Fabrizio Zilibotti

to obtain the degree of Bachelor of Arts in Economics

Author: Noemi Schramm Course of Studies: Economics Closing date: August 17, 2011

Abstract This bachelor thesis is giving an overview on previously performed research how family-planning-policies in China (explicitly the so-called One-Child-Policy) have affected economic growth since 1979 and tries to give possible predictions and forecasts on how it could affect economic growth until 2050 through critical model analysis. The Solow model gives theoretical answers but also yields analytical results through calculations subject to different population development scenarios (low, middle, high growth rates). The dependency ratio as a measurement of population age structure is analyzed and implemented into the Solow model to help understand the influence of family-planning-policies. It is shown that the One-Child-Policy affected heavily the last 32 years of China’s economic development and will continue to affect its future, but according to the calculations in this paper, the impact changes from a positive one to a negative one.

Acknowledgements
I would like to thank Professor Fabrizio Zilibotti for his supervision and for giving me the opportunity to write my thesis at his chair. Especially I would like to thank Yikai Wang for his very valuable and profound support and guidance for this thesis and I would like to thank Monika Egli, Andreas Braun and Rachel Waldvogel for helping me no matter which problems and obstacles I encountered.

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Contents
1 Introduction 2 Population-Control-Policies and their Effects on Economic Growth in China from 1979 to 2005 2.1 One-Child-Policy in China . . . . . . . . . . . . . . . . . . . . 2.2 How the One-Child-Policy changed China . . . . . . . . . . . 2.2.1 Decline of Fertility Rate . . . . . . . . . . . . . . . . . 2.2.2 Development of the Dependency Ratio . . . . . . . . . 2.2.3 Influence on Economic Growth . . . . . . . . . . . . . 3 Population-Control-Policy in the Solow Model 3.1 Theoretical Analysis of the Solow Model . . . . . . 3.1.1 Solow Model with Constant Capital Stock . 3.1.2 Solow Model with Dynamic Capital Stock . 3.2 Combining Data and Neo-Classical Growth Theory 5

8 8 11 12 14 16 19 19 21 25 26

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4 Upcoming Challenges for China linked with the One-ChildPolicy 33 5 Conclusion A Appendix 35 37

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List of Figures
1 2 3 4 5 6 7 8 9 10 11 12 Population Growth, Crude Birth and Death Rates of China 1949 - 2009 . . . . . . . . . . . . . . . . . . . . . . . . . . . Population and GDP per capita of China 1978 - 2005 . . . . Crude Birth Rate per 1000 Women 1978 - 2009 . . . . . . . Total Fertility Rate in % 1978 - 2009 . . . . . . . . . . . . . Population Age Structure 1960 - 2009. . . . . . . . . . . . . GDP annual growth rate 1978 - 2009 . . . . . . . . . . . . . Female Labour Participation 1980 - 2009 . . . . . . . . . . . Total Dependency Ratio 1960 - 2050 . . . . . . . . . . . . . Change of Working Population 2005 - 2050 . . . . . . . . . . Correlation of GDP Growth Rate and ∆ . . . . . . . . . . . Forecast of total GDP 2009 - 2050. . . . . . . . . . . . . . . Population Age Structure 2005 - 2050. . . . . . . . . . . . . . . . . . . . . . . . . 10 11 13 13 15 17 19 24 28 30 31 32

List of Tables
1 2 3 4 5 6 Regression Results for the Savings Rate . . . . . . . . . . . . Upper Middle Income Economies according to World Bank . Dependency Ratios for 28 Chinese Provinces 1978 - 1998 . . Demographic Contributors to GDP Growth 2006 - 2050 with constant Capital Stock . . . . . . . . . . . . . . . . . . . . . Forecasts according to Solow Model with dynamic Savings . Forecasts according to Solow Model with constant Savings . . 29 . 37 . 38 . 38 . 39 . 40

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1

Introduction

China’s growing economy is a phenomenon which has already fascinated and captivated various researchers and scientists. The surprisingly fast transition from a poorly developed country to an economy to be reckoned with has raised the question about its background and reasons. Some of the reasons for China’s development are the drastic political decisions and actions taken during the last 32 years. China has undergone essential market liberalization and opened its markets not only country-wide but also internationally. Furthermore, China has implemented strong population-control-policies to prevent a breakdown as predicted in the Malthusian model1 . The sanctions were not welcomed by everybody, especially human rights activists claimed a rigorous intrusion in personal freedom rights. But China was also given credit by development agencies for drastically improving living standards. More and more researchers analyze the impact the familyplanning-policies had in China and discover profound empirical results (see Li and Zhang (2007), Yu (2011), Crenshaw et al (1997) or Wei and Hao (2010) for reference) showing that the decelerated population growth has added to China’s uprising economy. With today’s knowledge we can predict possible scenarios for population growth in China until 2050 as done by Chen and Liu (2009). Using those numbers and inserting them into growth models underlying the usual assumptions the “net” effect of population dynamics on future economic growth in China can be shown. There has been recent research on the reasons for economic growth in China (Song et al (2011), Ding and Knight (2008) or Holz (2008)), but nobody tried to show the implications of one major contributor to economic growth: labor supply itself and therefore working age population size. This is inflicted with the population-control-policies heavily. Those policies first raise the relative amount of working population (because
The model according to Malthus predicts that because of scarcity of resources (especially land) population growth at some point leads to more poverty and therefore hampers economic growth.
1

5

fewer babies are given birth to) but in the longterm the working population shrinks relatively (because we have a higher amount of old people). The strict family-planning-policies have been enruled 32 years ago and therefore first implications of this transition were already enlighted in the past years. The academic responses to China’s fast economic development vary a lot. Some predict a new “super-power” (as for example Murray (1998)), some announce the collapse of China (Chang (2000)). The effects of population growth on economic development have already been analyzed extensively. What is lacking in today’s research is the effect of population distribution (refer the population age structure pyramid) on economic growth. An ageing population has other effects on economic growth than a likewise growing population with more working people. The dependency ratio – the proportion of not working (and therefore dependent) people to working people – is a good measurement for this distribution. As Bloom and Canning (2003) stated, the dependency ratio measures demographic dynamics more directly than crude birth and death rates, because it also includes to some extent the effect made by peoples changing behavior as it is able to reflect improvements in health conditions of a population. This thesis aims to give an overview on the topic and not only link population dynamics and economic growth in the past but also to give possible predictions and forecasts on the linkage of demographic dynamics and China’s economic growth through showing a modified way to analyze the Solow model. This paper is structured as follows: In the first section, I give an overview on the momentarily implemented population-control-policy in China and shortly explain the technics of the One-Child-Policy. Following, I will discuss existing literature on the past 32 years of population growth and its implications on economic development. During the whole thesis, focus is laid on the dependency ratio because this ratio shows very clearly the influence the population-control-policies have not only on total population growth but also 6

on the distribution of population. In the second part, I will develop an extended Solow model combining the dependency ratio and the classical Solow model and check analytically what this tells us. As this is only a bachelor thesis I focus on a model with simplifying assumptions. In a further study, it would be possible to loose these assumptions. Finally, making numerical forecasts in the third part yields a quantified prediction about the next 40 years of China’s economic development focusing on the demographic parts of economic growth.

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2

Population-Control-Policies and their Effects on Economic Growth in China from 1979 to 2005

Analyzing the existing neo-classical growth theories and models such as for example the model introduced by Robert Solow (1956), we can argue, that the demographic shock caused by the One-Child-Policy has in the short run resulted in higher capital per worker and therefore also higher output per worker. Barro and Sala-i-Martin (1995) show in their book that an increasing population growth tends to lower captial stock per capita and therefore we have a lower level of output per capita and vice versa. The One-ChildPolicy is not a one time demographic shock but a permanent change in the population growth rate which makes the (n + δ) ∗ k linear slope less steep than originally (because n ↓). This means that the effect of capital dilution is reduced and the pace of economic growth is accelerated (Weil, 2009). This increases savings and investment which ends up in a higher capitalstock per capita and hence higher income per capita. As we see in the coming section, this is also consistent with the estimations by various researchers. The following subsections give an introduction into the population-control policies up until today and discuss their effects on the fertility rate, the dependency ratio and economic growth.

2.1

One-Child-Policy in China

The Chinese Government was inspired by the work of the Club of Rome in the 1970s about scarcity of resources (Greenhalgh 2003) and argumented with the Malthusian breakdown (which says that given limited resources, never ending population growth hampers economic growth) when a populationcontrol-policy, commonly known as “One-Child-Policy” (for simplicity reasons hereafter called OCP) was introduced together with other drastic economic and societal reforms in 1979 (Li and Zhang 2007). From 1971 to 1979, the so-called “later marriage, longer birth intervals and fewer births”

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family-planning program was set into force as a response to rapid population growth. This resulted in declining birth rates but for the ruling party it was not enough and out of fear of re-increasing birth rates (because the babyboomers born after the Great Leap Forward were getting into childbearing-age) they reinforced the population-control measures by introducing the OCP (Yu 2011). One feared that the country could collapse as predicted in the Malthusian model. Indeed, the population growth rates and the forecasted populace were alarmingly high. So the officials implemented the family-planning-policy which allowed urban couples one child and rural couples two children with exceptions (for example for minorities) (Yu 2011). Earlier attempts in reducing the accelerating growth rate of the Chinese population had substantial impacts as well. The post-1949s were the beginning of a new era. Chinese government considered a big population as an asset, following traditional Chinese values. But after the first consensus in 1953, government representatives were surprised by the already high number of population (around 600 million (Yu 2011)). They started the first familyplanning program in 1956, which was interrupted shortly after by the Great Leap Forward and the following famine. Figure 1 shows very clearly how the population grew every year since 1949 except during the famine in the years 1958 to 1960. Those years left a incisive mark in the history of China, as it was the only time when the death rate was higher than the birth rate (illustrated in Figure 1). Birthrates jumped back at previous levels and even surpassed them, being responsible for a babyboomer generation in China born after the famine. China soon started a second attempt in controlling population growth through emphasizing late marriage in the 1960s (Yu 2011). This time, the Cultural Revolution in 1967 ended the program but the revolution itself was responsible for later marriage sending young people from urban areas to rural areas. The third birth-control program (the already mentioned “later, longer, fewer” policy) was implemented with the intention of a more overall ap9

Figure 1: Population Growth, Crude Birth and Death Rates of China 1949 - 2009. Source: China Statistical Yearbook, various years. proach. This campaign proved to be very successful and reduced birth rates drastically according to Yu (2011). But in contrary to the birth rate, the fertility rate was only slightly affected through all the programs and therefore the government implemented the OCP, trying to fundamentally decrease fertility rates and therefore permanently change demographic trends. Additionally, the babyboomers born after the famine would have started having children in 1979 and a new boost in population growth rates was expected. The two peaks in Figure 1 of birth rates in 1983 and 1987 can be either explained by the delaying strategies of couples due to the ”later, longer, fewer” policy or by the babyboomers which were at the peak of their reproductive years in 1987 (Yu 2011). The OCP was and is a tough population-control-policy, causing dissonances by human rights organizations (Greenhalgh 2003) and is still unpopular and disputed among many policymakers. But it reached its goal

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and prevented around 300 to 400 millions of births during the last decades (Greenhalgh 2003) having a dramatic impact on China’s economic and societal development. Weil (2009) estimates that by 2000, there were 70 million only-children as a result of the OCP. The policy was relaxed in 2000, allowing more exceptions, but Chinese government still maintains the family-planning program and also intends to do so according to the new five-year guideline issued in March 2011.

2.2

How the One-Child-Policy changed China

According to data in the Penn World Table (2011), China’s population grew from 960 million inhabitants in 1978 to 1.3 billion in 2009. In the same time, the Gross Domestic Product per capita (GDPcapita ) (Purchasing Power Parity (PPP) converted, in international dollar at 2005 constant prices) grew from $550 to $7000 as shown in Figure 2.

Figure 2: Total population and GDP per capita of China 1978 - 2005.
Penn World Table 2011.

Source:

Population-control-policies affect demographics and demographics affect 11

economic growth. In the following subsections, firstly the influence of the OCP on the fertility rate, the birth rate and the changes in the population age structure during the last 32 years are discussed and secondly the effects of those implications on past economic growth. In the last couple of years different researchers conducted empirical studies on the effects of the OCP. This different studies are presented and discussed. 2.2.1 Decline of Fertility Rate

According to the 2010 census (National Bureau of Statistics of China), the fertility rate in China is 1.4, however, the United Nations Population Division estimates the fertility rate at around 1.8 (refer Figure 4) as people in China tend to underreport the actual number of children because of fear of repression. Anyway, both rates are clearly below the replacement level of 2.1 and below those of the other countries classified as “Upper Middle Income Country” by the World Bank (for a list of all the countries with this classification refer appendix). The decline in total fertility rate is normally sequential to a decline in infant mortality (which according to Wei and Hao (2010) declined from 2% in 1960 to 0.66% in 1990, which is a level comparable to developed countries) because of improved health conditions. The OCP imposed an additional exogenously change to the total fertility rate by charging fines to couples not following the policy. In his textbook “Economic Growth”, Weil (2009) writes of a decline in total fertility rate from 5.99 in 1965 to 1970 to 1.76 in 1995. Li and Zhang (2007) argue that not only the policy influenced fertility rate but also the socalled “feedback effect” through higher living standards which again affected birth rate (refer Figure 3, also: Wei and Hao 2010). There is a significant reverse causality through lower birth rates, later marriage and extended life expectancy. In comparison with other countries, the feedback effects of income changes on the birth rate in China is even more salient (Wei and Hao

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Figure 3: Crude Birth Rate per 1000 Women 1978 - 2009. ment Indicators 2009, World Bank.

Source: World Develop-

Figure 4: Total Fertility Rate in % 1978 - 2009.
2009, World Bank.

Source: World Development Indicators

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2010). Another reason for lower fertility rates could be higher real wages for women through economic development, as Galor and Weil (2009) show. 2.2.2 Development of the Dependency Ratio

Demographics cover the age distribution of a population and demographic transitions means evolving from high fertility and mortality to low fertility and mortality rates. One of the main influences of the OCP affected the age distribution of people among the population as illustrated in Figure 5. The OCP prevented aroung 300 million births since its introduction (Greenhalgh 2003). During the first years, the amount of dependent youngsters (per definition aged 0-14 years) declined (as seen in Figure 5) and therefore the youth dependency ratio2 fell as well, mainly due to the lower fertility rate (Wei and Hao 2010) (as shown in the previous section 2.2.1 on page 12). This had major implications on the total dependency ratio as Wei and Hao (2010) have shown. The youth dependency ratio fell from 72.5% in 1965 to 30.2% in 2005 and logically the total dependency ratio declined as well. However, it did not decline at the same extent but by 38%3 due to the relatively stable elderly dependency ratio (increased from 4.8% (1960) to 8% (2009). The relative amount of workers rised to as much as 71.7% in 2009. This had further implications on economic growth which will be discussed in section 2.2.3 on page 16. Salditt et al (2008) speak of the demographic window4 which will last in China according to him until 2015. The demographic window is an indicator used when the economy enters a period with a total dependency ratio around 40-60% according to the United Nations Population Division (2004)
The youth dependency ratio equals total amount of youngsters over working populapeople aged 0-14 tion: people aged 15-64 years . years 3 In their paper of 2007, Li and Zhang also have data about the mean youth dependency ratio and old dependency ratio for 28 Chinese provinces for the period 1978 - 1998. Their numbers differ slightly from the ones of Wei and Hao, as can be seen in Table 3 in the appendix. 4 The demographic window is a period where the relative amount of workers is high and therefore it is a time of economic opportunities.
2

14

Figure 5: Population Age Structure 1960 - 2009.
Divison 2009.

Source: United Nations Population

(mainly due to a lower youth dependency ratio) (Salditt et al 2008, Wei and Hao 2010). If supported by a good legal framework and policies fostering economic environment the demographic window can lead to a demographic dividend5 (Bloom and Williamson 1998). In their report of 2004, the United Nations Population Divisions predicts the demographic window for China opened in 1990 and lasts until 2025, however, our own research (with data from Chen and Liu (2009)) predicts the demographic dividend to last until 2033 taking as treshold value a total dependency ratio of 50%. Together with the economic reforms undertaken since 1978, China has been able to profit a lot from the demographic dividend. GDP growth rates took off with the opening of the demographic window in 1990 (refer Figure 6). The discussed papers have the underlying assumption that people work during the age of 15-64 and do not work while they are younger than 15 or older than 65. Those assumptions are useful abstractions and are also used by Chen and Liu (2009) in their paper while forcasting population size, therefore these age classifications are maintained in this thesis. With these classifications, we calculated the dependency ratio for China from 1960 to
The demographic dividend is the part of economic growth attributable to a low dependency ratio through a rising share of working adults.
5

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2050 as illustrated in Figure 8 on page 24. 2.2.3 Influence on Economic Growth

Mankiw et al (1992) showed the general significant negative correlation between population size and output of a country in their article. Concerning China, Li and Zhang (2007) show in their paper that a decline of the birth 1 rate by 1000 increases the economic growth rate by an estimated 0.9% a year. They also conclude that the steady-state GDPcapita would be raised by 14.3%. Through an estimation employing the generalized method of moments (GMM) they find that the economic growth rates of the Chinese provinces decrease with increasing birth rates and vice versa. The two authors therefore reason along with the Malthus model stating that too high birth rates can hamper economic growth and probably have done so in China before implementing population-control-policies. Wei and Hao (2010) state in their paper that China had a significantly higher GDP per capita growth rate during 1978 to 2008 than the United States, Europe, Japan and India. In Figure 6 data from the World Bank also shows that China not only had higher growth rates than the worldwide average growth rate but also than other middle income countries. For sure, it was not only the demographic development that contributed to those high growth rates but also other factors such as institutional reform, rapid accumulation of capital, general elimination of inefficiencies or the enhancement of total factor productivity (Wei and Hao 2010, Holz 2006). Other factors are the reallocation of resources (Song et al 2011), market liberalization and the adoption of an open-door policy (Yu 2011). Researchers have estimated the influence of the population age structure on previous growth rates. Cai and Wang (2005, 2006) find that an increase of the total dependency ratio of 1% lowers the GDP per capita growth rate by 0.115%. Wei and Hao (2010) estimate a 0.065% increase in economic growth per 1% decrease in total dependency ratio. The correlation is clearly

16

Figure 6: GDP annual growth rate 1978 - 2009. ment Indicators 2009.

Source: World Bank, World Develop-

negative, their results show this at the 5% significance level. In their paper the two authors also show that the youth dependency ratio has a significant negative impact on economic growth while the old dependency ratio is negatively correlated, but the estimations are insignificant. A very interesting approach is shown by Yu (2011). He adds the averted average 13 million births a year to the dependency ratio and calculates China’s GDP per capita growth rate with the different numbers, comparing it afterwards with actual growth rates. He shows that for example in 1995, the real GDP per capita would have been 13.2% lower without the OCP. Combining different research theories, he concludes that the high ratio of working to non-working population led to higher savings, higher savings led to a higher level of investment and the large capital stock led to threshold externalities as shown as existing in developing countries. This all together ended in an economic take-off effect. The estimated threshold value of the ratio of working population and non-working population is 1.81. Given that

17

1.81 workers support one dependent non-worker6 , saving rates and investments were high enough for the economic take-off to occur. He calculated that the start of the economic take-off effect was around 1984 to 1985. Without the OCP, the treshold value would have been reached in 1996, hence the OCP accelerated economic growth for about twelve years. Another argument for the explosion of growth rates could be the rising participation of women at labor market (refer Figure 7). Chen and Hao (2010) argue that due to the OCP more women were released to the labor market which added to the working age population. This is also supported by research conducted by Bloom et al (2009) which argues that decreasing fertility rates enhance female labor participation. But data shows that the female participation rate at the labour market reached its peak in 1990 and decreased since then. This contradicts Chen and Hao’s argument and could possibly be explained by a renunciation of traditional communist equal opportunity policy which was another reason for the high female labor participation rate. But this still needs more research for clear clarification. According to a cross-country panel data analysis made by Ding and Knight (2008), the low population growth rate has contributed significantly to economic development in China. The two authors take the Solow model and add human capital and structural change to the classical model before estimating results. To conclude, many studies (among others: Cai and Wang 2006, Yu 2011, Wang and Mason 2008) have concluded that the demographic transitions during the last decades are responsible for one-sixth to two-fifths of China’s GDP per capita growth since 1978.

This corresponds to a dependency ratio of 0.55. Concerning the start of the economic take-off effect refer Figure 8 on page 24.

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Figure 7: Female Labour Participation 1980 - 2009.
Indicators 2009, World Bank.

Source: World Development

3

Population-Control-Policy in the Solow Model

This thesis is not covering population-control-policies in overlapping-generations (OLG) growth models because calculations are difficult to make using a simplified two-period OLG model. China has implemented the OCP only 32 years ago, which would be only one period. Hence, we focus on the neoclassical growth model as presented by Robert Solow (1966) and modify the standard model to integrate population dynamics. We use the data estimated and provided by Chen and Liu (2009). They made forecasts for population growth rates for China from 2005 to 2050 applying three different scenarios: low, middle and high projected growth rates. For further reference and explanations on the underlying assumptions of the projections, we refer to their paper.

3.1

Theoretical Analysis of the Solow Model

We use the Solow model with its standard assumptions as described in the textbook of David Weil (2009). As part of the technical analysis we add the

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dependency ratio to the model and use differentiation to see what happens with income per capita if the dependency ratio or the amount of dependent people change. This helps us to predict and understand possible changes in economic growth in the future. For simplicity reasons we assume zero international migration. This is realistic, because data shows that relative migration is near zero in China and therefore this assumption is widely used in various published papers. We also presume: • Y ... total income, GDP • y ... income per capita y = • A ... technical progress • K ... capital stock • α ... share of capital in the production function, α ∈ (0, 1) • s ... savings rate • L ... total population • W ... working population, people aged 15-64 • D ... dependent population, people aged under 15 and above 65 • ∆ ... dependency ratio (proportion of dependent people per worker) D =W • gY ... growth rate of total income =
Yt+1 −Yt Yt At+1 −At At Y L

= GDPcapita

• gA ... growth rate of technical progress = • gK ... growth rate of capital stock =

Kt+1 −Kt Kt Wt+1 −Wt Wt

• gW ... growth rate of working population =

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We do not show every step of the normal Solow model here. For reference and introduction we recommend to read David Weil’s book ”Economic Growth” (2009) or Barro and Sala-i-Martin’s book with the same title (1995). One of the main assumptions of the Solow model is that the whole population L is working. We adjust that in our framework and use only the working population combining this with the dependency ratio. This yields to slightly different results and allows us to integrate the population age structure in the model. In the first part, we hold capital stock constant, in the second part we integrate a dynamic capital stock into the model. 3.1.1 Solow Model with Constant Capital Stock

Given the definition for GDP per capita, we add the ratio of workers among total population and combine this with GDP per worker as follows: GDPcapita = GDPworker ∗ The term W = L
W L

W L

(1)

can be transformed as follows:
−1

L W

=

W +D W

−1

= (1 + ∆)−1 =

1 1+∆

.

(2)

Combining equations (1) and (2) we get GDPcapita = GDPworker ∗ (1 + ∆)−1 , (3)

D knowing that ∆ = W . Here we see mathematically what happens when the dependency ratio ∆ increases (which means that either D ↑ or W ↓ or both) or decreases: GDP per capita is negatively interrelated with ∆. If the dependent proportion of people in a population rises, GDP per capita falls.

The definition of GDP per capita as known from the Solow model is y = Y = GDPcapita . We now analyze a standard Cobb-Douglas producL tion function, taking into consideration that only part of the population is working. This yields: 21

Y = A ∗ K α ∗ W 1−α , with α ∈ (0, 1).

(4)

We divide with L to get GDP per capita and for later use we rearrange W .
1−α

Y W 1 Y 1 W = AK α α ⇐⇒ = AK α α . L W L L W L Here we use again equation (2) and insert it into (5) which yields 1 Y = AK α α L W 1 1+∆ .

(5)

(6)

We analyze GDP per capita, because what is interesting in our research is how population dynamics influence economic growth and GDP per capita yields the most salient results in terms of how it affects the economy cleared of population bias. We now differentiate this equation with respect to ∆ to check analytically, what happens with a change of the dependency ratio in the Solow model.

∂( Y ) L =A ∂∆

K W

α

∗ −

1 (1 + ∆)2 α which is < 0.

(7)

K 1 The first two terms A and W are positive, the last term − (1+∆)2 is negative. We showed analytically that in the standard Solow model the dependency ratio and hence the population age structure and GDP per capita are negatively correlated. Multiplying equation (6) with L and differentiating yields as well a negative result, hence total GDP is also negatively correlated with the dependency ratio. An interesting point to know is the effect of a change of the dependent population on economic output because China is expecting major changes in the amount of the dependent population in the coming years (especially

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ongoing ageing). Taking the derivatives of equation (4) is easy and yields α ∂Y K = A(1 − α) L−D ∗ (−1) < 0, stating that total GDP and the amount ∂D of dependent persons is negatively correlated. Analyzing GDP per capita is not as easy but yields very interesting results: ∂( Y ) L = AK α (1−α)(L−D)−α ∂D 1 1 −AK α (L−D)1−α . (8) W +D (W + D)2

The analysis if this term is positive or negative is not simple. The first part of the differentiation is negative, the second one positive. Therefore, it depends whether the first or the second part is bigger. This yields:

AK α W −α

W 1 [(1 − α) − ] W +D W +D

0?

(9)

Because all the first terms are positive, we simply have to check whether

(1 − α) −

W W +D

0?

(10)

W + D equals the total population L and therefore we can state the following: 1. if 2. if 3. if
W L W L W L

> (1 − α), then < (1 − α), then = (1 − α), then

∂( Y ) L ∂D ∂( Y ) L ∂D ∂( Y ) L ∂D

< 0. > 0. = 0.

In China, α is estimated around 0.35 to 0.5, depending on the researcher (refer Minghai et al 2010, Song et al 2011, Liang 2006). This implicates that as long as the proportion of working people among total population is below 0.5 to 0.65, a change in the dependent population is negatively correlated with output per capita. We know that W can be rewritten according to equaL 1 tion (2) as W = ∆+1 . Solving the equations with α = 0.5 yields the following: L

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1. if ∆ > 1, then 2. if ∆ < 1, then 3. if ∆ = 1, then

∂( Y ) L ∂D ∂( Y ) L ∂D ∂( Y ) L ∂D

> 0. < 0. = 0.

This means that as long as the dependency ratio is lower than 1 (which states that there are more workers than dependent people), the dependent population and GDP per capita are negatively correlated. Figure 8 shows that the dependency ratio always was and will be lower than the treshold value according to our data and therefore an increase in the dependent population yields to an decrease in output per capita. Knowing that, we presume in the calculations part that total GDP is affected negatively because of an increasing dependency ratio.

Figure 8: Total Dependency Ratio 1960 - 2050 (∗ is a forecast).
Bank and Chen and Liu, 2009.

Source: World

This thesis aims at showing the net effect of population dynamics on economic growth and hereby explicitly total GDP growth, therefore we now analyze growth rates. Taking logarithm of equation (4) and differentiating with respect to time yields the following equation: 24

gY = gA + αgK + (1 − α)gW

(11)

We also know that we can express either one of the three growth rates gW , g1+∆ , gL by two of them as for example gW = gL + g1+∆ (taking logarithm of equation (2) and differentiating with respect to time). We see that economic growth is composed by the growth rate of working population (slightly smoothed by α) and this again is influenced by the change of the dependency ratio and the total population growth. With this equation, we are able to calculate the demographic parts of the growth rate of GDP per year in the coming section 3.2. Holding capital stock and technological progress at a constant level, we see the net contribution of demographic dynamics on economic growth. 3.1.2 Solow Model with Dynamic Capital Stock

Let us now relax the assumption of a constant capital stock and assume capital stock as follows: Kt+1 = st Yt = st AKtα Wt1−α assuming that st = s Wt Lt
+

(12)

Consequently, s is increasing if the proportion of workers among population ( W ) is increasing. What we do now is to calculate growth rate of capital L stock gK and insert it into our growth equation.

gK =

sAKtα Wt1−α − Kt Kt+1 − Kt = = sA Kt Kt

Kt Wt

α−1

−1

(13)

gY = gA + α[sA

Kt Wt

α−1

− 1] + (1 − α)gW

(14)

25

We can use this equation and calculate GDP growth rates and total GDP until 2050 with our data. Running a regression with existing data on savings rates and proportion of working population helps us to calculate the corresponding savings rates until 2050.

3.2

Combining Data and Neo-Classical Growth Theory

In the following chapter, growth accounting with focus on population dynamics is executed. The GDP growth rate is decomposed according to the precedent chapter into growth of capital stock and working population. If not otherwise specified, we use data provided by Chen and Liu (2009). The two authors made an overall approach in projecting population until 2050 applying three different scenarios (low, middle, high growth rates). For the calculations presented here, we used the middle scenario. The following calculations underly certain assumpations: 1. The current political situation does not change dramatically. (This would have possible inflictions on population size). 2. The education is equally distributed among population and are not qualified in the calculations. Focus is laid on population growth and dependency ratio. 3. There exists an economy-wide aggregate production function (CobbDouglas production function) with constant returns to scale and constant output elasticities and the Inada7 conditions hold.
7

The six conditions are:

(a) the value of the function at 0 is 0, (b) the function is continuously differentiable, (c) the function is strictly increasing in x, (d) the derivative of the function is decreasing (thus the function is concave), (e) the limit of the derivative towards 0 is positive infinity, (f) the limit of the derivative towards positive infinity is 0.

26

4. To show the net effect of the OCP on economic growth, the other parameters are kept constant (such as A (technical progress). 5. The actual pension age in China is 55 for women and 60 for men. We maintain the assumptions of a working age between 15 and 65, firstly out of convenience and because data is separated like this and secondly because China will need to make adjustments here in the coming years, so we expect the retirement age to increase. Consistent with Song et al (2011), we set α (the share of capital) to 0.5. Others (Liang 2006) use 0.4 as value, but we take the most actual research paper and their assumptions. Additionally, it has been discussed that since 1990 capital’s share of national income has been increasing while labor’s share of income has been decreasing (Liang 2006). Since we are forecasting into the future, α equaling 0.5 is more likely. We start by calculating the growth rate of working population and from there we use equation (11) with constant capital stock which yields the demographic contributors of growth rates of GDP from 2006 to 2050. Knowing about the positive correlation of gW and gY , Figure 9 clearly shows that population first has a positive influence on total GDP growth. Beginning in 2027, population dynamics and especially the ongoing ageing of the society have a negative impact on economic growth. This also supports the statement of Chen and Liu (2009) speaking of a dependency ratio below 0.5 and accordingly stating that the demographic window closes in 2033 (middle population growth). Table 4 on page 38 summarizes the data for the middle population growth scenario. We incorporate gK as described in section 3.1.2. For our calculations, we first need to run a regression on the savings rate and the proportion of working people. The result of the regression is used in our further calculations to project s into future. Unfortunately, only 39 data sets are available, but since the results are highly significant and normally distributed, we use the

27

Figure 9: Change of working population 2005 - 2050, five year growth rates.
Source: own calculations with data based on Chen and Liu, 2009.

coefficients despite the rather small sample. The linear function graphs the relationship fairly according to R2 . We checked as well an exponential and polynominal relationship, but the numbers for R2 differ only slightly and therefore we apply a linear regression. The summary of the regression with data from the World Bank can be seen in Table 1. We use the numbers and express s as follows:

s

W L

= −0.38 + 1.19

W L

(15)

Hence, we can calculate the savings rate for the years 2010 to 2050 (we have data until 2009) using the population age structure data provided by Chen and Liu. The data is summarized in the appendix (refer Table 5). Using equation (13) and holding A constant (or normalized to 1) we can use the data we retrieved from the World Bank and calculate capital stock 2009. The coming procedure for our calculations can be summarized as follows: 28

Call: lm(formula = s ∼

W L

)

Residuals: Min 1Q Median 3Q Max -0.047119 -0.022194 0.001478 0.017017 0.063959 Coefficients: Estimate Std. Error t value Pr(>| t |) (Intercept) -0.38011 0.05718 -6.647 7.41e-08 *** W 1.18909 0.08893 13.371 6.02e-16 *** L — Signif. codes: 0 (***) 0.001 (**) 0.01 (*) 0.05 (.) 0.1 ( ) 1 Residual standard error: 0.02858 on 38 degrees of freedom Multiple R-squared: 0.8247, Adjusted R-squared: 0.8201 F-statistic: 178.8 on 1 and 38 DF, p-value: 6.022e-16 Table 1: Regression Results for the Savings Rates. data from the World Bank. Source: own calculations based on

1. Calculate capital stock Kt using equation (12). 2. Calculate gY with growth equation (14). 3. Calculate total GDP, Yt+1 . 4. Start again by calculating capital stock Kt+1 . This yields to our forecasts of economic growth for China until 2050 (PPP converted, international Dollars, in 2005 constant prices or percent (growth rates)). The whole data set is available in Table 5 in the appendix. Using a dynamic savings rate yields negative GDP growth rates because the shrinking working population has a multiple effect in our model. We conduct another forecast leaving the savings rate a a constant level of 0.5. This could also reflect reality as an uncertain pension system could be responsible for high savings rates no matter if the working population is decreasing. Those forecasts are displayed in Table 6 and we further analyze those second

29

calculations. As the whole thesis is about incorporating the dependency ratio into economic growth, we now run a non linear regression on the relation of ∆ and gY as plotted in Figure 10. The significant results are displayed in the Figure. The regression yields a quadratic function as result, which states that applying the Solow model, ∆ has a bigger impact on gY than overall expected. One possible explanation for the polynominal regression could be that ∆ has multiple effects in our model. But we need more data sets to verify those results; this could be part of another research project.

Figure 10: Correlation of GDP Growth Rate and ∆ with Regression Results.
Source: own calculations based on data from Chen and Liu, 2009.

Concluding this section we can state that China is still able to profit from the demographic dynamics at least until 2016 and also some years after. The result of our forecasts are graphed in Figure 11. We know that this is excluding other factors which additionally enhance China’s economic growth. 30

What we can state from our model analysis is, that an ageing China will have decelerating growth rates and the problems of the population-controlpolicies (fast and ongoing ageing) will hamper economic growth starting with the closing of the demographic window. Here we support the statement of Salditt et al (2008) of the closing of the demographic window in 2015 and therefore the end of the demographic dividend.

Figure 11: Forecast of total GDP 2009 - 2050. from Chen and Liu, 2009.

Source: own calculations based on data

In China, problems concerning the fast ageing population occur. The share of elderly people among population is increasing dramatically from 7% to nearly a quarter of total population, as Figure 12 with data from Chen and Liu (2009) shows. As the report of Salditt et al (2008) states, until 2006 only 50% of the urban population were part of the pension system and among the rural employees, the number is even lower. If China does not suceed in implementing a sustainable and equitable pension system, people are forced to save a high amount of their income and they are dependent on their family. The phenonemon called 4-2-1 will happen where one child has 31

to provide for two parents and four grandparents because all were subject to the OCP (Salditt et al 2008). The changes in the working population are shown in Figure 9. Furthermore, the peak of the ratio of workers per dependent person is reached (Figure 8 shows the inverted discussed graph) and this ratio is declining to half of what it is now until 2050. This has further implications on the “economic burden” each worker has to carry.

Figure 12: Population Age Structure 2005 - 2050.

Source: Chen and Liu, 2009.

32

4

Upcoming Challenges for China linked with the One-Child-Policy

A topic which has not been considered in this thesis is the sex ratio of the newborn as a consequence of the OCP. In 2005, the ratio of girls versus boys of newborns (aged 0 to 4) has been 100 to 122 (Salditt et al 2008). The ”missing girls” will be of relevance in the coming future as China is becoming a society with not enough women which could impose political unrest among unsatisfied young men. This also has implications on the reproduction rate as only girls can give birth again. While opening up the country, migration becomes another important topic. On one hand, Chinese workers are migrating to other countries (as for example to the rich Arabian peninsula) and on the other hand there is a big amount of inner-country migration. Since the beginning of the 1990s, an increasing amount of workers are recorded as not living in the place of work. This affects first of all the estimations made by researchers because the migrant workers normally send back remittances which could raise the savings rate and therefore end up in a bias in the estimations. Secondly, the workers could make the impression of a lower dependency ratio in certain areas. These migrant workers are a mass of around 115 million people (Salditt 2006, Jackson 2011) which do not have a real perspective for life. Combining this with fewer women available for marriage, the tension because of unsatisfied needs is growing. With the transition of China to an upper income economy, work becomes more expensive. The possibility of fast boosts of GDP through moving rural people to urban areas and let them work in badly paid jobs will not be possible anymore in the same amount. The undereducated workers will be jobless and this yields to a burden for the economy. As already Schultz (1961) wrote, investment in human capital and economic growth are directly linked. The transition from large families to smaller families brings one significant change: the enhancement of investment in human capital (Becker 33

et al 1990). Becker et al (1990) describe two steady-states: one with large families and small investment in human capital and one with small families and rising investment in human capital. They state the idea that a country can switch its steady-state given certain policies and adequate living standard. The OCP artificially accelerated the speed of this transition through exogenously influencing the family size. This forced China to switch from one steady-state to the other. Subsidizing and supporting puplic education system can be used to advance higher investment in human capital (Fanti and Gori 2011, Zhang 1997). Since private returns to education at the moment are possibly below its marginal value, as Holz (2008) states, China has to invest in the education system to further promote the investments in human capital. To give education more weight may help maintain economic growth. Or as Holz (2008) has remarked: ”If talent is randomly distributed among the world population and if China’s education system is able to identify the brightest students, then China has a larger pool of talent to draw from than any other country in the world.” To use those resources more efficiently means more innovation are possible and therefore a higher level of productivity and economic growth occur. In their new five-year-guidelines, China writes about creating an innovation promoting environment. But compared to other developing countries such as Sub-Saharan Africa and South Asia, the level of education makes the growth difference according to Ding and Knight (2008). China is on a better track than the other countries in terms of education. The two authors also found that compared with industrial countries, the growth rate of human capital is responsible for the growth difference. So investment in human capital is one major part of growth accounting in China compared to other countries’ growth rate.

34

5

Conclusion

Family-planning-policies have implications on economic growth and economic growth has implications on population growth. Even the World Bank calls for population-control-policies in order to promote economic development. An interesting ethical (and in this thesis unanswered) question is, if it is allowed and desirable to limit human rights (sexual and reproductive rights) to promote decent life and economic development. Bearing in mind that not only the economy grew during the last decades, but also the inequality as can be seen in the rise of the Gini coefficient as a measure for the distribution of income from 0.341 in 1988 8 to 0.415 in 2005 according to the World Bank 9 . In their technical report for the United Nations University, Renwei and Li (2007) even talk about a Gini coefficient of the distribution of wealth of 0.55 in 2001. China decided 32 years ago to implement a rigorous family-planningpolicy and they will still be affected by this decision during the coming years. The OCP is irreversible and has long-lasting implications: the policy first enhanced economic growth through a lower dependency ratio, which even led to the opening of a demographic window and hence China was able to profit of the demographic dividend. But the accelerated ageing of the population yields an increasing old dependency ratio. According to our forecasts applying the Solow model, China has to expect a negative impact on economic growth because of demographic dynamics. Interesting here is that the impact and the demographic contributors are rather small in numbers, but still it is able to hamper economic growth in the future. However, in the future adjustments to the convention on how to use and
Prior data on overall Gini coefficient in China is not available, this is data from the National Bureau of Statistics of China. However, the World Bank estimated the Gini coefficient in 1978 around 0.3 (Renwei et al 1999). 9 This is also consistent with calculations made by the United Nations Development Program which measured a Gini coefficient of 0.415 during 2000-2010.
8

35

calculate the dependency ratio is needed since people not only in China but all over the world start working later and retirement age varies also. This has significant implications on the population age structure and the used models in science. The calculations made here are to be understand as a net effect. A lot of other factors, which are main contributors to economic growth in China, have not been considered. But as from the population perspective we can state that China will no longer profit from a rising working population. They are encountered with the same problems as developed economies: an ageing society. It will be interesting to witness how China is handling this problem. China has already undergone major changes and addressed challenges with drastic answers — the OCP is one example. So China might be able to undertake drastic actions again. Next year the government is changing, this might be followed by other policy decisions. Whether an ageing China can be a rising China will be decided by the actions made by the government and their ability to adapt to the new situation. The positive impact of the OCP is coming to an end, it might be time to adjust China’s population-controlpolicies.

36

A

Appendix

The World Bank classified each country to a certain group, China is part of the “Upper Middle Income” economies (GDP per capita is $3,976 to $12,275). All countries in this group are listed in Table 2. Upper-middle-income economies Albania Ecuador Namibia Algeria Gabon Palau American Samoa Grenada Panama Antigua and Barbuda Iran, Islamic Rep. Peru Argentina Jamaica Romania Azerbaijan Jordan Russian Federation Belarus Kazakhstan Serbia Bosnia and Herzegovina Latvia Seychelles Botswana Lebanon South Africa Brazil Libya St. Kitts and Nevis Bulgaria Lithuania St. Lucia Chile Macedonia, FYR St. Vincent and the Grenadines China Malaysia Suriname Colombia Maldives Thailand Costa Rica Mauritius Tunisia Cuba Mayotte Turkey Dominica Mexico Uruguay Dominican Republic Montenegro Venezuela, RB Table 2: Upper Middle Income Economies according to World Bank.
World Bank. Source:

37

Ratios Youth Dependency Ratio Old Dependency Ratio

N 112 112

Mean 0.320 0.049

Standard Deviation 0.064 0.015

Min 0.179 0.022

Max 0.429 0.114

Table 3: Dependency Ratios for 28 Chinese Provinces 1978 - 1998. and Hao, 2010.

Source: Wei

Year 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 2023 2024 2025 2026 2027

gW 1.17 1.05 0.83 0.72 0.82 0.51 0.40 0.40 0.20 0.20 0.00 -0.20 -0.20 -0.30 -0.30 -0.20 -0.30 -0.10 0.30 0.20 0.51 -0.20

g1+∆ -0.63 -0.44 -0.23 -0.12 -0.15 0.16 0.26 0.25 0.45 0.38 0.57 0.70 0.63 0.66 0.66 0.55 0.52 0.38 -0.17 -0.06 -0.36 0.27

gL 0.54 0.61 0.60 0.60 0.67 0.67 0.66 0.66 0.65 0.58 0.57 0.50 0.43 0.35 0.35 0.35 0.21 0.28 0.14 0.14 0.14 0.07

gY 0.5857 0.5263 0.4103 0.3616 0.4103 0.2543 0.2024 0.2016 0.1004 0.1002 0.0000 -0.1000 -0.1002 -0.1506 -0.1511 -0.1010 -0.1518 -0.0508 0.1524 0.1013 0.2528 -0.1006

Year 2028 2029 2030 2031 2032 2033 2034 2035 2036 2037 2038 2039 2040 2041 2042 2043 2044 2045 2046 2047 2048 2049 2050

gW -0.91 -0.51 -0.61 -0.62 -0.52 -0.94 -0.84 -1.17 -0.96 -0.97 -0.87 -0.77 -0.78 -0.67 -0.45 -0.57 -0.57 -0.57 -0.58 -1.04 -0.59 -0.71 -0.59

g1+∆ 0.92 0.58 0.62 0.62 0.52 0.88 0.85 1.18 0.90 0.91 0.81 0.71 0.64 0.54 0.24 0.36 0.36 0.29 0.23 0.70 0.16 0.28 0.17

gL 0.00 0.07 0.00 0.00 0.00 -0.07 0.00 0.00 -0.07 -0.07 -0.07 -0.07 -0.14 -0.14 -0.21 -0.21 -0.21 -0.28 -0.35 -0.35 -0.43 -0.43 -0.43

gY -0.4536 -0.2543 -0.3067 -0.3086 -0.2588 -0.4683 -0.4202 -0.5826 -0.4823 -0.4870 -0.4372 -0.3859 -0.3889 -0.3359 -0.2255 -0.2831 -0.2847 -0.2893 -0.2880 -0.5214 -0.2927 -0.3534 -0.2966

Table 4: Demographic Contributors in % to GDP Growth 2006 - 2050 with constant Capital Stock, middle scenario. Source: own calculations, data retrieved from
Chen and Liu (2009).

38

39

Year 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 2023 2024 2025 2026 2027 2028 2029 2030 2031 2032 2033 2034 2035 2036 2037 2038 2039 2040 2041 2042 2043 2044 2045 2046 2047 2048 2049 2050
Source: World Bank (2005 - 2009), own

Savings Rate 48.70 48.56 48.34 48.12 47.73 47.41 46.92 46.33 45.81 45.26 44.72 44.26 43.84 43.53 43.66 43.71 44.01 43.79 43.05 42.58 42.09 41.59 41.18 40.49 39.83 38.93 38.24 37.55 36.94 36.41 35.93 35.54 35.36 35.10 34.84 34.62 34.46 33.96 33.84 33.64 33.52

GDP 8’688’348’912’522 8’655’353’281’464 8’648’805’891’040 8’643’270’571’202 8’638’338’225’840 8’609’716’559’868 8’575’142’281’741 8’513’959’087’494 8’421’785’517’280 8’320’430’624’740 8’208’739’753’945 8’092’637’920’464 7’986’536’112’441 7’884’501’408’782 7’802’521’968’536 7’785’805’498’199 7’789’958’045’713 7’838’397’709’170 7’835’008’452’324 7’731’408’468’819 7’619’143’092’170 7’496’860’930’625 7’370’232’752’050 7’253’024’353’788 7’101’829’213’966 6’941’322’963’640 6’745’192’984’709 6’559’332’486’027 6’379’445’249’316 6’213’797’453’851 6’065’992’762’081 5’931’551’549’937 5’814’064’790’802 5’729’089’339’309 5’650’072’340’520 5’574’120’587’596 5’503’854’040’530 5’440’487’805’784 5’341’656’480’540 5’268’557’255’848 5’198’396’930’968

Capital Stock 4’299’228’006’938 4’231’298’044’007 4’203’374’095’321 4’180’975’985’876 4’159’345’402’887 4’123’430’735’128 4’082’050’196’024 4’023’799’764’284 3’944’722’681’562 3’857’679’676’722 3’765’730’611’430 3’670’584’822’134 3’581’750’766’261 3’501’106’781’747 3’431’855’390’195 3’406’687’296’981 3’403’418’084’863 3’428’538’121’013 3’432’471’646’311 3’372’839’921’351 3’292’043’852’400 3’206’570’227’069 3’118’040’626’602 3’035’007’502’681 2’936’896’733’867 2’828’824’744’936 2’701’928’496’255 2’579’091’474’733 2’462’751’260’136 2’356’388’592’494 2’262’473’987’341 2’179’784’126’848 2’108’079’584’036 2’055’964’878’315 2’010’894’069’510 1’968’282’276’629 1’929’931’615’264 1’896’609’872’794 1’847’481’890’145 1’807’733’879’363 1’772’362’921’652

Working Population 983’000’000 988’000’000 992’000’000 996’000’000 998’000’000 1’000’000’000 1’000’000’000 998’000’000 996’000’000 993’000’000 990’000’000 988’000’000 985’000’000 984’000’000 987’000’000 989’000’000 994’000’000 992’000’000 983’000’000 978’000’000 972’000’000 966’000’000 961’000’000 952’000’000 944’000’000 933’000’000 924’000’000 915’000’000 907’000’000 900’000’000 893’000’000 887’000’000 883’000’000 878’000’000 873’000’000 868’000’000 863’000’000 854’000’000 849’000’000 843’000’000 838’000’000

gK -1.58 -0.66 -0.53 -0.52 -0.86 -1.00 -1.43 -1.97 -2.21 -2.38 -2.53 -2.42 -2.25 -1.98 -0.73 -0.10 0.74 0.11 -1.74 -2.40 -2.60 -2.76 -2.66 -3.23 -3.68 -4.49 -4.55 -4.51 -4.32 -3.99 -3.65 -3.29 -2.47 -2.19 -2.12 -1.95 -1.73 -2.59 -2.15 -1.96 -1.68

gW 0.82 0.51 0.40 0.40 0.20 0.20 0.00 -0.20 -0.20 -0.30 -0.30 -0.20 -0.30 -0.10 0.30 0.20 0.51 -0.20 -0.91 -0.51 -0.61 -0.62 -0.52 -0.94 -0.84 -1.17 -0.96 -0.97 -0.87 -0.77 -0.78 -0.67 -0.45 -0.57 -0.57 -0.57 -0.58 -1.04 -0.59 -0.71 -0.59

gY -0.38 -0.08 -0.06 -0.06 -0.33 -0.40 -0.71 -1.08 -1.20 -1.34 -1.41 -1.31 -1.28 -1.04 -0.21 0.05 0.62 -0.04 -1.32 -1.45 -1.60 -1.69 -1.59 -2.08 -2.26 -2.83 -2.76 -2.74 -2.60 -2.38 -2.22 -1.98 -1.46 -1.38 -1.34 -1.26 -1.15 -1.82 -1.37 -1.33 -1.14

∆ 0.3713 0.3735 0.3770 0.3805 0.3868 0.3920 0.4000 0.4098 0.4187 0.4280 0.4374 0.4453 0.4528 0.4583 0.4559 0.4550 0.4497 0.4536 0.4669 0.4755 0.4846 0.4938 0.5016 0.5147 0.5275 0.5456 0.5595 0.5738 0.5865 0.5978 0.6081 0.6167 0.6206 0.6264 0.6323 0.6371 0.6408 0.6522 0.6549 0.6595 0.6623

Table 5: Forecasts (rates in %) according to Solow Model with dynamic Savings.

calculations (2010 - 2050), data retrieved from Chen and Liu (2009)

40

Year 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 2023 2024 2025 2026 2027 2028 2029 2030 2031 2032 2033 2034 2035 2036 2037 2038 2039 2040 2041 2042 2043 2044 2045 2046 2047 2048 2049 2050
Source: World Bank (2005 - 2009), own

Savings Rate 50.00 50.00 50.00 50.00 50.00 50.00 50.00 50.00 50.00 50.00 50.00 50.00 50.00 50.00 50.00 50.00 50.00 50.00 50.00 50.00 50.00 50.00 50.00 50.00 50.00 50.00 50.00 50.00 50.00 50.00 50.00 50.00 50.00 50.00 50.00 50.00 50.00 50.00 50.00 50.00 50.00

GDP 8’507’543’929’361 8’672’405’997’160 8’778’490’373’976 8’849’951’619’309 8’903’815’751’277 8’939’851’309’985 8’966’899’777’812 8’980’464’930’728 8’978’277’302’958 8’968’187’485’681 8’949’641’940’074 8’926’869’246’089 8’906’494’832’434 8’882’808’870’251 8’866’488’344’388 8’871’859’062’767 8’883’534’760’888 8’911’836’144’043 8’917’066’287’317 8’879’232’492’172 8’837’813’881’400 8’790’091’319’374 8’739’228’973’390 8’691’327’901’282 8’626’810’436’265 8’558’544’064’105 8’474’816’584’828 8’392’487’073’301 8’310’849’714’977 8’234’096’513’341 8’164’299’979’409 8’097’947’473’038 8’037’836’097’554 7’989’879’870’374 7’943’423’413’723 7’897’712’295’679 7’852’371’673’621 7’807’215’234’572 7’744’057’158’003 7’690’063’628’305 7’636’081’722’033

Capital Stock 4’127’665’392’356 4’253’771’964’681 4’336’202’998’580 4’389’245’186’988 4’424’975’809’655 4’451’907’875’639 4’469’925’654’993 4’483’449’888’906 4’490’232’465’364 4’489’138’651’479 4’484’093’742’841 4’474’820’970’037 4’463’434’623’044 4’453’247’416’217 4’441’404’435’126 4’433’244’172’194 4’435’929’531’384 4’441’767’380’444 4’455’918’072’021 4’458’533’143’658 4’439’616’246’086 4’418’906’940’700 4’395’045’659’687 4’369’614’486’695 4’345’663’950’641 4’313’405’218’132 4’279’272’032’053 4’237’408’292’414 4’196’243’536’651 4’155’424’857’488 4’117’048’256’670 4’082’149’989’705 4’048’973’736’519 4’018’918’048’777 3’994’939’935’187 3’971’711’706’861 3’948’856’147’840 3’926’185’836’811 3’903’607’617’286 3’872’028’579’002 3’845’031’814’153

Working Population 983’000’000 988’000’000 992’000’000 996’000’000 998’000’000 1’000’000’000 1’000’000’000 998’000’000 996’000’000 993’000’000 990’000’000 988’000’000 985’000’000 984’000’000 987’000’000 989’000’000 994’000’000 992’000’000 983’000’000 978’000’000 972’000’000 966’000’000 961’000’000 952’000’000 944’000’000 933’000’000 924’000’000 915’000’000 907’000’000 900’000’000 893’000’000 887’000’000 883’000’000 878’000’000 873’000’000 868’000’000 863’000’000 854’000’000 849’000’000 843’000’000 838’000’000

gK 3.06 1.94 1.22 0.81 0.61 0.40 0.30 0.15 -0.02 -0.11 -0.21 -0.25 -0.23 -0.27 -0.18 0.06 0.13 0.32 0.06 -0.42 -0.47 -0.54 -0.58 -0.55 -0.74 -0.79 -0.98 -0.97 -0.97 -0.92 -0.85 -0.81 -0.74 -0.60 -0.58 -0.58 -0.57 -0.58 -0.81 -0.70 -0.70

gW 0.82 0.51 0.40 0.40 0.20 0.20 0.00 -0.20 -0.20 -0.30 -0.30 -0.20 -0.30 -0.10 0.30 0.20 0.51 -0.20 -0.91 -0.51 -0.61 -0.62 -0.52 -0.94 -0.84 -1.17 -0.96 -0.97 -0.87 -0.77 -0.78 -0.67 -0.45 -0.57 -0.57 -0.57 -0.58 -1.04 -0.59 -0.71 -0.59

gY 1.94 1.22 0.81 0.61 0.40 0.30 0.15 -0.02 -0.11 -0.21 -0.25 -0.23 -0.27 -0.18 0.06 0.13 0.32 0.06 -0.42 -0.47 -0.54 -0.58 -0.55 -0.74 -0.79 -0.98 -0.97 -0.97 -0.92 -0.85 -0.81 -0.74 -0.60 -0.58 -0.58 -0.57 -0.58 -0.81 -0.70 -0.70 -0.65

∆ 0.3713 0.3735 0.3770 0.3805 0.3868 0.3920 0.4000 0.4098 0.4187 0.4280 0.4374 0.4453 0.4528 0.4583 0.4559 0.4550 0.4497 0.4536 0.4669 0.4755 0.4846 0.4938 0.5016 0.5147 0.5275 0.5456 0.5595 0.5738 0.5865 0.5978 0.6081 0.6167 0.6206 0.6264 0.6323 0.6371 0.6408 0.6522 0.6549 0.6595 0.6623

Table 6: Forecasts (rates in %) according to Solow Model with constant Savings.

calculations (2010 - 2050), data retrieved from Chen and Liu (2009)