Population-Control-Policies and theirImplications for Economic Growth in
China
Bachelor’s Thesissupervised by the
Department of Economics at the University of Zurich
Prof. Dr. Fabrizio Zilibotti
to obtain the degree ofBachelor of Arts in Economics
Author: Noemi Schramm
Course of Studies: Economics
Student ID: 08-710-964
Address: Sudstrasse 10
8570 Weinfelden
E-Mail: [email protected]
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 eco-
nomic 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.
2
Contents
1 Introduction 5
2 Population-Control-Policies and their Effects on Economic
Growth in China from 1979 to 2005 8
2.1 One-Child-Policy in China . . . . . . . . . . . . . . . . . . . . 8
2.2 How the One-Child-Policy changed China . . . . . . . . . . . 11
2.2.1 Decline of Fertility Rate . . . . . . . . . . . . . . . . . 12
2.2.2 Development of the Dependency Ratio . . . . . . . . . 14
2.2.3 Influence on Economic Growth . . . . . . . . . . . . . 16
3 Population-Control-Policy in the Solow Model 19
3.1 Theoretical Analysis of the Solow Model . . . . . . . . . . . . 19
3.1.1 Solow Model with Constant Capital Stock . . . . . . . 21
3.1.2 Solow Model with Dynamic Capital Stock . . . . . . . 25
3.2 Combining Data and Neo-Classical Growth Theory . . . . . . 26
4 Upcoming Challenges for China linked with the One-Child-
Policy 33
5 Conclusion 35
A Appendix 41
3
List of Figures
1 Population Growth, Crude Birth and Death Rates of China
1949 - 2009 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2 Population and GDP per capita of China 1978 - 2005 . . . . . 11
3 Crude Birth Rate per 1000 Women 1978 - 2009 . . . . . . . . 13
4 Total Fertility Rate in % 1978 - 2009 . . . . . . . . . . . . . . 13
5 Population Age Structure 1960 - 2009. . . . . . . . . . . . . . 15
6 GDP annual growth rate 1978 - 2009 . . . . . . . . . . . . . . 17
7 Female Labour Participation 1980 - 2009 . . . . . . . . . . . . 19
8 Total Dependency Ratio 1960 - 2050 . . . . . . . . . . . . . . 24
9 Change of Working Population 2005 - 2050 . . . . . . . . . . . 28
10 Correlation of GDP Growth Rate and ∆ . . . . . . . . . . . . 30
11 Forecast of total GDP 2009 - 2050. . . . . . . . . . . . . . . . 31
12 Population Age Structure 2005 - 2050. . . . . . . . . . . . . . 32
List of Tables
1 Regression Results for the Savings Rate . . . . . . . . . . . . . 29
2 Upper Middle Income Economies according to World Bank . . 41
3 Dependency Ratios for 28 Chinese Provinces 1978 - 1998 . . . 42
4 Demographic Contributors to GDP Growth 2006 - 2050 with
constant Capital Stock . . . . . . . . . . . . . . . . . . . . . . 42
5 Forecasts according to Solow Model with dynamic Savings . . 43
6 Forecasts according to Solow Model with constant Savings . . 44
4
1 Introduction
China’s growing economy is a phenomenon which has already fascinated and
captivated various researchers and scientists. The surprisingly fast transi-
tion 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 liberaliza-
tion 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 liv-
ing standards. More and more researchers analyze the impact the family-
planning-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 assump-
tions 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 con-
tributor 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
1The model according to Malthus predicts that because of scarcity of resources (espe-cially land) population growth at some point leads to more poverty and therefore hamperseconomic growth.
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 pop-
ulation 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 pop-
ulation dynamics and economic growth in the past but also to give possi-
ble 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 impli-
cations 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.
7
2 Population-Control-Policies and their Ef-
fects 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-Child-
Policy 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 population-
control-policy, commonly known as “One-Child-Policy” (for simplicity rea-
sons hereafter called OCP) was introduced together with other drastic eco-
nomic and societal reforms in 1979 (Li and Zhang 2007). From 1971 to
1979, the so-called “later marriage, longer birth intervals and fewer births”
8
family-planning program was set into force as a response to rapid popula-
tion 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 child-
bearing-age) they reinforced the population-control measures by introducing
the OCP (Yu 2011). One feared that the country could collapse as pre-
dicted 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 begin-
ning 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 family-
planning 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, be-
ing 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 respon-
sible 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 ap-
9
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 there-
fore the government implemented the OCP, trying to fundamentally decrease
fertility rates and therefore permanently change demographic trends. Addi-
tionally, 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 ex-
plained 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 disso-
nances by human rights organizations (Greenhalgh 2003) and is still un-
popular and disputed among many policymakers. But it reached its goal
10
and prevented around 300 to 400 millions of births during the last decades
(Greenhalgh 2003) having a dramatic impact on China’s economic and soci-
etal 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 Par-
ity (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. Source:
Penn World Table 2011.
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 Divi-
sion 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 classi-
fication 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 ex-
ogenously 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 so-
called “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 in-
come changes on the birth rate in China is even more salient (Wei and Hao
12
Figure 3: Crude Birth Rate per 1000 Women 1978 - 2009. Source: World Develop-
ment Indicators 2009, World Bank.
Figure 4: Total Fertility Rate in % 1978 - 2009. Source: World Development Indicators
2009, World Bank.
13
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 (Green-
halgh 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 rel-
ative 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 indica-
tor used when the economy enters a period with a total dependency ratio
around 40-60% according to the United Nations Population Division (2004)
2The youth dependency ratio equals total amount of youngsters over working popula-tion: people aged 0-14 years
people aged 15-64 years .3In 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. Theirnumbers differ slightly from the ones of Wei and Hao, as can be seen in Table 3 in theappendix.
4The demographic window is a period where the relative amount of workers is high andtherefore it is a time of economic opportunities.
14
Figure 5: Population Age Structure 1960 - 2009. Source: United Nations Population
Divison 2009.
(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
5The demographic dividend is the part of economic growth attributable to a low de-pendency ratio through a rising share of working adults.
15
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 be-
tween 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
rate by 11000
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 there-
fore 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 accu-
mulation 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. Source: World Bank, World Develop-
ment Indicators 2009.
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 neg-
atively 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, compar-
ing 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 invest-
ments 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. With-
out 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 decreas-
ing 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 par-
ticipation 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.
6This corresponds to a dependency ratio of 0.55. Concerning the start of the economictake-off effect refer Figure 8 on page 24.
18
Figure 7: Female Labour Participation 1980 - 2009. Source: World Development
Indicators 2009, World Bank.
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 sim-
plified two-period OLG model. China has implemented the OCP only 32
years ago, which would be only one period. Hence, we focus on the neo-
classical 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 scenar-
ios: 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
19
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 = YL
= GDPcapita
• 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)
= DW
• gY ... growth rate of total income = Yt+1−YtYt
• gA ... growth rate of technical progress = At+1−At
At
• gK ... growth rate of capital stock = Kt+1−Kt
Kt
• gW ... growth rate of working population = Wt+1−Wt
Wt
20
We do not show every step of the normal Solow model here. For refer-
ence 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 ∗W
L(1)
The term WL
can be transformed as follows:
W
L=
(L
W
)−1
=
(W +D
W
)−1
= (1 + ∆)−1 =
(1
1 + ∆
). (2)
Combining equations (1) and (2) we get
GDPcapita = GDPworker ∗ (1 + ∆)−1, (3)
knowing that ∆ = DW
. 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 de-
pendent 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 = YL
= GDPcapita. We now analyze a standard Cobb-Douglas produc-
tion function, taking into consideration that only part of the population is
working. This yields:
21
Y = A ∗Kα ∗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
L= AKα W
Wα
1
L⇐⇒ Y
L= AKα 1
Wα
W
L. (5)
Here we use again equation (2) and insert it into (5) which yields
Y
L= AKα 1
Wα
(1
1 + ∆
). (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.
∂(YL
)
∂∆= A
(K
W
)α∗(− 1
(1 + ∆)2
)which is < 0. (7)
The first two terms A and(KW
)αare positive, the last term − 1
(1+∆)2is
negative. We showed analytically that in the standard Solow model the de-
pendency 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 pop-
ulation on economic output because China is expecting major changes in
the amount of the dependent population in the coming years (especially
22
ongoing ageing). Taking the derivatives of equation (4) is easy and yields∂Y∂D
= A(1− α)(
KL−D
)α ∗ (−1) < 0, stating that total GDP and the amount
of dependent persons is negatively correlated. Analyzing GDP per capita is
not as easy but yields very interesting results:
∂(YL
)
∂D= AKα(1−α)(L−D)−α
(1
W +D
)−AKα(L−D)1−α 1
(W +D)2. (8)
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:
AKαW−α 1
W +D[(1− α)− W
W +D] Q 0 ? (9)
Because all the first terms are positive, we simply have to check whether
(1− α)− W
W +DQ 0 ? (10)
W + D equals the total population L and therefore we can state the
following:
1. if WL> (1− α), then
∂(YL
)
∂D< 0.
2. if WL< (1− α), then
∂(YL
)
∂D> 0.
3. if WL
= (1− α), then∂(Y
L)
∂D= 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 be-
low 0.5 to 0.65, a change in the dependent population is negatively correlated
with output per capita. We know that WL
can be rewritten according to equa-
tion (2) as WL
= 1∆+1
. Solving the equations with α = 0.5 yields the following:
23
1. if ∆ > 1, then∂(Y
L)
∂D> 0.
2. if ∆ < 1, then∂(Y
L)
∂D< 0.
3. if ∆ = 1, then∂(Y
L)
∂D= 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 popu-
lation 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). Source: World
Bank and Chen and Liu, 2009.
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 log-
arithm 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 de-
pendency 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 = stYt = stAKαt W
1−αt assuming that st = s
(Wt
Lt
)︸ ︷︷ ︸
+
(12)
Consequently, s is increasing if the proportion of workers among popula-
tion (WL
) is increasing. What we do now is to calculate growth rate of capital
stock gK and insert it into our growth equation.
gK =Kt+1 −Kt
Kt
=sAKα
t W1−αt −Kt
Kt
= sA
(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 sav-
ings rates and proportion of working population helps us to calculate the
corresponding savings rates until 2050.
3.2 Combining Data and Neo-Classical Growth The-
ory
In the following chapter, growth accounting with focus on population dy-
namics 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 (Cobb-
Douglas production function) with constant returns to scale and con-
stant output elasticities and the Inada7 conditions hold.
7The 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 sup-
ports 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 42 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 ∼ WL
)
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 ***WL
1.18909 0.08893 13.371 6.02e-16 ***
—
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. Source: own calculations based on
data from the World Bank.
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. Us-
ing a dynamic savings rate yields negative GDP growth rates because the
shrinking working population has a multiple effect in our model. We con-
duct 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 responsi-
ble 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 eco-
nomic 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 ap-
plying 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-control-
policies (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. Source: own calculations based on data
from Chen and Liu, 2009.
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 de-
pendent 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 ”miss-
ing 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 ar-
eas. 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 unsat-
isfied 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 ru-
ral 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 sig-
nificant 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 stan-
dard. 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 ad-
vance 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 edu-
cation 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 possi-
ble 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-planning-
policy 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 en-
hanced 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 apply-
ing the Solow model, China has to expect a negative impact on economic
growth because of demographic dynamics. Interesting here is that the im-
pact 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
8Prior data on overall Gini coefficient in China is not available, this is data from theNational Bureau of Statistics of China. However, the World Bank estimated the Ginicoefficient in 1978 around 0.3 (Renwei et al 1999).
9This is also consistent with calculations made by the United Nations DevelopmentProgram which measured a Gini coefficient of 0.415 during 2000-2010.
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-control-
policies.
36
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40
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. Source:
World Bank.
41
Ratios N Mean Standard Deviation Min Max
Youth Dependency Ratio 112 0.320 0.064 0.179 0.429
Old Dependency Ratio 112 0.049 0.015 0.022 0.114
Table 3: Dependency Ratios for 28 Chinese Provinces 1978 - 1998. Source: Wei
and Hao, 2010.
Year gW g1+∆ gL gY Year gW g1+∆ gL gY
2006 1.17 -0.63 0.54 0.5857 2028 -0.91 0.92 0.00 -0.4536
2007 1.05 -0.44 0.61 0.5263 2029 -0.51 0.58 0.07 -0.2543
2008 0.83 -0.23 0.60 0.4103 2030 -0.61 0.62 0.00 -0.3067
2009 0.72 -0.12 0.60 0.3616 2031 -0.62 0.62 0.00 -0.3086
2010 0.82 -0.15 0.67 0.4103 2032 -0.52 0.52 0.00 -0.2588
2011 0.51 0.16 0.67 0.2543 2033 -0.94 0.88 -0.07 -0.4683
2012 0.40 0.26 0.66 0.2024 2034 -0.84 0.85 0.00 -0.4202
2013 0.40 0.25 0.66 0.2016 2035 -1.17 1.18 0.00 -0.5826
2014 0.20 0.45 0.65 0.1004 2036 -0.96 0.90 -0.07 -0.4823
2015 0.20 0.38 0.58 0.1002 2037 -0.97 0.91 -0.07 -0.4870
2016 0.00 0.57 0.57 0.0000 2038 -0.87 0.81 -0.07 -0.4372
2017 -0.20 0.70 0.50 -0.1000 2039 -0.77 0.71 -0.07 -0.3859
2018 -0.20 0.63 0.43 -0.1002 2040 -0.78 0.64 -0.14 -0.3889
2019 -0.30 0.66 0.35 -0.1506 2041 -0.67 0.54 -0.14 -0.3359
2020 -0.30 0.66 0.35 -0.1511 2042 -0.45 0.24 -0.21 -0.2255
2021 -0.20 0.55 0.35 -0.1010 2043 -0.57 0.36 -0.21 -0.2831
2022 -0.30 0.52 0.21 -0.1518 2044 -0.57 0.36 -0.21 -0.2847
2023 -0.10 0.38 0.28 -0.0508 2045 -0.57 0.29 -0.28 -0.2893
2024 0.30 -0.17 0.14 0.1524 2046 -0.58 0.23 -0.35 -0.2880
2025 0.20 -0.06 0.14 0.1013 2047 -1.04 0.70 -0.35 -0.5214
2026 0.51 -0.36 0.14 0.2528 2048 -0.59 0.16 -0.43 -0.2927
2027 -0.20 0.27 0.07 -0.1006 2049 -0.71 0.28 -0.43 -0.3534
2050 -0.59 0.17 -0.43 -0.2966
Table 4: Demographic Contributors in % to GDP Growth 2006 - 2050 withconstant Capital Stock, middle scenario. Source: own calculations, data retrieved from
Chen and Liu (2009).
42
Year
Sav
ings
Rat
eG
DP
Cap
ital
Sto
ckW
ork
ing
Pop
ula
tion
g Kg W
g Y∆
2010
48.7
08’
688’
348’
912’
522
4’29
9’2
28’0
06’9
38
983’0
00’0
00
-1.5
80.8
2-0.38
0.3
713
2011
48.5
68’
655’
353’
281’
464
4’23
1’2
98’0
44’0
07
988’0
00’0
00
-0.6
60.5
1-0.08
0.3
735
2012
48.3
48’
648’
805’
891’
040
4’20
3’3
74’0
95’3
21
992’0
00’0
00
-0.5
30.4
0-0.06
0.3
770
2013
48.1
28’
643’
270’
571’
202
4’18
0’9
75’9
85’8
76
996’0
00’0
00
-0.5
20.4
0-0.06
0.3
805
2014
47.7
38’
638’
338’
225’
840
4’15
9’3
45’4
02’8
87
998’0
00’0
00
-0.8
60.2
0-0.33
0.3
868
2015
47.4
18’
609’
716’
559’
868
4’12
3’4
30’7
35’1
28
1’0
00’0
00’0
00
-1.0
00.2
0-0.40
0.3
920
2016
46.9
28’
575’
142’
281’
741
4’08
2’0
50’1
96’0
24
1’0
00’0
00’0
00
-1.4
30.0
0-0.71
0.4
000
2017
46.3
38’
513’
959’
087’
494
4’02
3’7
99’7
64’2
84
998’0
00’0
00
-1.9
7-0
.20
-1.08
0.4
098
2018
45.8
18’
421’
785’
517’
280
3’94
4’7
22’6
81’5
62
996’0
00’0
00
-2.2
1-0
.20
-1.20
0.4
187
2019
45.2
68’
320’
430’
624’
740
3’85
7’6
79’6
76’7
22
993’0
00’0
00
-2.3
8-0
.30
-1.34
0.4
280
2020
44.7
28’
208’
739’
753’
945
3’76
5’7
30’6
11’4
30
990’0
00’0
00
-2.5
3-0
.30
-1.41
0.4
374
2021
44.2
68’
092’
637’
920’
464
3’67
0’5
84’8
22’1
34
988’0
00’0
00
-2.4
2-0
.20
-1.31
0.4
453
2022
43.8
47’
986’
536’
112’
441
3’58
1’7
50’7
66’2
61
985’0
00’0
00
-2.2
5-0
.30
-1.28
0.4
528
2023
43.5
37’
884’
501’
408’
782
3’50
1’1
06’7
81’7
47
984’0
00’0
00
-1.9
8-0
.10
-1.04
0.4
583
2024
43.6
67’
802’
521’
968’
536
3’43
1’8
55’3
90’1
95
987’0
00’0
00
-0.7
30.3
0-0.21
0.4
559
2025
43.7
17’
785’
805’
498’
199
3’40
6’6
87’2
96’9
81
989’0
00’0
00
-0.1
00.2
00.05
0.4
550
2026
44.0
17’
789’
958’
045’
713
3’40
3’4
18’0
84’8
63
994’0
00’0
00
0.7
40.5
10.62
0.4
497
2027
43.7
97’
838’
397’
709’
170
3’42
8’5
38’1
21’0
13
992’0
00’0
00
0.1
1-0
.20
-0.04
0.4
536
2028
43.0
57’
835’
008’
452’
324
3’43
2’4
71’6
46’3
11
983’0
00’0
00
-1.7
4-0
.91
-1.32
0.4
669
2029
42.5
87’
731’
408’
468’
819
3’37
2’8
39’9
21’3
51
978’0
00’0
00
-2.4
0-0
.51
-1.45
0.4
755
2030
42.0
97’
619’
143’
092’
170
3’29
2’0
43’8
52’4
00
972’0
00’0
00
-2.6
0-0
.61
-1.60
0.4
846
2031
41.5
97’
496’
860’
930’
625
3’20
6’5
70’2
27’0
69
966’0
00’0
00
-2.7
6-0
.62
-1.69
0.4
938
2032
41.1
87’
370’
232’
752’
050
3’11
8’0
40’6
26’6
02
961’0
00’0
00
-2.6
6-0
.52
-1.59
0.5
016
2033
40.4
97’
253’
024’
353’
788
3’03
5’0
07’5
02’6
81
952’0
00’0
00
-3.2
3-0
.94
-2.08
0.5
147
2034
39.8
37’
101’
829’
213’
966
2’93
6’8
96’7
33’8
67
944’0
00’0
00
-3.6
8-0
.84
-2.26
0.5
275
2035
38.9
36’
941’
322’
963’
640
2’82
8’8
24’7
44’9
36
933’0
00’0
00
-4.4
9-1
.17
-2.83
0.5
456
2036
38.2
46’
745’
192’
984’
709
2’70
1’9
28’4
96’2
55
924’0
00’0
00
-4.5
5-0
.96
-2.76
0.5
595
2037
37.5
56’
559’
332’
486’
027
2’57
9’0
91’4
74’7
33
915’0
00’0
00
-4.5
1-0
.97
-2.74
0.5
738
2038
36.9
46’
379’
445’
249’
316
2’46
2’7
51’2
60’1
36
907’0
00’0
00
-4.3
2-0
.87
-2.60
0.5
865
2039
36.4
16’
213’
797’
453’
851
2’35
6’3
88’5
92’4
94
900’0
00’0
00
-3.9
9-0
.77
-2.38
0.5
978
2040
35.9
36’
065’
992’
762’
081
2’26
2’4
73’9
87’3
41
893’0
00’0
00
-3.6
5-0
.78
-2.22
0.6
081
2041
35.5
45’
931’
551’
549’
937
2’17
9’7
84’1
26’8
48
887’0
00’0
00
-3.2
9-0
.67
-1.98
0.6
167
2042
35.3
65’
814’
064’
790’
802
2’10
8’0
79’5
84’0
36
883’0
00’0
00
-2.4
7-0
.45
-1.46
0.6
206
2043
35.1
05’
729’
089’
339’
309
2’05
5’9
64’8
78’3
15
878’0
00’0
00
-2.1
9-0
.57
-1.38
0.6
264
2044
34.8
45’
650’
072’
340’
520
2’01
0’8
94’0
69’5
10
873’0
00’0
00
-2.1
2-0
.57
-1.34
0.6
323
2045
34.6
25’
574’
120’
587’
596
1’96
8’2
82’2
76’6
29
868’0
00’0
00
-1.9
5-0
.57
-1.26
0.6
371
2046
34.4
65’
503’
854’
040’
530
1’92
9’9
31’6
15’2
64
863’0
00’0
00
-1.7
3-0
.58
-1.15
0.6
408
2047
33.9
65’
440’
487’
805’
784
1’89
6’6
09’8
72’7
94
854’0
00’0
00
-2.5
9-1
.04
-1.82
0.6
522
2048
33.8
45’
341’
656’
480’
540
1’84
7’4
81’8
90’1
45
849’0
00’0
00
-2.1
5-0
.59
-1.37
0.6
549
2049
33.6
45’
268’
557’
255’
848
1’80
7’7
33’8
79’3
63
843’0
00’0
00
-1.9
6-0
.71
-1.33
0.6
595
2050
33.5
25’
198’
396’
930’
968
1’77
2’3
62’9
21’6
52
838’0
00’0
00
-1.6
8-0
.59
-1.14
0.6
623
Tab
le5:
For
ecas
ts(r
ates
in%
)ac
cord
ing
toSol
owM
odel
wit
hdynam
icSav
ings
.S
ou
rce:
Worl
dB
an
k(2
005
-2009),
ow
n
calc
ula
tion
s(2
010
-2050),
data
retr
ieved
from
Ch
enan
dL
iu(2
009)
43
Year
Sav
ings
Rat
eG
DP
Cap
ital
Sto
ckW
ork
ing
Pop
ula
tion
g Kg W
g Y∆
2010
50.0
08’
507’
543’
929’
361
4’12
7’6
65’3
92’3
56
983’0
00’0
00
3.0
60.8
21.94
0.3
713
2011
50.0
08’
672’
405’
997’
160
4’25
3’7
71’9
64’6
81
988’0
00’0
00
1.9
40.5
11.22
0.3
735
2012
50.0
08’
778’
490’
373’
976
4’33
6’2
02’9
98’5
80
992’0
00’0
00
1.2
20.4
00.81
0.3
770
2013
50.0
08’
849’
951’
619’
309
4’38
9’2
45’1
86’9
88
996’0
00’0
00
0.8
10.4
00.61
0.3
805
2014
50.0
08’
903’
815’
751’
277
4’42
4’9
75’8
09’6
55
998’0
00’0
00
0.6
10.2
00.40
0.3
868
2015
50.0
08’
939’
851’
309’
985
4’45
1’9
07’8
75’6
39
1’0
00’0
00’0
00
0.4
00.2
00.30
0.3
920
2016
50.0
08’
966’
899’
777’
812
4’46
9’9
25’6
54’9
93
1’0
00’0
00’0
00
0.3
00.0
00.15
0.4
000
2017
50.0
08’
980’
464’
930’
728
4’48
3’4
49’8
88’9
06
998’0
00’0
00
0.1
5-0
.20
-0.02
0.4
098
2018
50.0
08’
978’
277’
302’
958
4’49
0’2
32’4
65’3
64
996’0
00’0
00
-0.0
2-0
.20
-0.11
0.4
187
2019
50.0
08’
968’
187’
485’
681
4’48
9’1
38’6
51’4
79
993’0
00’0
00
-0.1
1-0
.30
-0.21
0.4
280
2020
50.0
08’
949’
641’
940’
074
4’48
4’0
93’7
42’8
41
990’0
00’0
00
-0.2
1-0
.30
-0.25
0.4
374
2021
50.0
08’
926’
869’
246’
089
4’47
4’8
20’9
70’0
37
988’0
00’0
00
-0.2
5-0
.20
-0.23
0.4
453
2022
50.0
08’
906’
494’
832’
434
4’46
3’4
34’6
23’0
44
985’0
00’0
00
-0.2
3-0
.30
-0.27
0.4
528
2023
50.0
08’
882’
808’
870’
251
4’45
3’2
47’4
16’2
17
984’0
00’0
00
-0.2
7-0
.10
-0.18
0.4
583
2024
50.0
08’
866’
488’
344’
388
4’44
1’4
04’4
35’1
26
987’0
00’0
00
-0.1
80.3
00.06
0.4
559
2025
50.0
08’
871’
859’
062’
767
4’43
3’2
44’1
72’1
94
989’0
00’0
00
0.0
60.2
00.13
0.4
550
2026
50.0
08’
883’
534’
760’
888
4’43
5’9
29’5
31’3
84
994’0
00’0
00
0.1
30.5
10.32
0.4
497
2027
50.0
08’
911’
836’
144’
043
4’44
1’7
67’3
80’4
44
992’0
00’0
00
0.3
2-0
.20
0.06
0.4
536
2028
50.0
08’
917’
066’
287’
317
4’45
5’9
18’0
72’0
21
983’0
00’0
00
0.0
6-0
.91
-0.42
0.4
669
2029
50.0
08’
879’
232’
492’
172
4’45
8’5
33’1
43’6
58
978’0
00’0
00
-0.4
2-0
.51
-0.47
0.4
755
2030
50.0
08’
837’
813’
881’
400
4’43
9’6
16’2
46’0
86
972’0
00’0
00
-0.4
7-0
.61
-0.54
0.4
846
2031
50.0
08’
790’
091’
319’
374
4’41
8’9
06’9
40’7
00
966’0
00’0
00
-0.5
4-0
.62
-0.58
0.4
938
2032
50.0
08’
739’
228’
973’
390
4’39
5’0
45’6
59’6
87
961’0
00’0
00
-0.5
8-0
.52
-0.55
0.5
016
2033
50.0
08’
691’
327’
901’
282
4’36
9’6
14’4
86’6
95
952’0
00’0
00
-0.5
5-0
.94
-0.74
0.5
147
2034
50.0
08’
626’
810’
436’
265
4’34
5’6
63’9
50’6
41
944’0
00’0
00
-0.7
4-0
.84
-0.79
0.5
275
2035
50.0
08’
558’
544’
064’
105
4’31
3’4
05’2
18’1
32
933’0
00’0
00
-0.7
9-1
.17
-0.98
0.5
456
2036
50.0
08’
474’
816’
584’
828
4’27
9’2
72’0
32’0
53
924’0
00’0
00
-0.9
8-0
.96
-0.97
0.5
595
2037
50.0
08’
392’
487’
073’
301
4’23
7’4
08’2
92’4
14
915’0
00’0
00
-0.9
7-0
.97
-0.97
0.5
738
2038
50.0
08’
310’
849’
714’
977
4’19
6’2
43’5
36’6
51
907’0
00’0
00
-0.9
7-0
.87
-0.92
0.5
865
2039
50.0
08’
234’
096’
513’
341
4’15
5’4
24’8
57’4
88
900’0
00’0
00
-0.9
2-0
.77
-0.85
0.5
978
2040
50.0
08’
164’
299’
979’
409
4’11
7’0
48’2
56’6
70
893’0
00’0
00
-0.8
5-0
.78
-0.81
0.6
081
2041
50.0
08’
097’
947’
473’
038
4’08
2’1
49’9
89’7
05
887’0
00’0
00
-0.8
1-0
.67
-0.74
0.6
167
2042
50.0
08’
037’
836’
097’
554
4’04
8’9
73’7
36’5
19
883’0
00’0
00
-0.7
4-0
.45
-0.60
0.6
206
2043
50.0
07’
989’
879’
870’
374
4’01
8’9
18’0
48’7
77
878’0
00’0
00
-0.6
0-0
.57
-0.58
0.6
264
2044
50.0
07’
943’
423’
413’
723
3’99
4’9
39’9
35’1
87
873’0
00’0
00
-0.5
8-0
.57
-0.58
0.6
323
2045
50.0
07’
897’
712’
295’
679
3’97
1’7
11’7
06’8
61
868’0
00’0
00
-0.5
8-0
.57
-0.57
0.6
371
2046
50.0
07’
852’
371’
673’
621
3’94
8’8
56’1
47’8
40
863’0
00’0
00
-0.5
7-0
.58
-0.58
0.6
408
2047
50.0
07’
807’
215’
234’
572
3’92
6’1
85’8
36’8
11
854’0
00’0
00
-0.5
8-1
.04
-0.81
0.6
522
2048
50.0
07’
744’
057’
158’
003
3’90
3’6
07’6
17’2
86
849’0
00’0
00
-0.8
1-0
.59
-0.70
0.6
549
2049
50.0
07’
690’
063’
628’
305
3’87
2’0
28’5
79’0
02
843’0
00’0
00
-0.7
0-0
.71
-0.70
0.6
595
2050
50.0
07’
636’
081’
722’
033
3’84
5’0
31’8
14’1
53
838’0
00’0
00
-0.7
0-0
.59
-0.65
0.6
623
Tab
le6:
For
ecas
ts(r
ates
in%
)ac
cord
ing
toSol
owM
odel
wit
hco
nst
ant
Sav
ings
.S
ou
rce:
Worl
dB
an
k(2
005
-2009),
ow
n
calc
ula
tion
s(2
010
-2050),
data
retr
ieved
from
Ch
enan
dL
iu(2
009)
44
