Population Control, Technology and EconomicGrowth

Xianjuan Zoey Chen

Abstract

The evolution of population, technology, and income has been animportant topic in growth theory since Malthus’s (1798) “An Essayon the Principle of Population”. Galor and Weil (2000) develop aunified endogenous growth model that is consistent with the long-term comovements of these variables in Western Europe. Motivatedby the Galor-Weil model, this paper examines the long-term effectsof China’s one-child policy on economic growth. The new elementhere is within family intergenerational transfers. When a populationcontrol policy is implemented, transfers from children decrease as thenumber of children decreases. In response, parents increase investmentin their children’s education in order to compensate for the reductionin transfers.

Technological progress is assumed to be driven by two forces: pop-ulation size and the level of education. With population control, thetotal number of children decreases and the average level of educa-tion increases. Thus, the overall effect on technological progress isambiguous without specifying functional forms for technology and hu-man capital. Data suggest that education increased in response to theone-child policy. However, further quantitative analysis is needed inorder to isolate the causal effect.

1 Introduction

The evolution of population and income levels has been an important topicin economic growth. Malthus (1798) first proposed the most basic descrip-tion of this relationship. The Malthusian model posits a positive effect ofincome per capita on population growth. The Malthusian model successfully

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explained a long period of observed population and income data. However,most empirical studies now find that fertility rates fall as income grows. Forexample, Barlow (1994), which draws on data from 86 countries and severaltime periods, shows that per capita income growth is negatively related topopulation growth. Other empirical analyses find no significant relationship,including Simon(1989) and Kelly(1988). Becker, Murphy and Tamura(1990)argue that the failure of the Malthusian model stems from its neglect of hu-man capital investment. Denison(1985) provides evidence showing that 25percent of the increase in GDP per capita in the US between 1929 to 1982is explained by increased schooling.

Figure 1 depicts the growth rates of population and income per-capitain western Europe from AD600 to the 1900s (Lagerlof (2006)). Galor andWeil (2000) develop a single, unified growth model that captures this histor-ical evolution between population growth and income per capita. Based onthe behavior of per-capita income, and the relationship between the level ofincome per capita and the growth rate of population, they separate the evo-lution of population and income into three regimes. The first regime is calledthe “Malthusian” regime. In this stage, income and population growth arepositively correlated, which is consistent with the Malthusian model’s pre-diction. In the absence of changes in technology, and when the populationis small, income per capita is high, and population grows naturally. Whenpopulation is large, income per capita will be low, thus reducing populationgrowth. Hence, population growth will be stable around a slowly evolvinglevel of technological progress.

As population gradually rises, technological progress speeds up becausecountries with denser population should have superior technology. Accord-ing to Kuznets (1960), Simon (1977, 1981) and Aghion and Howitte(1992),a larger population means more potential inventors and higher chances oftechnological breakthrough. The resulting increase in technological progressallows the economy to transition to a second regime, which is called the “post-Malthusian” regime. During this regime, income and population growth arestill positively correlated, but both grow at a faster rate due to the effect ofmore rapid technological progress.

As population and technological progress continue, the economy eventu-ally transitions to a third regime, called the “Modern Growth” regime. Thisregime differs from the previous two because income and population growthnow become negatively correlated. This negative relation is due to the de-mographic transition, in which parents switch to having fewer, higher quality

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children. As Schultz(1964) argued, technological progress raises the returnto human capital because new technology requires the ability to analyze andwork with new production techniques. Thus, an advance in technology in-creases the level of resources invested in each child, and decreases the totalnumber of children each family has.

Although Galor and Weil’s (2000) model can be used to explain the threestages of the historical evolution of population and economic growth in West-ern Europe, a natural question arises - Can the Galor-Weil model also explainthe evolution in China? Figure 2 shows the growth rate of population andGDP per capita in China from 1500 to 2008, based on Maddison’s (2007)estimates. As the graph shows, the historical evolution of population andeconomic growth appears to be consistent with the three stages of the Galor-Weil model. However, one thing that is worth of noticing is that populationgrowth drops around 1980. This was not due to a natural transition betweenregimes. Instead, it was caused by the imposition of a government policy. In1979, China introduced a population control policy, the so-called “One-ChildPolicy”, in order to reduce population growth and alleviate social, economicand environmental pressures. The policy stated that each couple could haveonly one child. However, some exceptions were allowed. For example, eth-nic minorities and some families in rural areas were exempted. This policyreduced the fertility rate significantly in China, especially in urban areas.According to China Census, the average urban fertility rate was around 3per woman in 1970s. It decreased to very close to 1 by the mid-1980s. Asthe fertility rate kept falling, declining population growth was accompaniedby several serious problems. For example, sex imbalance, population agingand other potential social problems. In 2013, China announced the decisionto relax the one-child policy. Under the new policy, families can now havetwo children if one parent is an only child.

China’s one-child policy is a very unique population control scheme. Ithas recently attracted the attention of economic researchers. Choukhmane,Coeurdacier and Jin (2014) investigate the effect of the one-child policy onChina’s household saving rate and human capital. Song, Stroresletten, Wangand Zilibotti(2015) analyze the welfare effects of alternative pension systems,taking the one-child policy into consideration. Li and Zhang (2007) providean empirical analysis of the impact of the birth rate on economic growth.They find that the birth rate has a negative impact on economic growth.Chen (2015) argues that exogenous fertility restrictions affect economic deci-sions at the household level, and demographic composition at the aggregate

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level. The demographic transition combined with domestic financial andcontractual imperfections can explain the recent increase in China’s foreignreserves.

Xue, Yip and Tou (2013) analyze the effect of exogenous population con-trol on China’s long run economic development in the Galor-Weil model.They extend Galor-Weil model by introducing a policy variable on popu-lation growth. According to Galor and Weil (2000), lower population den-sity leads to slower technological progress. Thus, they find that in the longrun, population control results in a steady state of lower education, andslower technological progress and economic growth. Following Galor andWeil (2000), Xue, Yip and Tou (2013) also considered the substitution be-tween the quality and quantity in their model. Rapid technological progressresults in high return to education. Thus it triggers a demographic transitionin which fertility rates permanently decrease. However, they didn’t study theeffect of the quantity of children on quality.

In countries like China, where the social pension system is not so well es-tablished, within-family intergenerational transfers are very important. Par-ents raise and educate their children when they are young, and childrenfinancially support their parents when their parents are retired. Intergener-ational transfers are not just based on cultural norms, but also stipulatedby Constitutional Law. Children provide a very important source of old agesupport in China. Figure 3 shows the main sources of livelihood for the el-derly in urban areas (Choukhmane, Coeurdacier and Jin (2014)). Accordingto Census 2005 (left panel), family support is 41% of the total for the elderly.From the China Health and Retirement Longitudinal Study (CHARLS), thispattern is expected to continue in the future (right panel). In addition, Fig-ure 3 shows more detailed data on intergenerational transfers (choukhmane,Coeurdacier and Jin (2014)). The data show that there are positive nettransfers from children to parents in 65% of families. More importantly, av-erage transfers, as a percentage of pre-transfer income, are increasing in thenumber of children. When the one-child policy was implemented, parentalexpected future income decreases as the number of children they have de-creases. To compensate for this loss, parents can substitute quantity forquality. That is, parents will increase investment in their children’s educa-tion in order to accumulate financial wealth in expectation of lower supportfrom their children. Choukhmane, Coeurdacier and Jin (2014) argue thatthe policy significantly increased the human capital of the only child gener-ation due to the quantity and quality trade-off effect. They also provide an

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empirical check by using the birth of twins as an exogenous deviation fromthe policy. The results show that the per-capita education expenditure on atwin is significantly lower than on an only child.

In this paper, I extend and modify the Galor and Weil (2000) model toexamine the long run effects of the one-child policy on economic growth. Mytheoretical framework incorporates one new element into the model: intra-family transfers. Agents make decisions about how many children to have,and their level of education. When they retire, they live off their children’stransfer and savings. Bearing children is not simply for utility purposes,but is also an investment. This model thus allows the one-child policy toimpact both long run technological progress and the level of education. Onone hand, according to Galor and Weil (2000), lower population densityleads to a slower technological progress, thus slowing down economic growthin long run. On the other hand, fertility restrictions provide incentives forhouseholds to increase their offspring’s education, which increases humancapital accumulation, which then accelerates economic growth.

2 Model

Consider a small, open, overlapping-generations economy. In each period,the economy produces a single homogeneous good . The output produced attime t, Yt, is:

Yt = AtHαt K

1−αt (1)

where Kt is physical capital, which is accumulated through aggregate savingand international borrowing, Ht is efficiency units of labor, and At representsthe endogenously determined technology level. Assume this economy oper-ates in a perfectly competitve world capital market, and the world interestrate is constant at a level of R. The marginal product of capital thereforeequals R. Substituting the level of capital into the production function yieldsoutput per worker ,

yt = (1− α)1−αα R

α−1α A

1αt ht (2)

where yt = Yt/Lt and ht = Ht/Lt. Income per wroker at time t, is

zt = wtht = γRα−1α A

1αt ht (3)

where γ = α(1− α)α−1α .

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2.1 Individuals

Each individual lives for three periods. They are children in the first period,and do not make economic decisions. They simply consume a fraction oftheir parents’ income. In the second period, they become adults and startmaking decisions. They supply labor and earn wage wt per efficiency unit oflabor, which is used for consumption, transfers, and savings. In this period,they also need to decide the amount of human capital to endow each of theirchildren. In the third period, individuals do not work, and live off theirsavings and transfers from their children.

Preferences:Ut = ln(ct) + βln(ct+1) + νln(nt)

where nkt is the number of children of individual t.Budget constraint:

ct + st = zt − (τ q + τ eet+1)ntzt − φnω−1t−1

ωzt

ct+1 = Rst + φnωtωzt+1

An individual born in time t− 1 starts making economic decisions in time t.Individuals are endowed with one unit of time. The time cost of raising ntchildren,(τ q + τ eet+1)ntzt, is propotional to current income, where τ q is thetime cost regardless of the level of education; τ e is the cost per each unit of

education. φnω−1t−1

ωzt is the transfer made to parents, where nt−1 is the number

of the agent’s siblings, with φ > 0 and 0 < ω < 1. Thus, an agent’s transferto his parents is decreasing as the number of siblings increases. In periodt − 1, the agent lives off his savings from period t, and the transfers fromhis own chidlren: φ

nωtωzt+1. The transfer increases as the number of children

increases, and as his the wage of his children increases.

2.1.1 Human Capital

An individual’s level of human capital is determined by education and tech-nology. I assume that education and technological progress, gt+1 = (At+1 −At)/At, increases human capital. In addition, according to Schultz(1964),technological progress raises the return to education in producing humancapital.

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Assumption 1(A1):ht+1 = h(et+1, gt+1) (4)

where for all h(et+1, gt+1) ≥ 0

he(et+1, gt+1) > 0;hee(et+1, gt+1) < 0

hg(et+1, gt+1) > 0;hgg(et+1, gt+1) < 0;heg(et+1, gt+1) > 0

h(et+1, gt+1) > 0; limgt+1→∞h(0, gt+1) = 0;

Thus individual human capital is an increasing, concave function of educationand the rate of technological progress. In addition, technological progressincreases the rate of return to education.

2.1.2 Optimization

Log utility implies that optimal consumption is a constant fraction of thepresent value of lifetime income, thus

ct =1

1 + β[(1− (τ q + τ eet+1)nt − φ

nω−1t−1

ω)zt +

1

Rφnωtωzt+1] (5)

Therefore, from the budget constraint,

st =β

1 + β[(1− (τ q + τ eet+1)nt − φ

nω−1t−1

ω)zt −

1

βRφnωtωzt+1] (6)

Saving increases as the number of children decreases due to the decrease inthe cost of raising children and the prospect of lower future transfers.

Number of children:

ν

nt=β

ct[(τ q + τ eet+1)zt −

1

Rφnω−1t zt+1] (7)

Education influences the optimal number of children through two chan-nels. First, higher education raises the cost per child, thus reducing theincentive to have more children. Second, higher eduction raises future trans-fers from each child, thus motivating parents to have more children. If thesecond effect dominates, the marginal benefit from future transfers is greaterthan marginal cost, in which case as et+1 increases, the number of childrennt increases. On the other hand, if the first effect dominates, nt is decreasingin et+1. In addition,

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MC = τ eh(et, gt)

MB =φ

αRnω−1t g

1αt+1he(et+1, gt+1)

Note marginal cost is independent of et+1, while the marginal benefit is de-creasing in et+1. In this paper, I assume that there exists an education levele, such that when et+1 < e, the marginal benefit is bigger than the marginalcost, so nt is increasing in et+1. On the other hand, when et+1 > e, themarginal benefit is lower than marginal cost. Therefore, nt decreases in et+1.

Education:

τ enkt zt =1

Rφnωtω

δzt+1

δet+1

(8)

Define G(et+1, gt+1) as the difference between MB and MC. For all et+1 >0 and gt+1 ≥ 0,

G(et+1, gt+1) =1

Rφnω−1t

ωg

1αt+1he(et+1, gt+1)− τ eh(et, gt) = 0 if et+1 > 0

(9)

≤ 0 if et+1 = 0(10)

Following from Assumption 1,

Gg(et+1, gt+1) =φ

Rωnω−1t g

1αt+1(heg +

1

α

he(et+1, gt+1)

gt+1

) > 0 (11)

Ge(et+1, gt+1) =φ

Rωnω−1t g

1αt+1hee(et+1, gt+1) < 0 (12)

Gn(et+1, nt) = (ω − 1)φ

R

nω−2t

ωg

1αt+1he < 0 (13)

Ge(et+1, nt) =φ

Rωnω−1t g

1αt+1((ω − 1)n−1t

δntδet+1

+ hee) < 0 (14)

In addition, G(0, 0) = −τ eh(et, gt) < 0. Thus, there exists a positive levelof gt+1, such that the optimal choice of et+1 is 0.

Lemma 1. Education et+1 is a concave function of the rate of techno-logical progress gt+1.

et+1 = e(gt+1) = 0 if gt+1 ≤ g

> 0 if gt+1 = g

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where g > 0. e′t+1(gt+1) = −heg+

1α

hegt+1

hee. Following from (11) and (12), thus

e′(gg+1) > 0 ∀gt+1 > g (15)

In addition, assume that

e”(gt+1) < 0 ∀gt+1 > g (16)

Lemma 2 Education et+1 is a decreasing, convex function of the fertility

rate nt, holding gt+1constant. e′t+1(nt) = −Gn(et+1,nt)Ge(et+1,nt)

= −(ω−1)he

nt

(ω−1)n−1t

δntδet+1

+hee.

Following from (13) and (14), assume when et+1 > e, |hee| > |(ω−1)n−1tδntδet+1|

e′t+1(nt) < 0

et+1”(nt) > 0

Furthermore,substituting et+1 = e(gt+1) into (7),

ν

nt=β

ct[(τ q + τ ee(gt+1))zt −

1

Rφnω−1t zt+1]

wherezt = wtht = γR

α−1α A

1αt h(et, gt) = z(et, gt)

ze(et, gt) > 0; zg(et, gt) > 0 (17)

2.2 Comparative Statics

The effect of technological progress on quantity and quality of children:

δntδgt+1

> 0 (18)

δet+1

δgt+1

> 0 (19)

The quantity and quality trade-off effect:

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δntδet+1

> 0 if e < e (20)

δntδet+1

< 0 if e > e (21)

δet+1

δnt< 0 (22)

2.3 Technological progress

Technological progress gt+1 depends on the education level of generation t,et, and the population size in period t, Lt.

gt+1 =At+1

At= g(et)f(Lt) (23)

where for all et > 0 and Lt > 0

g(0) > 0, g′(et) > 0,g′′(et) < 0

f(Lt) > 0, f ′(Lt) > 0,f ′′(Lt) < 0

Thus, gt+1 is an increasing and concave function of et and Lt. In addition,when the education level of generation t is zero, gt+1 > 0.

3 The Dynamical System

The evolution of the economy is fully determined by the following system

et+1 = e(g(et, Lt), nt)

gt+1 = g(et, Lt)

Lt+1 = nt(g(et, Lt), et+1)Lt

This system governs the co-evolution of output per worker, population,technology, education, and human capital per worker.

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3.1 The Evolution of Quantity and Quality

The dynamical sub-system of childrens’ quantity and quality consists of:

QQ : et+1 = e(nt)

NN : nt = n(et+1)

QQ represents the response of education to fertility while NN representsthe response of the quantity of children to their planned education, hold-ing technology constant. From equation (7) and lemma 2, the QQ curve isdecreasing and convex in nt. NN is increasing in et+1 when et+1 < e anddecreasing in et+1 when et+1 > e.

Figure 5a depicts the evolution of the fertility rate and education levelwhen et+1 < e. I assume that NN is convex in e (Note: convexity is notessential. Alternative assumption will not change the result). Given therate of technological progress, the intersection of the NN and QQ curvesdetermines the temporary stable equilibrium (e1, n1). From lemma 2 andequation 7, the NN and QQ curves shift to the right in response to an increasein gt. In response, the fertility rate increases. The effects on education workthrough two channels. On one hand, as the rate of technological progressincreases, the rate of return to education increases, which increases the chosenlevel of education. On the other hand, as the number of children increases, thecost increases, which decreases the incentive to invest in children’s education.From Lemma 1 and Lemma 2, the positive effect always dominates whenδntδet+1

> 0. Thus, as the rate of technological progress increases, the educationlevel and fertility rate both increase.

Figure 5b on the other hand shows the evolution of fertility and educationwhen et+1 > e. I assume that NN is flatter (This assumption is made toensure a unique intersection. Alternative assumption will not change theresult). As before, when the rate of technological progress, gt+1, increases, theNN and QQ curves shift to the right. Thus, the fertility rate again increases.Recall that δnt

δet+1< 0 if et+1 > e. Thus, in contrast to the previous case, now

the change in education is ambiguous. China yearbook provides data on thepercentage of graduates entering higher education. In this paper, I use thepercentage of graduates of junior middle school entering senior middle schoolas a proxy for the average education level. (Note: data for the percentageof graduates of senior middle school entering college is not available untilyear 1990). In 1966, China’s Communist leader Mao Zedong launched the

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Cultural Revolution. This revolution had a massive impact on education. Inthe early months of the Cultural Revolution, schools and universities wereclosed. Even though primary and middle schools later gradually reopened,the youth in urban areas were sent to live and work in agrarian areas inorder to obtain a better understanding of the role of manual agrarian labor inChinese society. In addition, most universities did not reopen until 1972. Theuniversity entrance exams were not restored until 1977 under Deng Xiaoping.Thus 1977 is often considered as the end of the Cultural Revolution. Thus,the Cultural Revolution severely damaged China’s education system. In thisresearch, in order to eliminate this exogenous impact on education, I focuson the period after the Culture Revolution. Data shows that the percentageof graduates of junior middle school entering senior middle school was 45.9%in 1980. Thereafter, it was pretty stable around 40% to 45% until 1994 (seeFigure 8). In order to be consistent with the data, I assume that the cut-offeducation level e occurs when the percentage of graduates of junior middleschool entering senior middle school is 45%. When et+1 > e, as the rate oftechnological progress increases, the education level stays constant and thefertility rate increases.

3.2 The Evolution of Technology and Education

The dynamical sub-system of Technology and Education consists of:

EE : et+1 = e(g(et))

GG : gt+1 = g(e(gt))

From equation (21) and lemma 1, the EE and GG curves are both con-cave. In the graph above, gl = g(0, L), is the technology growth rate wheneducation is zero. g is such that, when g ≤ g, the optimal level of educationis 0.

As in Galor and Weil(1998), I separate the analysis into two regimes,depending on whether the optimal level of education is zero or positive.When the population size is small enough, there is a temporary steady statewhere (e, g) = (0, gl) for a given population size. From equation 23, therate of technological progress increases steadily as the population graduallyincreases, while the education level remains at zero. This is because techno-logical progress is too low to invest in education.

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At a certain threshold level of population, gl is high enough, such thatgl > g. For a given population size, there now exists an interior stablesteady state equilibrium: (e, g) = (e∗, g∗). As discussed in section 2.1, anincrease in the rate of technological progress increases both the fertility rateand education level at the beginning when et+1 < e. As Lt increases, the GGand QQ curves shift upwards. Thus, technological progress and educationincrease over time, as well as the fertility rate. However, the positive impactof technological progress on education only operates while et+1 < e. Aseducation increases, once et+1 > e, further increases in technology no longerincrease the education level. Thus, once the economy crosses the thresholdwhere et+1 < e, education stays constant. As education stays constant,equation 23 then implies the population size converges to a constant level L∗

(population growth rate is zero). Figure 6b shows that in the steady state,the education level and the rate of technological progress will be constant.

4 The Impact of the One Child Policy

Now assume the government imposes an exogenous fertility control policy,such that each individual can only have one child. Thus, nt = 1. The fixedfertility rate affects the GG curve through the change in Lt. In addition,it also shifts the EE curve due to quantity and quality trade-off effects. Asthe number of children decreases, parents’ future transfers decrease. Thus,according to lemma 2, reducing the fertility rate increases the incentive forparents to invest more in their children’s education.

First, suppose the economy is in the Malthusian regime when the policyis implemented. In this regime, the optimal level of education is 0. If thefertility rate is fixed at nt = 1, the rate of technological progress remainsconstant and the education level stays at zero. The economy will never beable to move to the second regime.

As the benchmark model is section 2 revealed, there exists a thresholdlevel of education. When education is above this level, the effect of techno-logical progress on education vanishes in the absence of exogenous shocks.Given the concavity of technological progress in population, as assumed inequation 23, the population will be stable around a constant level in the longrun equilibrium. In other words, each family will eventually choose to vol-untarily have only “one-child” in the long run equilibrium, even without anypolicy restriction. Thus, when considering the timing of the policy, it is only

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binding before the long run equilibrium is reached. Technological progressand education level instead of moving between steady states, they will jumpto their new saddle path.

Now assume the policy is introduced during the second regime, in whichgl > g. In this case, as nt is decreased to 1, the GG curve shifts down.From lemma 2, the EE curve also shifts to the right. Introducing the one-child-policy before the steady state is reached will not change the fertilityrate in the long run. It only decreases the total population. This decreasesthe long-run technological growth rate. On the other hand, given the quan-tity/quality trade-off effect, as the number of children decreases, the chosenlevel of education increases. A higher level of education advances technolog-ical progress. Thus, the change in the rate of technological progress dependson whether the negative effect from smaller population dominates the pos-itive effect from the higher education. Figure 7a depicts the case when thenegative effect dominates. The new steady state following the implementa-tion of the one child policy is: (e, g) = (e′, g′), where g′ < g∗ and e′ < e∗.Notice that the effect on education also works through two channels. First,the chosen level of education increases as the fertility rate decreases. Second,as technological progress decreases, the rate of return to education decreasesthus reducing the incentive to invest in children. Following Lemma 1 andLemma 2, when one child policy is introduced, δnt

δet+1= 0, thus the technologi-

cal effect always dominates, which means education decreases. In contrast, ifthe positive effect from higher education on technological progress dominatesthe negative effect from lower population, long run technological progress andthe education level increase. Figure 7b shows the new steady state after theone child policy is introduced is: (e, g) = (e′, g′), where g′ > g∗ and e′ > e∗.

Therefore, when we take the negative effect of fertility on the chosenlevel of education into consideration, the impact of the one-child policy oneconomic growth in China is ambiguous. Consider an economy with par-ticular technological progress and human capital functions such that, whenthe one-child policy is introduced, the quantity-quality effect is not largeenough to compensate the negative population spillover effect on techno-logical progress. This situation is represented in Figure 7a, in which bothtechnological progress and education level converge to a lower long run equi-librium level. In addition, the growth rate of output per capita is lower thanthe benchmark model’s prediction. On the other hand, now consider an alter-ative human capital function such that, when number of children decreases,the chosen level of education increases by a significant magnitude. In addi-

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tion, the technological progress function allows the positive education effectto dominate the negative population effect. Thus, the economy converges toa higher rate of technological progress and higher level of education in thelong run as shown in Figure 7b. Output per capita also grows at a higherrate compared to the benchmark model.

5 Conclusion

Motivated by Galor and Weil (2000), this paper examines the effects China’sexogenous population control on economic growth. This paper adopts twokey assumptions from the Galor-Weil model: (1) higher population leads totechnological progress, and (2) technological progress raises the return tohuman capital. On the other hand, it incorporates one new element into themodel, which is the negative effect of fertility on education. Taking withinfamily intergenerational transfers into consideration, raising children is nolonger just for pleasure, but it also becomes an investment.

The theoretical analysis shows that in response to exogenous populationcontrol intervention, total population decreases, which produces a negativeeffect on technological progress. However, transfers from children to parentsdecrease as number of children decreases. Thus, parents increase the educa-tion endowment in their only child in order to increase their child’s futureincome to compensate the loss from reduced transfers. Higher educationlevels then trigger more rapid technological progress. Based on the theo-retical framework in this paper, we are not able to conclude unambiguouslywhether the one-child policy will have a positive or negative effect on longrun economic growth in China.

Figure 8 shows the time path of education index, which is the percentageof graduates of junior secondary schools entering senior secondary schools.The figure shows that the education level fluctuates around 40 to 45 % from1978 to 1993. It starts rising after 1994. In 2014, the percentage of Gradu-ates of junior secondary schools entering senior secondary schools is as highas 95%. Since the policy was implemented in 1980, the “only-child” will startentering senior high around 1995. Thus, the timing of the increase in edu-cation is coincident with the implemention of the one-child policy. The datasuggested that education increases after the population control intervention,which is consistent with our quantity-quality trade off effect assumption.However, in order to understand the casual relationship, it requires further

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quantitative analysis. The forms for technological progress and human capi-tal need to be specified in order to provide a quantitative estimation. Giventhat this paper has provided a theoretical framework for examining the im-pact of one-child policy on long run economic development, it allows me toextend the analysis by studying the quantitative effects in the future.

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[12] Aghion, Philippe and Howitt, Peter. “Amodel of Growth Through Cre-ative Destruction”, Econometrica 1992, Vol 60, No. 2, 323-351

[13] Schultz, T. W. “Transforming Traditional Technological Agriculture”,New Haven: Yale University Press, 1964

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[14] Maddison, Angus. “Chinese Economic Performance in the Long Run960-2030 “, OECD Paris, 2007

[15] Choukhmane, Taha; Coeurdacier, Nicolas and Jin, Keyu. ”The One-Child Policy and Household Savings”, Yale University, 2014

[16] Li, Hongbin and Zhang, Junsen “Do High Birth Rates Hamper EconomicGrowth?”, The Review of Economics and Statistics 2007, 89 (1), 110–117

[17] Song, Zheng; Storesletten, Kjetil; Wang, Yikai and Zilibtti, Fabrizio.”Sharing High Growth across Generations: Pensions and DemographicTransition in China”, American Economic Jounal: Macroeconomics2015, 7(2), 1 -39

[18] Chen, Xianjuan “Born Like China, Growning Like China”, Simon FraserUniversity, 2015

[19] Xue, Jianpo; Yip, Kong K. and Tou, Wai-kit Si. One-Child Policy andthe Long-Run Development of China: A Unified Growth Approach, 2013

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Figure 1: Growth Rates in Western Europe

19

 

Percentage  change  %  

Figure 2: Growth Rates in China

20

 

Figure 3: Main Source of Livelihood for the Elderly (65+) in urban areas

21

Figure 4: Transfers towards elderly: Descriptive Statistics

22

Panel  A:  QQ  v.s.  NN  (when  𝑒 < 𝑒  )                                                Panel  B:  QQ  v.s.  NN  (when  𝑒 > 𝑒  )                                            

𝑒!  

 

NN  

QQ  𝑒!  

𝑒!  QQ’  

NN’  

𝑛!!!  𝑛!   𝑛!  

𝑒!  

 

𝑛!!!  

e*  

NN  

NN’  QQ  

QQ’  

𝑛!  𝑛!  

Figure 5: QQ vs. NN

23

Panel  A:  𝑒!!! = 0        

                                 Panel  B:  𝑒!!! >  0      

                                     

𝑔!!!  

𝑒!!!  

 

𝑔!!!  

𝑒!!!  

GG  

EE  

𝑔!    

𝑔!  

GG  

EE  

𝑔!    

𝑔!  

𝑔!  

 𝑔∗    

𝑒∗  

Figure 6: EE vs. GG

24

Panel  A        

   

𝑔(!!!)  

𝑒!!!  

𝑔∗  

𝑔!  

𝑔!  

𝑔!  

𝑒∗  𝑒!  

𝑔(!!!)  

𝑒!!!  

Panel  B  

𝑔!  

𝑔!  

𝑔∗  

𝑒∗   𝑒!  

𝑔!  

Figure 7: Impact of One-Child-Policy

25

 

 

     

       Data  Source:  China  year  book(2015)  

0  

10  

20  

30  

40  

50  

60  

70  

80  

90  

100  

Percentage    %

 

Figure 8: graduates of junior secondary schools entering senior secondaryschools (%)

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