fertility, human capital, and economic growth over the demographic transition

NNational ational TTransfer ransfer AAccountsccounts11

Fertility, Human Capital, Fertility, Human Capital, and Economic Growth and Economic Growth over the Demographic over the Demographic

TransitionTransition

Ronald Lee, University of California - Ronald Lee, University of California - BerkeleyBerkeley

Andrew Mason, University of Hawaii and Andrew Mason, University of Hawaii and the East-West Centerthe East-West Center

Research funded by NIAResearch funded by NIA

National Transfer Accounts2

►Paper presented at PAAPaper presented at PAA►Should be on NTA website soonShould be on NTA website soon


Economic consequences of Economic consequences of demographic transitiondemographic transition► Support ratios change.Support ratios change.

First dividendFirst dividend Population agingPopulation aging

► Aggregate demand for wealth rises leading Aggregate demand for wealth rises leading to more capital per worker.to more capital per worker. Second dividendSecond dividend Lower mort, fewer kids, more elderly who hold Lower mort, fewer kids, more elderly who hold

assets.assets.

► Third: Investment in human capital rises???Third: Investment in human capital rises??? Subject of this paperSubject of this paper


Support Ratio for China, 1950-2100, Based on UN population projections and average LDC age profiles from NTA

0.5

0.6

0.7

0.8

0.9

1

1950 1970 1990 2010 2030 2050 2070 2090

Year

Eff

ecti

ve

Pro

du

cers

Per

Co

nsu

mer

2007

Population aging

First Dividend

High saving, rising capital intensity

Declining saving rates, rising capital intensity

The issue here: Could investment in human capital lead to a similar outcome?


Starting point is an empirical Starting point is an empirical observation based on National Transfer observation based on National Transfer Account dataAccount data►Data for 19 countries for various years, Data for 19 countries for various years,

poor and rich, 1994-2005.poor and rich, 1994-2005.►Measure public and private Measure public and private

expenditures on health and education expenditures on health and education at each age.at each age. Sum these for health ages 0-18Sum these for health ages 0-18 Sum for education ages 0-26Sum for education ages 0-26 Gives total HK investment per childGives total HK investment per child


This is not usual measure of This is not usual measure of investment in HKinvestment in HK►Usually, people look just at education.Usually, people look just at education.►Direct expenditures on education are Direct expenditures on education are

not taken into account at all. not taken into account at all. ►Emphasis is on the opportunity cost of Emphasis is on the opportunity cost of

the time spent by a child or young the time spent by a child or young adult getting an educationadult getting an education

►The rate of return to this investment The rate of return to this investment can be easily estimated from a simple can be easily estimated from a simple earnings equation.earnings equation.


►Can invest more in HK at the extensive Can invest more in HK at the extensive margin by going to school for more margin by going to school for more yearsyears

►Can invest in HK at the intensive margin Can invest in HK at the intensive margin by studying harder each year, and by studying harder each year, and spending more each year. spending more each year. Getting private tutoring after public school. Getting private tutoring after public school. Going to cram school after public school. Going to cram school after public school.

► Investment at intensive margin would Investment at intensive margin would not show up in standard measure.not show up in standard measure.


Measure labor income by ageMeasure labor income by age

► Average males and females, including those Average males and females, including those who have zero labor income at each age. who have zero labor income at each age.

► Include Include wages and salaries, wages and salaries, fringe benefits, fringe benefits, self employment income, self employment income, estimated unpaid family laborestimated unpaid family labor

► Form average for ages 30-49 = w. Form average for ages 30-49 = w. ► Construct ratio of HK spending to average w. Construct ratio of HK spending to average w. ► Plot log of HK/w against log of TFR.Plot log of HK/w against log of TFR.


Figure 1. Per Child HK Spending (Public and Private) vs. Fertility

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

1.80

2.00

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40

ln(TFR)

ln(H

K p

er C

hild

/Av

Lab

Inc

30-

49)



AustBrz

Chl

CR

Fin

FrHng

India

Indonesia

Jpn

Mex

Phil

Slv

Kor

SwdTwn

Thai

Urg

US

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

1.80

2.00

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40

ln(TFR)

ln(H

K p

er C

hild

/Av

Lab

Inc

30-

49)



0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

1.80

2.00

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40

ln(TFR)

ln(H

K p

er C

hild

/Av

Lab

Inc

30-

49)

y = -1.0493x + 1.9233R2 = 0.6238


Now calculate total HK spending Now calculate total HK spending on all childrenon all children►Multiply TFR times HK per child, and Multiply TFR times HK per child, and

plot its log against log(TFR).plot its log against log(TFR).


Total Expenditures Per Woman for Children's HK vs. Fertility for 19 NTA countries

y = -0.0493x + 1.9233

R2 = 0.0036

0.00

0.50

1.00

1.50

2.00

2.50

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40

ln(TFR)

ln(T

FR

tim

es P

er C

hild

HK

Sp

end

ing

R

elat

ive

to A

vera

ge

Lab

or

Inco

me

Ag

es 3

0-49

)


Total Expenditures Per Woman for Children's HK vs. Fertility for 19 NTA countries

y = -0.0493x + 1.9233

R2 = 0.0036

0.00

0.50

1.00

1.50

2.00

2.50

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40

ln(TFR)

ln(T

FR

tim

es P

er C

hild

HK

Sp

end

ing

R

elat

ive

to A

vera

ge

Lab

or

Inco

me

Ag

es 3

0-49

)

Average ln(HK spending) is 1.9

Exp(1.9) = 6.7

So couple spends 6.7 years worth of labor income out of their total labor income of 80 years

6.7/80 = .084.

About 1/12 of life time labor income is spent on HK for all children.


►Now look at this by componentsNow look at this by components


Total Educ Spending vs. Fertility

y = -1.3505x + 1.9235R2 = 0.6175

-1.00

-0.50

0.00

0.50

1.00

1.50

2.00

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40

ln(TFR)

ln(P

er C

hild

Ed

uca

tio

n/A

vera

ge

Lab

or

Inco

me

Ag

es 3

0-49

)


Total Health Spending vs. Fertility

y = -0.0376x - 0.6655R2 = 0.0008

-2.00

-1.80

-1.60

-1.40

-1.20

-1.00

-0.80

-0.60

-0.40

-0.20

0.00

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40

ln(TFR)

ln(P

er C

hild

Hea

lth

/Ave

rag

e L

abo

r In

com

e A

ges

30

-49)


Private Educ Spending vs. Fertility

y = 0.1989x - 0.708R2 = 0.0041

-3.50

-3.00

-2.50

-2.00

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40

ln(TFR)

ln(P

er C

hild

Pri

vate

Ed

uca

tio

n/A

vera

ge

Lab

or

Inco

me

Ag

es

30-4

9)


Public Educ Spending vs. Fertility

y = -1.8626x + 1.836R2 = 0.565

-2.50

-2.00

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

2.00

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40

ln(TFR)

ln(P

er C

hild

Pu

blic

Ed

uca

tio

n/A

vera

ge

Lab

or

Inco

me

Ag

es 3

0-49

)


How is this related to standard How is this related to standard Quantity-Quality models?Quantity-Quality models?►Assume that the share of total labor Assume that the share of total labor

income spent on HK is fixed, income spent on HK is fixed, consistent with scatter plot.consistent with scatter plot.

►Draw budget constraints for differing Draw budget constraints for differing levels of income.levels of income.


The Standard Model: Rising Income Leads to Choice of Lower Fertility and Higher HK Investment per Child

0

1

2

3

4

5

6

7

1 2 3 4 5 6 7 8

Number of children

Hu

man

Cap

ital

In

vest

men

t p

er

chil

d

Yn=1

Yn=6

Yn=4


The Standard Model: Rising Income Leads to Choice of Lower Fertility and Higher HK Investment per Child

0

1

2

3

4

5

6

7

1 2 3 4 5 6 7 8

Number of children

Hu

man

Cap

ital

In

vest

men

t p

er

chil

d

Yn=1

Yn=6

Yn=4

B

A

C

With same data, plot ln(HK/w) instead of HK, against ln(TFR) instead of n.

The budget lines collapse onto a single straight line.


Ln(n)

Ln(pqq/w)

A

C

B

D

ln(d)

Figure: The transformed budget constraint showing different quantity-quality choices.

Slope (elasticity) = -1

d is HK expenditure expressed in years of work at rate w

Quite similar to empirical scatter

Intercept of scatter indicates years of work expended on HK is 6.8.

Share of lifetime labor income is 1/12.


►So our scatter plot shows a common So our scatter plot shows a common transformed budget constraint with transformed budget constraint with different fertility-HK choices. different fertility-HK choices.

►Differing incomes is one possible Differing incomes is one possible cause of different fertility choices. cause of different fertility choices.

►There are many others.There are many others.


Other sources of variation in Other sources of variation in fertility/HK choicefertility/HK choice► Pref for HKPref for HK: Rate of return to HK; survival : Rate of return to HK; survival

rates; consumption value of HK.rates; consumption value of HK.► Price of HKPrice of HK due to medical technology, due to medical technology,

transportation improvements, etc.transportation improvements, etc.► Price of numberPrice of number: family allowances, fines : family allowances, fines

for second child, changing access to for second child, changing access to effective contraceptiveseffective contraceptives

► Cultural influencesCultural influences on varying share of on varying share of income allocated to total HK expenditures income allocated to total HK expenditures and on number.and on number.


Association is non-causalAssociation is non-causal

►We don’t know whether fertility We don’t know whether fertility decline causes rising HK investments decline causes rising HK investments per child.per child.

►Desire to make bigger HK investments Desire to make bigger HK investments causes fertility decline.causes fertility decline.

►Some other factor causes both fertility Some other factor causes both fertility and HK changes. and HK changes.


► To estimate a causal relationship we would To estimate a causal relationship we would need to have some way of isolating an need to have some way of isolating an independent cause of fertility variation, and independent cause of fertility variation, and then look at the HK variation. then look at the HK variation.

► Possibilities at micro levelPossibilities at micro level Whether first two births are daughters, for Whether first two births are daughters, for

countries with son preferencecountries with son preference TwinsTwins Sterility due to disease, after some births.Sterility due to disease, after some births. Access to contraception in areaAccess to contraception in area Other ideas?Other ideas?


Here we need at national Here we need at national levellevel►Paper by Bloom, Canning, et al uses Paper by Bloom, Canning, et al uses

abortion laws of countryabortion laws of country►Access to contraception in a country is Access to contraception in a country is

another possibility, but less clear that another possibility, but less clear that it is exogenous.it is exogenous.

►Any ideas?Any ideas?


►Now we are going to develop a simple Now we are going to develop a simple model. model.

►Goal is to simulate the effects of Goal is to simulate the effects of fertility and mortality change over the fertility and mortality change over the transition on HK investment. transition on HK investment.

►Combine this with other estimates of Combine this with other estimates of effect of HK on wages. effect of HK on wages.


Model—basic structureModel—basic structure

►Take fertility variations as given, trace Take fertility variations as given, trace out consequences for HK, w, out consequences for HK, w, consumption.consumption.

►3 generations: children, workers, 3 generations: children, workers, retirees; usual accounting identities.retirees; usual accounting identities.

►No saving or physical capital.No saving or physical capital.


NotationNotation

►HHtt is the human capital of generation t is the human capital of generation t

►FFtt is the NRR of generation t, so it is the NRR of generation t, so it includes survival from birth to working includes survival from birth to working ages.ages.

►WWtt is the wage of generation t. is the wage of generation t.


Basic fertility-HK relationsBasic fertility-HK relations

► The last equation shows how wages for one generation The last equation shows how wages for one generation result from the wages of the generation’s parents and result from the wages of the generation’s parents and their fertility. their fertility.

► Given fertility over the demographic transition, and Given fertility over the demographic transition, and initial wage level, we can trace out the trajectory of initial wage level, we can trace out the trajectory of wages. wages.

1t t t t tH h F W h F g H

1 1t tW g H

1t t tW g h F W


Constant elasticity functions are Constant elasticity functions are a special casea special case

1t t t t tH h F W F W

1 1t tg H H

► The earlier analysis suggested The earlier analysis suggested αα = 1/12 = .083 = 1/12 = .083 ββ = -1 = -1 From other literature, From other literature, δδ = .33 (maybe) = .33 (maybe) γγ doesn’t matter in this formulation doesn’t matter in this formulation


Production and Human capitalProduction and Human capital

► Human capital (HK)Human capital (HK) Portion of wage, W(t), Portion of wage, W(t),

workers invest in their workers invest in their children is inversely children is inversely related to their fertility, related to their fertility, F(t)F(t)

Human capital of workers Human capital of workers one period later isone period later is

HK(t+1) = h(F(t)) W(t)HK(t+1) = h(F(t)) W(t)

► Wage (W)Wage (W) Wage is increasing in Wage is increasing in

human capitalhuman capital W(t) = g(HK(t))W(t) = g(HK(t))

112

W tHK t

F t

.33W t HK t

Baseline Specifications


►That .33 comes reviewing a large That .33 comes reviewing a large literature on micro level estimates of literature on micro level estimates of earnings in relation to education, and earnings in relation to education, and a smaller macro level literature on a smaller macro level literature on aggregate production functions that aggregate production functions that include the education of the labor include the education of the labor force, usually median education or force, usually median education or proportions enrolled.proportions enrolled.


Equilibrium wage when fertility Equilibrium wage when fertility is constantis constant

► Given those parameter values, this tells us Given those parameter values, this tells us that the equilibrium wage is inversely that the equilibrium wage is inversely proportional to the square root of the proportional to the square root of the constant level of fertility, Fconstant level of fertility, F.5.5..

1

111 ˆ

tF W


Linking fertility and wages to Linking fertility and wages to the aggregate economythe aggregate economy► Demography notationDemography notation

Let N0Let N0tt be number of children be number of children

N1N1tt be number of working age be number of working age

N2N2tt be number of elderly be number of elderly F = NRR, so survival from birth to wrking age is F = NRR, so survival from birth to wrking age is

included. included. s = survival from working age to old ages = survival from working age to old age

► EquationsEquations N1N1t+1 t+1 == F*N1F*N1t t

N2N2tt = s*N1 = s*N1t t


Total output TTotal output T

►TTtt = W = Wtt*N*Ntt

►We can derive many analytic results We can derive many analytic results for T, W and F, but instead we will go for T, W and F, but instead we will go on to consider consumption. on to consider consumption.


Get consumption by stubtracting from Get consumption by stubtracting from total wages the amount spent on human total wages the amount spent on human capital investmentcapital investment

► The amount The amount consumed is consumed is

► The share of The share of aggregate aggregate production T that is production T that is consumed isconsumed is

► In our constant In our constant elasticity special elasticity special case, this becomes:case, this becomes:

0 ( )t t t t tC T w N h F

1 ( )t t t tC T Fh F

11t t tC T F


Now get consumption per Now get consumption per equivalent adult consumerequivalent adult consumer►Take expression for CTake expression for Ctt from the from the

previous slide. previous slide. ►Divide it by population weighted by Divide it by population weighted by

equivalent adult consumers, e.g. from equivalent adult consumers, e.g. from NTA c(x) schedules. NTA c(x) schedules.

►This gives cThis gives ctt

0 2/ ( )t t t t tc C a N0 N1 a N2


Simulation results for steady Simulation results for steady statestate► Fixed fertility leads to steady-state withFixed fertility leads to steady-state with

Constant wage and HK Constant wage and HK GDP grows at the same rate as the population.GDP grows at the same rate as the population.

► Consequences of different fixed level of fertility Consequences of different fixed level of fertility under baseline assumptions.under baseline assumptions. Lower fertility leads to a higher steady-state wage, GDP/N, Lower fertility leads to a higher steady-state wage, GDP/N,

and consumption per equivalent adult (C/EA). and consumption per equivalent adult (C/EA). Population aging goes with higher consumption, not Population aging goes with higher consumption, not

lowerlower..► However, if fertility-HK-productivity links are weaker However, if fertility-HK-productivity links are weaker

than baseline, then: than baseline, then: relationship between TFR and consumption can be hump relationship between TFR and consumption can be hump

shaped with a maximum at an intermediate fertility level. shaped with a maximum at an intermediate fertility level. Thus, under some circumstances there is an optimal level Thus, under some circumstances there is an optimal level

of fertility as Samuelson conjectured.of fertility as Samuelson conjectured.


Dynamic simulationsDynamic simulations

►Now assume a stylized fertility Now assume a stylized fertility transition going to sub-replacement transition going to sub-replacement fertility and then recovering to fertility and then recovering to replacement level. replacement level.

►Simulate consequences for Simulate consequences for consumption per equivalent adult.consumption per equivalent adult.


Figure 6. Macro Indicators: Baseline Results

60.070.080.090.0

100.0110.0120.0130.0140.0150.0160.0

0 1 2 3 4 5 6

Period

Va

lue

(p

erc

en

t o

f y

ea

r 0

)

Support ratio

C/ EA

GNP/N

Boom (demoraphic

dividend)

Fertility bust, but consumption remains high

Fertility recovers: modest effect on C/EA

Bottom line: Low fertility leads to higher consumption. Human capital investment has moderated

the impact of fertility swings on standards of living.


Figure 6. Macro Indicators: Baseline Results

60.070.080.090.0

100.0110.0120.0130.0140.0150.0160.0

0 1 2 3 4 5 6

Period

Va

lue

(p

erc

en

t o

f y

ea

r 0

)

Support ratio

C/ EA

GNP/N

During first dividend phase, consumption does not rise as much as support ratio.

The difference is invested in HK.

That is why ih later periods, consumption is proportionately higher than the support ratio.


Figure 7. Consumption per equivalent adult,

alternative elasticities of h wrt F

60.0

70.0

80.0

90.0

100.0110.0

120.0

130.0

140.0

150.0

0 1 2 3 4 5 6

Period

Rel

ativ

e to

C/E

A p

erio

d 0

Support ratio

Baseline

-1.50

-0.70


Figure 8. Consumption per equivalent adult, altenative elasticities of w wrt h

60.070.080.090.0

100.0110.0120.0130.0140.0150.0160.0

0 1 2 3 4 5 6

Relative to C/EA period 0

Per

iod

Support ratio

Baseline

0.50

0.16



varying both elasticities

60.0

80.0

100.0

120.0

140.0

160.0

180.0

0 1 2 3 4 5 6

Period

Rel

ativ

e to

C/E

A p

erio

d 0

Support ratio

Baseline

-1.5, .5

-.7, .16



alternative fertility scenarios

80.085.090.095.0

100.0105.0110.0115.0120.0125.0130.0

0 1 2 3 4 5 6

Period

Rel

ativ

e to

C/E

A in

per

iod

0

Baseline

Slow decline to 1

Fast decline to 1

Slow decline to .6


Key FindingsKey Findings

►Strong tradeoff between fertility and Strong tradeoff between fertility and human capital investment.human capital investment.

►Given plausible parametersGiven plausible parameters Lower fertility leads to higher standards of Lower fertility leads to higher standards of

livingliving Swings in support ratio do not lead to Swings in support ratio do not lead to

swings in standards of livingswings in standards of living


QualificationsQualifications

►Parameter estimates quite uncertainParameter estimates quite uncertain Literature on impact of human capital Literature on impact of human capital

investment on economic growth is investment on economic growth is unsettled.unsettled.

NTA-based estimates on HK:TFR NTA-based estimates on HK:TFR relationship is preliminary and based on relationship is preliminary and based on fewer than 20 countriesfewer than 20 countries

►Model is highly stylized and abstracts Model is highly stylized and abstracts from many important details.from many important details.


►This is a promising area for further This is a promising area for further work.work.

► It is another way that NTA can It is another way that NTA can illuminate the relations of illuminate the relations of demographic change to economic demographic change to economic development. development.


AcknowledgementAcknowledgement

Support for this project has been provided by the Support for this project has been provided by the following institutions:following institutions:

► the John D. and Catherine T. MacArthur Foundation; the John D. and Catherine T. MacArthur Foundation; ► the National Institute on Aging: NIA, R37-AG025488 the National Institute on Aging: NIA, R37-AG025488

and NIA, R01-AG025247; and NIA, R01-AG025247; ► the International Development Research Centre the International Development Research Centre

(IDRC);(IDRC);► the United Nations Population Fund (UNFPA); the United Nations Population Fund (UNFPA); ► the Academic Frontier Project for Private Universities: the Academic Frontier Project for Private Universities:

matching fund subsidy from MEXT (Ministry of matching fund subsidy from MEXT (Ministry of Education, Culture, Sports, Science and Technology), Education, Culture, Sports, Science and Technology), 2006-10, granted to the Nihon University Population 2006-10, granted to the Nihon University Population Research Institute.Research Institute.

NNational ational TTransfer ransfer AAccountsccounts5353

The EndThe End

fertility, human capital, and economic growth over the demographic transition

Documents

total hk investment

measure labor income

total hk spending

hk expenditure

share of total labor

years worth of labor

different fertilityhk

share of lifetime labor