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Fertility, Human Capital, and Economic Growth over the Demographic Transition. Ronald Lee, University of California - Berkeley Andrew Mason, University of Hawaii and the East-West Center Research funded by NIA. Paper presented at PAA Should be on NTA website soon. - PowerPoint PPT Presentation
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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
National Transfer Accounts3
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
National Transfer Accounts4
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?
National Transfer Accounts5
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
National Transfer Accounts6
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.
National Transfer Accounts7
►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.
National Transfer Accounts8
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.
National Transfer Accounts9
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)
National Transfer Accounts10
Figure 1. Per Child HK Spending (Public and Private) vs. Fertility
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)
National Transfer Accounts11
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)
y = -1.0493x + 1.9233R2 = 0.6238
National Transfer Accounts12
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).
National Transfer Accounts13
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
)
National Transfer Accounts14
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.
National Transfer Accounts15
►Now look at this by componentsNow look at this by components
National Transfer Accounts16
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
)
National Transfer Accounts17
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)
National Transfer Accounts18
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)
National Transfer Accounts19
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
)
National Transfer Accounts20
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.
National Transfer Accounts21
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
National Transfer Accounts22
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.
National Transfer Accounts23
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.
National Transfer Accounts24
►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.
National Transfer Accounts25
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.
National Transfer Accounts26
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.
National Transfer Accounts27
► 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?
National Transfer Accounts28
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?
National Transfer Accounts29
►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.
National Transfer Accounts30
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.
National Transfer Accounts31
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.
National Transfer Accounts32
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
National Transfer Accounts33
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
National Transfer Accounts34
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
National Transfer Accounts35
►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.
National Transfer Accounts36
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
National Transfer Accounts37
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
National Transfer Accounts38
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.
National Transfer Accounts39
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
National Transfer Accounts40
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
National Transfer Accounts41
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.
National Transfer Accounts42
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.
National Transfer Accounts43
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.
National Transfer Accounts44
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.
National Transfer Accounts45
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
National Transfer Accounts46
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
National Transfer Accounts47
Figure 9. Consumption per equivalent adult,
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
National Transfer Accounts48
Figure 10. Consumption per equivalent adult,
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
National Transfer Accounts49
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
National Transfer Accounts50
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.
National Transfer Accounts51
►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.
National Transfer Accounts52
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