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

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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

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• Paper presented at PAA
• Should be on NTA website soon

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Economic consequences of demographic transition

• Support ratios change.
• First dividend
• Population aging
• Aggregate demand for wealth rises leading to more
  capital per worker.
• Second dividend
• Lower mort, fewer kids, more elderly who hold
  assets.
• Third Investment in human capital rises???
• Subject of this paper

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Population aging
Declining saving rates, rising capital intensity
The issue here Could investment in human capital
lead to a similar outcome?
First Dividend
High saving, rising capital intensity
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Starting point is an empirical observation based
on National Transfer Account data

• Data for 19 countries for various years, poor and
  rich, 1994-2005.
• Measure public and private expenditures on health
  and education at each age.
• Sum these for health ages 0-18
• Sum for education ages 0-26
• Gives total HK investment per child

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This is not usual measure of investment in HK

• Usually, people look just at education.
• Direct expenditures on education are not taken
  into account at all.
• Emphasis is on the opportunity cost of the time
  spent by a child or young adult getting an
  education
• The rate of return to this investment can be
  easily estimated from a simple earnings equation.

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• Can invest more in HK at the extensive margin by
  going to school for more years
• Can invest in HK at the intensive margin by
  studying harder each year, and spending more each
  year.
• Getting private tutoring after public school.
• Going to cram school after public school.
• Investment at intensive margin would not show up
  in standard measure.

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Measure labor income by age

• Average males and females, including those who
  have zero labor income at each age.
• Include
• wages and salaries,
• fringe benefits,
• self employment income,
• estimated unpaid family labor
• Form average for ages 30-49 w.
• Construct ratio of HK spending to average w.
• Plot log of HK/w against log of TFR.

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y -1.0493x 1.9233 R2 0.6238
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Now calculate total HK spending on all children

• Multiply TFR times HK per child, and plot its log
  against log(TFR).

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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.
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• Now look at this by components

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How is this related to standard Quantity-Quality
models?

• Assume that the share of total labor income spent
  on HK is fixed, consistent with scatter plot.
• Draw budget constraints for differing levels of
  income.

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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.
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d is HK expenditure expressed in years of work at
rate w
Slope (elasticity) -1
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.
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• So our scatter plot shows a common transformed
  budget constraint with different fertility-HK
  choices.
• Differing incomes is one possible cause of
  different fertility choices.
• There are many others.

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Other sources of variation in fertility/HK choice

• Pref for HK Rate of return to HK survival
  rates consumption value of HK.
• Price of HK due to medical technology,
  transportation improvements, etc.
• Price of number family allowances, fines for
  second child, changing access to effective
  contraceptives
• Cultural influences on varying share of income
  allocated to total HK expenditures and on number.

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Association is non-causal

• We dont know whether fertility decline causes
  rising HK investments per child.
• Desire to make bigger HK investments causes
  fertility decline.
• Some other factor causes both fertility and HK
  changes.

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• To estimate a causal relationship we would need
  to have some way of isolating an independent
  cause of fertility variation, and then look at
  the HK variation.
• Possibilities at micro level
• Whether first two births are daughters, for
  countries with son preference
• Twins
• Sterility due to disease, after some births.
• Access to contraception in area
• Other ideas?

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Here we need at national level

• Paper by Bloom, Canning, et al uses abortion laws
  of country
• Access to contraception in a country is another
  possibility, but less clear that it is exogenous.
• Any ideas?

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• Now we are going to develop a simple model.
• Goal is to simulate the effects of fertility and
  mortality change over the transition on HK
  investment.
• Combine this with other estimates of effect of HK
  on wages.

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Modelbasic structure

• Take fertility variations as given, trace out
  consequences for HK, w, consumption.
• 3 generations children, workers, retirees
  usual accounting identities.
• No saving or physical capital.

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Notation

• Ht is the human capital of generation t
• Ft is the NRR of generation t, so it includes
  survival from birth to working ages.
• Wt is the wage of generation t.

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Basic fertility-HK relations

• The last equation shows how wages for one
  generation result from the wages of the
  generations parents and their fertility.
• Given fertility over the demographic transition,
  and initial wage level, we can trace out the
  trajectory of wages.

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Constant elasticity functions are a special case

• The earlier analysis suggested
• a 1/12 .083
• ß -1
• From other literature, d .33 (maybe)
• ? doesnt matter in this formulation

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Production and Human capital
Baseline Specifications

• Human capital (HK)
• Portion of wage, W(t), workers invest in their
  children is inversely related to their fertility,
  F(t)
• Human capital of workers one period later is
• HK(t1) h(F(t)) W(t)
• Wage (W)
• Wage is increasing in human capital
• W(t) g(HK(t))

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

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Equilibrium wage when fertility is constant

• Given those parameter values, this tells us that
  the equilibrium wage is inversely proportional to
  the square root of the constant level of
  fertility, F.5.

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Linking fertility and wages to the aggregate
economy

• Demography notation
• Let N0t be number of children
• N1t be number of working age
• N2t be number of elderly
• F NRR, so survival from birth to wrking age is
  included.
• s survival from working age to old age
• Equations
• N1t1 FN1t
• N2t sN1t

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Total output T

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

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

• The amount consumed is
• The share of aggregate production T that is
  consumed is
• In our constant elasticity special case, this
  becomes

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Now get consumption per equivalent adult consumer

• Take expression for Ct from the previous slide.
• Divide it by population weighted by equivalent
  adult consumers, e.g. from NTA c(x) schedules.
• This gives ct

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Simulation results for steady state

• Fixed fertility leads to steady-state with
• Constant wage and HK
• GDP grows at the same rate as the population.
• Consequences of different fixed level of
  fertility under baseline assumptions.
• Lower fertility leads to a higher steady-state
  wage, GDP/N, and consumption per equivalent adult
  (C/EA).
• Population aging goes with higher consumption,
  not lower.
• However, if fertility-HK-productivity links are
  weaker than baseline, then
• relationship between TFR and consumption can be
  hump shaped with a maximum at an intermediate
  fertility level.
• Thus, under some circumstances there is an
  optimal level of fertility as Samuelson
  conjectured.

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Dynamic simulations

• Now assume a stylized fertility transition going
  to sub-replacement fertility and then recovering
  to replacement level.
• Simulate consequences for consumption per
  equivalent adult.

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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.
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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.
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Key Findings

• Strong tradeoff between fertility and human
  capital investment.
• Given plausible parameters
• Lower fertility leads to higher standards of
  living
• Swings in support ratio do not lead to swings in
  standards of living

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Qualifications

• Parameter estimates quite uncertain
• Literature on impact of human capital investment
  on economic growth is unsettled.
• NTA-based estimates on HKTFR relationship is
  preliminary and based on fewer than 20 countries
• Model is highly stylized and abstracts from many
  important details.

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• This is a promising area for further work.
• It is another way that NTA can illuminate the
  relations of demographic change to economic
  development.

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Acknowledgement

• Support for this project has been provided by the
  following institutions
• the John D. and Catherine T. MacArthur
  Foundation
• the National Institute on Aging NIA,
  R37-AG025488 and NIA, R01-AG025247
• the International Development Research Centre
  (IDRC)
• the United Nations Population Fund (UNFPA)
• the Academic Frontier Project for Private
  Universities matching fund subsidy from MEXT
  (Ministry of Education, Culture, Sports, Science
  and Technology), 2006-10, granted to the Nihon
  University Population Research Institute.

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The End