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

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

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

1 Support Ratio for China, 1950-2100, Based on UN population projections and average LDC age profiles from NTA Population aging Effective Producers Per Consumer 0.9 0.8 0.7 0.6 First Dividend High saving, rising capital intensity 200 Declining saving rates, rising capital intensity The issue here: Could investment in human capital lead to a similar outcome? 0.5 1950 1970 1990 2010 2030 2050 2070 2090 Year

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

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.

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.

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.

Figure 1. Per Child HK Spending (Public and Private) vs. Fertility 2.00 ln(hk per Child/Av Lab Inc 30-49) 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)

Figure 1. Per Child HK Spending (Public and Private) vs. Fertility 2.00 ln(hk per Child/Av Lab Inc 30-49) 1.80 1.60 1.40 1.20 1.00 0.80 0.60 0.40 Twn Jpn Slv Hng Kor Aust Swd Fr Fin Thai US CR Chl Brz Mex Urg Indonesia Phil 0.20 India 0.00 0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 ln(tfr)

Figure 1. Per Child HK Spending (Public and Private) vs. Fertility ln(hk per Child/Av Lab Inc 30-49) 2.00 1.80 1.60 1.40 1.20 1.00 0.80 0.60 0.40 0.20 y = -1.0493x + 1.9233 R2 = 0.6238 0.00 0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 ln(tfr)

Now calculate total HK spending on all children Multiply TFR times HK per child, and plot its log against log(tfr).

Total Expenditures Per Woman for Children's HK vs. Fertility for 19 NTA countries 2.50 ln(tfr times Per Child HK Spending Relative to Average Labor Income Ages 30-49) 2.00 1.50 1.00 0.50 y = -0.0493x + 1.9233 R 2 = 0.0036 0.00 0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 ln(tfr)

Total Expenditures Per Woman for Children's HK vs. Fertility for 19 NTA countries 2.50 ln(tfr times Per Child HK Spending Relative to Average Labor Income Ages 30-49) 2.00 1.50 1.00 0.50 Average ln(hk spending) is 1.9 Exp(1.9) = 6.7 y = -0.0493x + 1.9233 R 2 = 0.0036 So couple spends 6.7 years worth of labor income out of their total labor income of 80 years 6.7/80 =.084. 0.00 0.00 About 0.201/12 of life 0.40time labor 0.60income 0.80 1.00 1.20 1.40 ln(tfr) is spent on HK for all children.

Now look at this by components

Total Educ Spending vs. Fertility 2.00 ln(per Child Education/Average Labor Income Ages 30-49) 1.50 1.00 0.50 0.00-0.50-1.00 y = -1.3505x + 1.9235 R 2 = 0.6175 0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 ln(tfr)

Total Health Spending vs. Fertility 0.00-0.20 ln(per Child Health/Average Labor Income Ages 30-49) -0.40-0.60-0.80-1.00-1.20-1.40-1.60-1.80 y = -0.0376x - 0.6655 R 2 = 0.0008-2.00 0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 ln(tfr)

Private Educ Spending vs. Fertility 1.50 ln(per Child Private Education/Average Labor Income Ages 30-49) 1.00 0.50 0.00-0.50-1.00-1.50-2.00-2.50-3.00 y = 0.1989x - 0.708 R 2 = 0.0041-3.50 0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 ln(tfr)

Public Educ Spending vs. Fertility 2.00 ln(per Child Public Education/Average Labor Income Ages 30-49) 1.50 1.00 0.50 0.00-0.50-1.00-1.50-2.00 y = -1.8626x + 1.836 R 2 = 0.565-2.50 0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 ln(tfr)

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.

The Standard Model: Rising Income Leads to Choice of Lower Fertility and Higher HK Investment per Child Human Capital Investment per child 7 6 5 4 3 2 1 Yn=6 Yn=4 Yn=1 0 1 2 3 4 5 6 7 8 Number of children

The Standard Model: Rising Income Leads to Choice of Lower Fertility and Higher HK Investment per Child Human Capital Investment per child 7 6 5 4 3 2 1 0 Yn=6 Yn=4 Yn=1 B 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. 1 2 3 4 5 6 7 8 A Number of children

Figure: The transformed budget constraint showing different quantity-quality choices. d is HK expenditure expressed in years of work at rate w ln(d) Ln(p q q/w) B D Slope (elasticity) = -1 C Quite similar to empirical scatter A Intercept of scatter indicates years of work expended on HK is 6.8. Share of lifetime labor income is 1/12. Ln(n)

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.

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.

Association is non-causal We don t 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.

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?

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?

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.

Model basic 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.

Notation H t is the human capital of generation t F t is the NRR of generation t, so it includes survival from birth to working ages. W t is the wage of generation t.

Basic fertility-hk relations H = h F W = + h F g H ( ) ( ) ( ) t 1 t t t t W W = g H ( ) t+ 1 t+ 1 = ( ) + 1 g h F W t t t The last equation shows how wages for one generation result from the wages of the generation s parents and their fertility. Given fertility over the demographic transition, and initial wage level, we can trace out the trajectory of wages.

Constant elasticity functions are a special case ( ) β t+ 1 = t t =α t t H h F W F W ( ) g H = t+ 1 t+ 1 H δ γ The earlier analysis suggested α = 1/12 =.083 β = -1 From other literature, δ =.33 (maybe) γ doesn t matter in this formulation

Production and Human capital 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(t+1) = h(f(t)) W(t) Wage (W) Wage is increasing in human capital W(t) = g(hk(t)) Baseline Specifications W ( t) HK ( t + 1) = 12F t W t () ( ) = γ HK( t).33

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.

Equilibrium wage when fertility is 1 constant 1 δ 1 βδ ( 1 δ ) ˆ δ αγ Ft = W 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.

Linking fertility and wages to the aggregate economy Demography notation Let N0 t be number of children N1 t be number of working age N2 t be number of elderly F = NRR, so survival from birth to wrking age is included. s = survival from working age to old age Equations N1 t+1 =F*N1 t N2 t = s*n1 t

Total output T T t = W t *N t We can derive many analytic results for T, W and F, but instead we will go on to consider consumption.

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: C = T w N h( F) t t t 0 t t C T = 1 Fh( F) t t t t = 1 α F 1 + β t t t C T

Now get consumption per equivalent adult consumer Take expression for C t from the previous slide. Divide it by population weighted by equivalent adult consumers, e.g. from NTA c(x) schedules. This gives c t c = C /( a N0 + N1 + a N2) t t 0 t t 2 t

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.

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.

Figure 6. Macro Indicators: Baseline Results 160.0 150.0 140.0 Boom 130.0 (demoraphic 120.0 dividend) 110.0 100.0 90.0 Fertility bust, but 80.0 consumption 70.0 remains high 60.0 Value (percent of year 0) 0 1 2 3 4 5 6 Period Fertility recovers: modest effect on C/EA Support ratio C/ EA GNP/N 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 Value (percent of year 0) 160.0 150.0 140.0 130.0 120.0 110.0 100.0 90.0 80.0 70.0 60.0 During first dividend phase, consumption 0 does not 1 rise 2 as much 3 as support 4 ratio. 5 6 Period The difference is invested in HK. Support ratio C/ EA GNP/N 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 Relative to C/EA period 0 150.0 140.0 130.0 120.0 110.0 100.0 90.0 80.0 70.0 60.0 0 1 2 3 4 5 6 Period Support ratio Baseline -1.50-0.70

Figure 8. Consumption per equivalent adult, altenative elasticities of w wrt h Period 160.0 150.0 140.0 130.0 120.0 110.0 100.0 90.0 80.0 70.0 60.0 0 1 2 3 4 5 6 Relative to C/EA period 0 Support ratio Baseline 0.50 0.16

Figure 9. Consumption per equivalent adult, varying both elasticities Relative to C/EA period 0 180.0 160.0 140.0 120.0 100.0 80.0 60.0 0 1 2 3 4 5 6 Period Support ratio Baseline -1.5,.5 -.7,.16

Figure 10. Consumption per equivalent adult, alternative fertility scenarios Relative to C/EA in period 0 130.0 125.0 120.0 115.0 110.0 105.0 100.0 95.0 90.0 85.0 80.0 0 1 2 3 4 5 6 Period Baseline Slow decline to 1 Fast decline to 1 Slow decline to.6

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

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

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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