1. N ational T ransfer A ccounts 1 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

2. N ational T ransfer A ccounts 2 ► Paper presented at PAA ► Should be on NTA website soon

3. N ational T ransfer A ccounts 3 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

4. N ational T ransfer A ccounts 4 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?

5. N ational T ransfer A ccounts 5 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

6. N ational T ransfer A ccounts 6 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.

7. N ational T ransfer A ccounts 7 ► 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.

8. N ational T ransfer A ccounts 8 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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11. N ational T ransfer A ccounts 11 y = -1.0493x + 1.9233 R2 = 0.6238

12. N ational T ransfer A ccounts 12 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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14. N ational T ransfer A ccounts 14 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.

15. N ational T ransfer A ccounts 15 ► Now look at this by components

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20. N ational T ransfer A ccounts 20 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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22. N ational T ransfer A ccounts 22 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.

23. N ational T ransfer A ccounts 23 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.

24. N ational T ransfer A ccounts 24 ► 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.

25. N ational T ransfer A ccounts 25 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.

26. N ational T ransfer A ccounts 26 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.

27. N ational T ransfer A ccounts 27 ► 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?

28. N ational T ransfer A ccounts 28 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?

29. N ational T ransfer A ccounts 29 ► 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.

30. N ational T ransfer A ccounts 30 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.

31. N ational T ransfer A ccounts 31 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.

32. N ational T ransfer A ccounts 32 Basic fertility-HK relations ► 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.

33. N ational T ransfer A ccounts 33 Constant elasticity functions are a special case ► The earlier analysis suggested α = 1/12 =.083 α = 1/12 =.083 β = -1 β = -1 From other literature, δ =.33 (maybe) From other literature, δ =.33 (maybe) γ doesn’t matter in this formulation γ doesn’t matter in this formulation

34. N ational T ransfer A ccounts 34 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

35. N ational T ransfer A ccounts 35 ► 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.

36. N ational T ransfer A ccounts 36 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.

37. N ational T ransfer A ccounts 37 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

38. N ational T ransfer A ccounts 38 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.

39. N ational T ransfer A ccounts 39 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:

40. N ational T ransfer A ccounts 40 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

41. N ational T ransfer A ccounts 41 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.

42. N ational T ransfer A ccounts 42 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.

43. N ational T ransfer A ccounts 43 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.

44. N ational T ransfer A ccounts 44 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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49. N ational T ransfer A ccounts 49 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

50. N ational T ransfer A ccounts 50 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.

51. N ational T ransfer A ccounts 51 ► This is a promising area for further work. ► It is another way that NTA can illuminate the relations of demographic change to economic development.

52. N ational T ransfer A ccounts 52 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.

53. N ational T ransfer A ccounts 53 The End