Theoretical Perspectives on Transfers and the Role of NTA

1. Theoretical Perspectives on Transfers and the Role of NTA Ronald Lee UC Berkeley Jan 19, 2006 Thanks to Gretchen Donehower, Tim Miller, Andy Mason and Paul Lau.

2. Goal of this talk • overview of how transfers fit into various economic theories • Explain relevance of NTA • Will not give much detail.

3. Outline of talk • Overview of transfers and theory • Fertility, altruism, HK and transfers • Altruism and bequests • Population and Economic Growth • Optimal paths • Population change, life cycle saving and economic growth • Comparative simulations over demographic transition

4. Transfers are central to theories of both fertility and economic growth • Capital intensity of economy depends on willingness of population to hold capital rather than spending it for current gratification. • Motivations to hold capital include • Life cycle consumption smoothing (yl(x), c(x)) • Desire to make transfers to next generation, inter vivos or end of life (bequests, other downward transfers). • But expected transfers for old age substitute for K. • Planned total transfer per child is the (shadow) price of a child to a parent.

5. Theory also bears on form of transfers • Transfer as cash (K) or HK? • Invest in HK of child until its rate of return equals rate of return on K (this is optimal amount of HK). • Give balance of desired transfer amount as K if positive. • If desired transfer amount is less than the optimal investment in HK, then • Investment in child is inefficiently low, or • Parent seeks to ensure repayment of part of full cost of optimal HK investment.

6. Theory also bears on public-private interaction • Becker-Murphy etc: • Govt may introduce public education in response to parental under-investment in education • Parents are compensated for cost in excess of their desired transfer amount by introducing a public pension program.

7. Efficacy of public intergenerational redistribution depends on private motivations • Motivation: altruism or exchange? • Real transfers are motivated by altruism in our use of the word “transfers” • Apparent transfers may actually be exchanges within the family: loans and their repayment, money for services, etc. • Altruistically motivated private transfers will be used to undo the effects of public transfer programs, provided parents wish to make positive bequests to their children before the public program.

8. Efficacy (cont.) • Barro: If parents were already giving bequests or other transfers, then they will increase their transfers to their kids to undo the effects of the public pension. • If parents do not wish to make positive bequests then public policies will be effective. • If apparent transfers are really exchanges then parents do not want to make bequests. • There is a growing empirical literature on altruism versus exchange.

9. Those are general theoretical ideas; now more detail • NTA includes countries at different levels of development, different public sector programs, different levels of mortality etc. • NTA will include changes over time within countries. • These theories often predict what observable changes will occur as income rises, as public sector programs become more important etc.

10. Basic altruistic fertility theory with bequests • “bequests” B here means all transfers to children. • Utility of parents depends on own life time cons, children’s av life time cons, and number of kids. • They decide how much to bequeath to child, B. For now, take n as given. • Bequest is larger if: • They are more altruistic • Their wage is higher • Their kid’s wage will be lower.

11. Now consider human capital • Parents can either invest in education, e, or leave a cash bequest, b, where B=b+e. • Earnings of child as adult are: g(e)wt+1. • Income of child as adult is: (1+r)b + g(e)wt+1 • Optimal parental plan is invest in education up to e* where its marginal product = r:r = g′(e*)wt+1

12. How does e* compare to B? • If e* less than B, the intended total bequest or transfer, then parents simple leave a cash bequest b = B-e* of the difference. No problem. • If e* greater than B then things get interesting. • Parents make loans to children for e*-B, and children repay them with old age support if repayment can be assured. • If repayment cannot be assured, then investment in education is too low (e<e*), income remains low, and fertility remains high. More later.

13. What is B? Public and private components of “bequests” in NTA • Costs of rearing, other consumption (OC) (Exclude from B?): • Parental transfer for other consumption (OC). • Public welfare for kids in poor families • Investment in HK (HK) public and private: • Education • Health • Inter vivos transfers to adult children (AIV) • End of life bequests, public and private (EOL) • Public: National debt, public infrastructure and other capital, natural resources (not yet included) • Private: end of life bequests

14. More on estimating B • B is the sum of pub and priv downward transfers per child, B = OC + HK + AIV + EOL • This is a longitudinal net present value at birth measure, which might be constructed from the cross-sectional accounts under appropriate assumptions. • Eventually perhaps it can be calculated longitudinally as we did for the main public transfers in the US and in France

15. B in the US for generation born in 2000 (rough, many assumps) • Use cross-section for 2000. • Assume transfers rise at 1.5% per year (prod gr) • Discount at 3% • Adjust public transfers for future budget balance (50-50 cut taxes, cut benefits) • Assume public debt = public capital

16. Value of B for US newborns in 2000 (NPV at birth) • NPV of Public Transfers (Pub Ed, Soc Sec and Medicare only) assuming budget is balanced 50-50 by cutting taxes and benefits: +47K(assumes govt debt = value of pub capital) • NPV of Intervivos familial transfers received including consumption: 220K • Private end of life bequests: 27K • Total:   294K

17. B in context • Relative to NPV of child’s life time earnings = 34% • Health and Education as a share of total bequest = 33% • Private as a share of B = 84%

18. Some questions for future work • How has B changed over 20th Cent? • Has it fallen with rise of transfers to elderly in second half of century? • Private transfers have surely fluctuated along with fertility, lower for baby boom gens, higher after. • Compare similar calculations across countries.

19. P is sum of gross upward transfers to adults, mainly to elderly (double counting with B, so caution needed) • Components of P • Familial transfers to elderly • Public transfers including

20. Hypotheses about these components of B and P per individual cross nationally • Basic idea: • Altruism sets size of total B, P. • Private takes public as given and makes up the target total. • HK spending per child is positively associated with income and negatively with fertility. • Here is a rough and preliminary look at six countries.

21. Total Spending on Education and Health Care for Children by TFR in Preceding Years, Selected Countries Relative to labor income age 30-49

22. For given income and fertility • public and private HK expenditures per child are negatively correlated. • Public and private P are negatively correlated. • Public pensions and elder co-residence with adult children are negatively related (but kids may co-reside with parents who receive pensions) • Public P and private transfers to adult children (AIV + EOL) are positively related. (Barro idea: private undoes public)

23. Hypotheses (cont.) • Private AIV and Public transfers per child are positively correlated with income and negatively with fertility. • Holding income and fertility constant • K (capital per capita) is positively associated with B. (e.g. Kotlikoff-Summers: bequest motive accounts for most K) • K (capital per capita) is negatively associated with P. (e.g. Feldstein: pub PAYGO pensions displace capital; here also familial transfers) • National saving rates are negatively associated with P, other things equal. (Flow version of K argument).

24. Empirical questions for a single country • What is the sign of B? What is its size relative to per capita income or labor inc 30-49 or life time earnings? • How has it changed historically? • What are the shares of public and private components of B? • What are the relative public and private shares of OC, HK, AIV and EOL? • How does B vary across countries? Is it related to income? Fertility? How about HK alone?

25. Fertility, altruism, HK and transfers (a la Willis, 1987) • Think of three stages of economic development • 1. Poor, very low returns to human capital • 2. Technical Progress and declining mortality raises returns to HK and incomes • 3. Continuing tech progress means high rates of return to HK and incomes • Now consider implications for fertility and transfers

26. 1. Poor and low returns to HK means • B is low relative to income (low shadow price) • Consequently fertility is high • Child labor • Relatively large material bequests to children, e.g. dowries, farms • Minimal old age support

27. 2. Medium, returns to HK have started to rise • With higher returns to HK and higher income, parents choose higher B (higher shadow price) • Fertility falls • Optimal HK exceeds desired B, then parents make familial loans to children (if repayment is assured) • These are repaid as Old Age Support, which in NTA appear to be transfers for OAS but are in fact exchange. • parents make implicit loan to children to get to optimal investment in HK.

28. But if institutions do not support repayment of HK loans, then • inability to enforce negative bequests (repayment of implicit loans) means there is too little investment in education. • In this case, public education may lead to efficient investment in education. • If followed by public pensions (repayment of parents) then this could be Pareto improvement (see Becker and Murphy)

29. 3. High income, low mortality, and very high returns to HK. • B grows to exceed optimal HK so parents want to make additional transfers to children • so familial support of the elderly declines • Elderly do life cycle saving and/or receive public pensions. • parents start to make private transfers to their children at every life cycle stage. • Children very costly so fertility very low

30. Population and Economic Growth • Consider the demographic transition and population aging • How can NTA measures and concepts help? • Accounting measures describe what is but don’t tell us what might be if something changes – that requires theory, assumptions.

31. Alternative Approaches • How is the optimal outcome affected by population change and life cycle measures? • How does population change affect the economy given a rule of individual behavior (life cycle saving)? • If existing patterns of transfers and asset accumulation remain similar, how will the economy be affected by population change? • In all cases ignore effects of scale and natural resources; focus on age distribution and growth rates.

32. Concepts • For given life time c(x) and yl(x), life cycle wealth W(x) is the wealth a generation would need to hold at age x to achieve the consumption path c(x) for given earnings path yl(x), per original member • Assumes generational sharing of mortality risk. • I have suppressed t, but this is a longitudinal concept.

33. Aggregate life cycle wealth • Aggregate life cycle wealth W is the population weighted average of W(x). • N(x) is the proportion of the population at age x, so W is life cycle wealth per capita in the population. • It is a cross-sectional weighted average of the longitudinal W(x) values.

34. Transfer wealth • T(x) is transfer wealth at age x • It is the survival weighted present value of expected future transfers received minus future transfers made to others. • T is the population weighted sum analogous to W, expressed as per capita average.

35. Capital • K(x) is holding of capital at age x. • K is per capita figure.

36. W(x) = T(x) + K(x) • Life cycle wealth can be held either as K or as expected net transfers in the future. Credit is another possibility I ignore here for simplicity. • Aggregate identity: W= T + K • Positive transfer wealth substitutes for K in satisfying demand for life cycle wealth. • Or let B# = -T be Aggregate Bequest Wealth • K = W + B# = W+(-T), and the demand for capital is the demand for life cycle wealth plus the demand for bequest wealth.

37. Figure 1. The demand for K by producers, the demand for life cycle wealth W, and transfer wealth T (all measured at population level on per capita basis) W(r,n)= life cycle wealth K(r,n)=demand for capital by producers r>n r=n Wealth, capital After Willis (1988); Lee (1994)

38. Figure 1. The demand for K by producers, the demand for life cycle wealth W, and transfer wealth T (all measured at population level on per capita basis) W(r,n)= life cycle wealth K(r,n)=demand for capital by producers T=0; pure life cycle saving T=0; pure life cycle saving. Demand for K is just for consumption smoothing over life cycle. r>n r=n Modigliani’s Dream Wealth, capital After Willis (1988); Lee (1994)

39. Figure 1. The demand for K by producers, the demand for life cycle wealth W, and transfer wealth T (all measured at population level on per capita basis) K(r,n)=demand for capital by producers W(r,n)= life cycle wealth T>0 T>0; life cycle demand for wealth partly satisfied by PAYGO pensions or by familial transfers to elderly. Less K and higher r than in pure life cycle saving case. r>n Golden Rule Golden Rule r=n Feldstein’s Nightmare Wealth, capital After Willis (1988); Lee (1994)

40. Figure 1. The demand for K by producers, the demand for life cycle wealth W, and transfer wealth T (all measured at population level on per capita basis) W(r,n)= life cycle wealth K(r,n)=demand for capital by producers T<0: bequest motive supplements life cycle demand for wealth. Total demand for K exceeds life cycle demand. K higher, r lower = n. Any more K than this would be inefficient. r>n Golden Rule Golden Rule r=n T(r,n)= transfer wealth<0 Bequests or govt budget surplus T(r,n)= transfer wealth<0 Bequests or govt budget surplus Wealth, capital Kotlikoff and Summers After Willis (1988); Lee (1994)

41. Consider optimal paths • Simplest case: Maximize steady state per capita consumption: Golden Rule. • This case shows clearly the role of transfers and transfer wealth, T.

42. Population aging and golden rule steady states • Population aging is mostly due to low population growth rates stemming from low fertility, rather than due to long life. • Consider the effect of population aging across golden rule steady states (g.r.s.s.) • dc/dn=-k • That is, a decline of .01 in n would lead to an increase in c by .01*k. • Slower pop gr and pog aging always raise per capita consumption across g.r. steady states.

43. II. Golden rule steady states with age structure: basic ideas • Now let the population have a steady state age structure e-nxl(x), and let steady state consumption and earnings by age be c(x) and yl(x). • In golden rule, the rate of return on capital and the discount rate equal n, the pop gr rate. • Let C = the present value of life time consumption discounted at rate n and survival weighted. NTA consumption age profile

44. Golden rule steady states with age structure (2): An Elegant Result • This result is due to Arthur and McNicoll • The effect of a small variation in n on C is found by differentiating across golden rule steady states, and is: • The effect on consumption depends on the balance of the capital dilution effect and an intergenerational transfer effect (actually, all reallocations combined) NTA average ages of consumption and earning.

45. Golden rule steady states with age structure (2): An Elegant Result • This result is due to Arthur and McNicoll • The effect of a small variation in n on C is found by differentiating across golden rule steady states, and is: • The effect on consumption depends on the balance of the capital dilution effect and an intergenerational transfer effect (actually, all reallocations combined) Proportional change in life time consumption when n changes. NTA average ages of consumption and earning.

46. Interpretation (cont.) • After manipulation, the expression can be seen to equal simply T/c, the ratio of transfer wealth to per capita consumption. In other words, the effect of more rapid or less rapid population growth, across golden rule steady states, depends only on the ratio of transfer wealth, in family and public systems, to per capita consumption. This quantity is readily calculated from NTA measures.

47. With age we get a different picture • Define life time consumption C=P.V. of survival-weighted life time consumption, c(x). • Striking result: dln(C)/dn = T/c • Life cycle consumption either rises or falls depending on whether the T necessary to achieve r=n is positive or negative. • In case shown in diagram T<0 for golden rule, so slower pop growth and pop aging raise C. Result due to Willis (1988); also see Lee (1994).

48. A more interesting optimal setup: Ramsey-Cass-Koopmans model • Social Planner maximizes discounted value of per capita utility from consumption. • Here utility is not weighted by population size; pop gr is irrelevant if it is.

49. Can be decentralized to planning by dynastic families a la Becker-Barro • Then don’t need social planner • Discounting is per generation. • Future generations also get weighted in a flexible way by their size, allowing for weights proportional to size, or for no weighting by size (per capita utility criterion), or intermediate cases. • Will not pursue here; for future.

50. Other assumptions made here • c(s) is aggregate consumption per equivalent adult consumer net of tech prog, that is times e-g(s-t) • Cobb Douglas production • Parameter values: g=.015 tech progress ρ=.01 discount rate (degree of altruism) δ=.03 depreciation Cobb-Douglas coeffs: labor=2/3, cap=1/3 Elasticity of intertemporal sub (theta)=.4 Setup similar to Cutler et al (1990), but some critical diffs, too. • Perfect demographic foresight by planner.