Theoretical Perspectives on Transfers and the Role of NTA

Ronald LeeUC BerkeleyJan 19, 2006

Thanks to Gretchen Donehower, Tim Miller, Andy Mason and Paul Lau.

Goal of this talk

• overview of how transfers fit into various economic theories

• Explain relevance of NTA

• Will not give much detail.

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

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.

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.

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.

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.

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.

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.

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.

1, 1

1 1

max , ,

. .

1

t tc c t t t t

t t t

t t

u c n c

s t c w n B

c r B w

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

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.

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

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

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

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

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%

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.

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

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.

Total Spending on Education and Health Care for Children by TFR in Preceding

Years, Selected Countries

0

1

2

3

4

5

6

0 0.5 1 1.5 2 2.5 3 3.5

TFR in preceding five years

Rat

io o

f T

ot

Sp

nd

to

Av

Lab

Inc

30-4

9Relative to labor income age 30-49

• 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)

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).

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?

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

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

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.

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)

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

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.

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.

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.

rxlx

W x e l a c a y a da

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.

0( ) ( )W N x W x dx

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.

Capital

• K(x) is holding of capital at age x.

• K is per capita figure.

• 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.

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)

r=n

K(r,n)=demand for capital by producers

W(r,n)= life cycle wealth

r>n

After Willis (1988); Lee (1994)

Wealth, capital

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)

r=n

K(r,n)=demand for capital by producers

W(r,n)= life cycle wealth

r>n

After Willis (1988); Lee (1994)

T=0; pure life cycle saving

Wealth, capital

T=0; pure life cycle saving. Demand for K is just for consumption smoothing over life cycle.

Modigliani’s Dream

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)

r=n

K(r,n)=demand for capital by producers W(r,n)= life cycle wealth

r>n

After Willis (1988); Lee (1994)

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.

Wealth, capital

Golden RuleGolden Rule

T>0

Feldstein’s Nightmare

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)

r=n

K(r,n)=demand for capital by producers

W(r,n)= life cycle wealth

r>n

T(r,n)= transfer wealth<0

Bequests or govt budget surplus

After Willis (1988); Lee (1994)

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.

Wealth, capital

Golden Rule

T(r,n)= transfer wealth<0

Bequests or govt budget surplus

Golden Rule

Kotlikoff and Summers

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.

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.

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.

0

nxC e l x c x dx

NTA consumption age profile

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)

lnlc y

d C kA A

dn c

NTA average ages of consumption and earning.

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)

lnlc y

d C kA A

dn c

NTA average ages of consumption and earning.

Proportional change in life time consumption when n changes.

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.

lc y

kA A

c

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).

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.

s

tV t e u c s ds

1( )

1

c su c s

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.

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 progressρ=.01 discount rate (degree of altruism)δ=.03 depreciationCobb-Douglas coeffs: labor=2/3, cap=1/3Elasticity of intertemporal sub (theta)=.4Setup similar to Cutler et al (1990), but some critical diffs, too.

• Perfect demographic foresight by planner.

Now look at optimal trajectories for three countries

• US, Taiwan (without immig from Mainland), Niger

• Assume demographic steady state reached in 2300 (UN projections) and economic also; can solve this analytically

• Find optimal trajectory from 2006 to 2300 by numerical search.

Support Ratios for US, Niger, and Pseudo-Taiwan, with own c(x) and yl(x) age profiles

(2000-2150)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1980 2000 2020 2040 2060 2080 2100 2120 2140 2160

Date

Rat

io o

f E

ffec

tive

Wo

rker

s to

eff

ecti

ve c

on

sum

ers

US

Niger

Taiwan

Taiwan Niger

US

US has declining support ratio because cons is very high for old age.

Niger shows effect of demographic transition, demog dividend, then pop aging.

Consumption per Effective Consumer net of tech progress: Social Planner, 2006-2150

Consumption per Effective Consumer relative to 2006; Social Planner, 2006 to 2150

0

0.5

1

1.5

2

2.5

3

3.5

4

1980 2000 2020 2040 2060 2080 2100 2120 2140 2160

Date

Co

nsu

mp

tio

n p

er E

ffec

tive

Co

nsu

mer

net

of

tech

no

log

ical

p

rog

ress US

Niger

Taiwan

Consumption rises in all countries.

Most in Niger, because it started out with little capital and rapid pop gr.

Even in US and Taiwan consumption rises despite population aging.

Life Cycle Wealth, Transfer Wealth and Capital in US, Niger and Taiwan: Social Planner, 2006-2150

Life Cycle Wealth, Transfer Wealth and Capital in Social Planner's Taiwan, Ratios to Labor Income

-50.00

-40.00

-30.00

-20.00

-10.00

0.00

10.00

20.00

1980 2000 2020 2040 2060 2080 2100 2120 2140 2160

Date

Rat

ios

to L

abo

r In

com

e

Series1

Series2

Series3

Life Cycle Wealth, Transfer Wealth and Capital in Social Planner's US as Ratios to Labor Income

-50.00

-40.00

-30.00

-20.00

-10.00

0.00

10.00

20.00

1980 2000 2020 2040 2060 2080 2100 2120 2140 2160

Date

Rat

io t

o L

ab

or

Inco

me

(W/YL)

(K/YL)

(T/YL)

Life Cycle Wealth, Transfer Wealth and Capital in Niger, Ratios to labor income

-50.00

-40.00

-30.00

-20.00

-10.00

0.00

10.00

20.00

1980 2000 2020 2040 2060 2080 2100 2120 2140 2160

Date

Rat

io t

o L

ab

or

Inco

me

(W/YL)

(K/YL)

(T/YL)

TaiwanUS

Niger

Some points to note:

All three end up at same cap intensity.

Life cycle wealth is greater in US due to high consumption in old age.

Taiwan and Niger both require much greater downward transfers (bequests) to achieve optimal capital intensity.

T/Yl

K/Yl

W/Yl

Population change, life cycle saving and economic growth

• This part does not use NTA estimates, except labor income over the life cycle.

• Household members supply labor based on yl(x) profiles. • Unisex household composition by age of head simulated

based on fertility, mortality, and age of kids at leaving home.

• Household labor income is projected based on expected productivity growth.

• Consumption is allocated to household members in proportion to equivalent adult consumer weights.

Life cycle saving (cont.)

• Life time budget constraint for household is P.V. of survival weighted expected future labor earnings of all household members.

• Consumption path for household is chosen to maximize expected utility of household head, given subjective discount rate and rate of intertemporal substitution.

• No bequests; no transfers; no public sector. Open economy, so r and w are given.

Demographic transition has several effects

• Lower mortality means longer period in retirement, requires higher saving rate (behavioral).

• Lower fertility means adults keep greater share of life time income for own consumption, including in retirement, so need to save more (behavioral)

• Older population implies a greater population share of older adults who hold the most wealth (capital), and therefore more capital per person in population (compositional).

Cases simulated

1. Pure life cycle saving, as just described2. Life cycle saving wrapped around familial transfers to

elderly– Need to save less or nothing for old age– May need to save in anticipation of supporting own parents.

3. Persistent share of transfers – Observed cross-sectional age profile of consumption is

maintained through intergenerational sharing.– shares of old age consumption funded by transfers and by

assets remains fixed as the population ages.– Changing transfers to children as fertility and mortality fall also

taken into account– Determines unique trajectories

Simulated Capital/Income Ratio Under Life Cycle Savings for Taiwan Demography, 1900 to 2050, Assuming No Familial Transfers to Elderly

0

1

2

3

4

5

6

1900 1950 2000 2050

Ra

tio

LC Model Results

No Transfers

Simulated Capital/Income Ratio Under Life Cycle Savings for Taiwan Demography, 1900 to 2050, Assuming NTA Style Familial Transfers to

Elderly with Co-Residence

0

1

2

3

4

5

6

1900 1950 2000 2050

Ra

tio

LC Model Results

No Transfers

Family Transfers

Simulated Capital/Income Ratio Under Persistent Transfers Model (.35, .65) Compared to Life Cycle

Savings for Taiwan Demography, 1900 to 2050

0

1

2

3

4

5

6

1900 1950 2000 2050

Ra

tio

LC Model Results

Constant Tau Results

No Transfers

Family Transfers

Tau=0.35

Tau=0.65

Simulated Capital/Income Ratio Under Fixed Tau Model (.35, .65) Compared to Life Cycle Savings for Taiwan Demography, 1900 to

2050, and showing Actual Capital/Income Ratio and Wealth/Income Ratio

0

1

2

3

4

5

6

1900 1950 2000 2050

Ra

tio

LC Model Results

Constant Tau Results

Actual Capital/Income Ratio

Actual Wealth/Income Ratio

No Transfers

Family Transfers

Tau=0.35

Tau=0.65

All four show major capital deepening following fertility decline and pop aging.

Timing is several decades earlier in the Persistent Transfers model.

Simulated Saving Rate Under Life Cycle Savings for Taiwan Demography, 1900 to 2050, Assuming No Familial Transfers to Elderly

-5

0

5

10

15

20

25

30

1900 1950 2000 2050

Pe

rce

nta

ge

LC Model Results

No Transfers

Simulated Savings Rate Under Life Cycle Savings for Taiwan Demography, 1900 to 2050, with NTA Style Transfers to Elderly and

Coresidence

-5

0

5

10

15

20

25

30

1900 1950 2000 2050

Pe

rce

nta

ge

LC Model Results

No Transfers

Family Transfers

Simulated Savings Rate Under Fixed Tau Model (.35, .65) Compared to Life Cycle Savings for Taiwan Demography, 1900 to 2050

-5

0

5

10

15

20

25

30

1900 1950 2000 2050

Pe

rce

nta

ge

LC Model Results

Constant Tau Results

No Transfers

Family Transfers

Tau=0.35

Tau=0.65

Simulated Savings Rate Under Fixed Tau Model (.35, .65) Compared to Life Cycle Savings for Taiwan Demography, 1900 to 2050

-5

0

5

10

15

20

25

30

1900 1950 2000 2050

Pe

rce

nta

ge

LC Model Results

Constant Tau Results

Actual Net Private Savings Rate

Actual Household Savings Rate

No Transfers

Family Transfers

Tau=0.35

Tau=0.65

Saving rates rise following fertility and mortality decline in all approaches, but earliest in the Persistent Transfer approach. Only under Social Planner do they stay high with population aging.

Conclusion

• Transfers are central to theory about fertility, investment in human capital, investment in physical capital, economic growth, and the efficacy of public policies targeted to age groups.

• Theories provide many insights, but can become sterile if divorced from observation.

• NTA can provide valuable information about relevant transfers and processes, deepening our understanding in a number of areas.