Transfers, Age Profiles, and Economic Growth: Contributions of NTA Ronald Lee, October 22, 2006 Tokyo

Transfers, Age Profiles, and Economic Growth:

Contributions of NTA

Ronald Lee, October 22, 2006

Tokyo

• This is a workshop. In spirit of workshop, I will discuss some theoretical ideas that are not fully worked out and some empirical work in progress.

• Gretchen Donehower and Avi Ebenstein carried out the empirical analyses I will be reporting in the second half of my talk.

Plan of talk

• Population change, transfers and economic growth—theoretical perspectives.

• Implementation and comparison of these theoretical approaches for Taiwan.

• Historical US data on changing age profiles, and how these are related to growth.

Some of the topics that NTA estimates can be used to study

• Issues of generational equity that arise when public sector transfer systems change. Ditto for private transfers systems—generational squeezes..

• Guidance in designing and reforming systems of social support.• Population change and economic growth (dividends and beyond). • Long run projections of government budgets (Tim has worked on this with

you). • Estimation of fiscal externalities to the birth of a child, or the arrival of an

immigrant, or the departure of an emigrant.• Mapping the systems through which income is reallocated within an

economy, including nonmarket reallocations. Understanding the unusual features of a country’s systems.

• How transfer systems in a country are changing over time and the implications of these changes.

• Make it possible to take transfer behavior into account in studies of saving behavior.

• Study social inequities in transfer systems, for example by level of education or by race/ethnicity (the Brazil project has a paper on this).

Outline of rest of talk

• Demographic transition, intergenerational transfers, and economic growth: theoretical approaches.

• Empirical/Simulation explorations of these theories.

• The changing shape of the economic life cycle in the US: preliminary historical results.

I. Golden rule steady states without age structure

• Consider standard Solow growth model on golden rule steady state growth path– Saving rate is chosen to maximize steady state consumption, c– This requires that all labor earnings Yl be consumed and all

capital earnings, Yk, be saved. – Together with a production function and a rate of population

growth, n, this determines the level of consumption per capita, c, and capital per worker, k.

• We can find the effect of a change in the population growth rate, n, on the steady state consumption, c, by differentiating:

dc dn k

– With more rapid population growth, more output must be saved to equip new workers, and the optimal levels of k, y, and c will all be a bit lower. “capital dilution”.

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 r changes.

Golden rule steady states with age structure (3): Interpreting this result

• Capital dilution will always be negative when n is higher (e.g. with higher fertility).

• However, the age structure effect can be positive or negative, depending on the sign of Ac-Ayl

• In most Third World countries, I expect that Ac-Ayl <0, with both public and private transfers going mainly to children and the population age distribution young. – In such countries, higher fertility and more rapid population

growth is costly, reinforces the capital dilution effect, and leads unambiguously to lower life cycle consumption.

– Is Ac-Ayl <0 in the NTA studies we have seen so far? I think so, but I have not seen the average ages calculated.

Golden rule steady states with age structure (4): Interpreting for industrial

countries• In Industrial countries, Ac-Ayl is probably

small or possibly positive because the populations are old, the public sectors transfer heavily to the elderly, and retirement is early. – We need much more evidence from industrial

countries. Currently we just have the US and Japan.

– I look forward to seeing estimates for France, Sweden, Austria, and Slovenia.

Interpretation (cont.)

• If reallocations are strongly upward, so that

is a large enough number, then the effects of capital dilution can be reversed, and life time consumption can rise even if simple per capita consumption falls.

lc y

kA A

c

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

Golden rule steady states with age structure: Limitations to this approach

• Real populations are not stable (steady state)• Real economies are not steady state.• Real economies are not golden rule – generally saving

and capital accumulation are lower for various reasons. • There was no theory here about how or why the

economy reached the golden rule steady state; I just assumed it.

• So now turn to more realistic approaches, and have in mind a changing demographic situation typical of the demographic transition.

• Also introduce theory of savings behavior.

III. Pure life cycle saving, with no transfers to the elderly (1): Basic idea

• Suppose a typical individual has a particular plan for labor supply and earnings over the life cycle, given by yl(x), possibly with a time trend reflecting productivity growth.

• This individual (or married couple) wishes to have a smooth consumption path over the life cycle, taking account of: – consumption needs of their children (private transfers to them)– survival probabilities of all members. – Annuities and life insurance enable individuals to budget for the

average mortality experience at each age. – Expectations about future productivity growth and interest rates.– Each individual maximizes life time consumption, subject to

these constraints and given an intertemporal utility function.

Pure life cycle saving, with no transfers to the elderly (2): Demog transition

• Original theories: Modigliani, Andy Mason added realistic demography.

• Adults accumulate wealth during working years to fund retirement.• After retirement, they dissave. • 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).

• Combined effect of demographic transition is to raise capital per worker, thereby raising productivity and income, thereby raising consumption (second dividend effect).– This comes in addition to any first dividend effects (Ac-Ayl)

Pure life cycle saving, with no transfers to the elderly (3): Interpretation

• In general, there will be less capital than golden rule or than optimal on non-steady state trajectory.

• The demog transition will interact with LCS – First, higher saving rates will lead to lower

consumption– Later, the greater capital intensity that results will lead

to higher consumption.

• The demog transition with LCS may move the economy closer to the optimal capital intensity.

Pure life cycle saving, with no transfers to the elderly (4): Limitations

• LCS theory is controversial– People may not plan as rationally as the theory assumes.– There are complex motives for saving, including precautionary

and to make bequests• In reality, there are also intergenerational transfers which

must influence rational saving plans– Public education reduces need to provide for own children– Familial old age support and public pensions reduce need to

save for old age– If all old age consumption needs were met by transfers, that

motive for saving would be removed entirely (but others might appear – e.g. to prepare for costs of supporting elderly parents).

• Important to study actual reallocation mechanisms to learn what mix of transfers and savings is used.

IV. Mixed Life Cycle Saving, with transfers to the elderly: (1) basic idea

• Theory is exactly as for Pure Life Cycle Saving, but now they take as given all public and private patterns of transfers (from NTA estimates!)– what they themselves can expect to receive in the future, and – what they can expect to have to pay in the future in taxes and

private transfers

• Transfer wealth T is a perfect substitute here for wealth held as Capital, K– Public education reduces future transfers to own children– Transfers to coresident elderly raises need for wealth at time

they move in– Transfers expected from own adult children or public pensions

reduce need to save for own retirement, etc.

Mixed Life Cycle Saving, with transfers to the elderly: (2) Interpretation

• Transfer systems can have a down side: they can reduce saving, capital accumulation, and economic growth

• Countries should carefully balance these costs of transfer systems against their many benefits when deciding about– Encouraging family support systems– Starting PAYGO public pension systems

Mixed Life Cycle Saving, with transfers to the elderly: (3) limitations

• Interaction of private optimization behavior with public and private transfer systems is no doubt complex– E.g. Instead of substituting for private capital, a public

pension may simply be used by elderly to fund a bequest to their adult children (Barro, Ricardian Equivalence)

– Parents may accumulate wealth, and then transfer ownership to their adult children when they move in with them, funding the future transfers they will receive from their children.

• Also all the usual concerns about hyper-rationality, complex motives for saving, etc.

V. Save so as to maintain transfer wealth as a constant fraction of total

pension wealth (fixed τ)• Originally developed by Andy Mason in Mexico City

paper• Presented in detail yesterday by Andy, so I won’t repeat.• Appeal is that it is based firmly on the observed realities

of public and private transfer systems and actual past saving behavior.

• Limitations– Don’t know how τ has changed in the past– Don’t know whether there are systematic sources of change in

the future– Note entirely clear what motivation for saving is in this model.

VI. Social Planner saving optimally to maximize welfare function depending

on level of c(x) profile

• Original idea from Cutler, Poterba, Sheiner and Summers (1990)– They assert that optimal saving problem is

independent of allocation of total consumption across ages, can solve separately, citing Calvo and Obstfeld.

• In Cutler et al, the planner chooses saving and consumption to maximize a social welfare function

Social Planner saving optimally to maximize welfare function depending

on level of c(x) profile

0

0

Max V T

,

te N T t u c T t dt

C tc t

N x t x dx

Max discounted time path of consumption per equivalent adult consumer γ

Social Planner saving to optimize trajectory of c(x)

• Transfers from labor earnings are determined in the model.

• It is not clear who owns the capital, so that component of transfers (0 in golden rule) is indeterminate.

• I believe this approach will be tractable and yield interesting results on the effects of the demographic transition.

• Not yet implemented. • More on this at our January meeting, I hope.

Empirical/Simulation Implementations of these approaches

• I draw on some older studies and some newer ones to give examples of the results of these theoretical approaches when applied to a population resembling Taiwan’s, 1900 to 2050, but without the immigration in the 1940s.

• I will show pure and mixed life cycle saving compared to fixed tau, and look at both savings rates and capital/income ratios.

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 Fixed Tau 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


Actual Capital/Income Ratio

Actual Wealth/Income Ratio

No Transfers

Family Transfers

Tau=0.35

Tau=0.65

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


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


Actual Net Private Savings Rate

Actual Household Savings Rate

No Transfers

Family Transfers

Tau=0.35

Tau=0.65

Discussion of these simulations

• The most realistic specifications, a priori, are life cycle savings with family transfers, and constant tau=.65.

• Comparing these, we note that – under fixed tau, saving rates rise earlier than

under LCS, but don’t rise as high.– Same is true for the capital/income ratio– The timing under fixed tau corresponds better

to actual savings and capital/income ratios

Exploring changing patterns of consumption and labor earnings in the

US, 1888-2002

• The US has a striking consumption profile as shown in the next slide.

• Consumption rises strongly with age, unlike virtually all other countries where it is flat or falls after the early 20s.

• This will have implications for all the kinds of calculations I have discussed before.

• How and when did the US get this way?

Figure 2B. Per Capita Labor Income and Consumption, US (2000)

0

5,000

10,000

15,000

20,000

25,000

30,000

35,000

40,000

45,000

50,000

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90

Age

Source: See Lee, Lee and Mason (2005) for methods and data sources for these estimates.

Historical studies for the US

• For the US, we have some CEX type surveys of special subpopulations at a few dates– 1888: Industrial workers and their children– 1917: Industrial workers and their children– 1935: Urban Families with Native-Born Head– 1960, 1980, 1990, 2002: US Households

• Analyzed (with great care and ingenuity) by Avi Ebenstein and Gretchen Donehouser

More on the historical data

• Profiles have been adjusted to national control totals

• Limitations– These do not include public inkind transfers,

only private. – They do not include the flow of services from

consumer durables and housing. – Because of varying sample limitations, not

strictly comparable. But let’s take a look anyway…

1888 (Industrial Workers and Their Children)

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

0 20 40 60 80

Labor Earnings Current Private Consumption

1917 (Industrial Workers and Their Children)

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

0 20 40 60 80


1935 (Urban Families with Native-Born Head)

0

2000

4000

6000

8000

10000

12000

0 20 40 60 80


1960 (US Households)

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

0 20 40 60 80


Comment on 1888-1960

• Over this 72 year period, consumption has generally been declining with age– At earlier dates, declines following early 20s,

like most other NTA countries– By 1960, decline does not start until after 50

or 60– In the next slide, for 1980, we will see it has

become flat across all ages after age 30 or so


0

5000

10000

15000

20000

25000

30000

35000

0 20 40 60 80



0

5000

10000

15000

20000

25000

30000

35000

40000

0 20 40 60 80


In 1990, we see that consumption is rising until age 60, and then is flat until 80.


0

5000

10000

15000

20000

25000

30000

35000

40000

0 20 40 60 80


This pattern has become even stronger in 2002. Private consumption is about 50% higher in old age than in early 20s.

Now let’s look at average ages of private consumption and earnings

Average Age of Earning and Private Current Consumption (Weighted by Actual National

Population in each year)

25

30

35

40

45

1880 1900 1920 1940 1960 1980 2000

Av age of private cons

Av age of earnings



25

30

35

40

45

1880 1900 1920 1940 1960 1980 2000

Av age of private consumption rises by 12 years!

Av age of earnings



25

30

35

40

45

1880 1900 1920 1940 1960 1980 2000


Av age of earnings also rises by 8 years



25

30

35

40

45

1880 1900 1920 1940 1960 1980 2000


Av age of earnings

Av age of consumption is above earnings in 1980 and 1990, then age of earnings rises more.

Is this due population aging, or to changing age profiles?

• Those were weighted by national population age distribution for each year.

• Now do it again, using the same weights each year – here taken from a survival schedule with life expectancy of 60.

Average Age of Earning and Private Current Consumption (weighted by constant

population age distribution, survival for e0=60)

25

30

35

40

45

1880 1900 1920 1940 1960 1980 2000

YLE Current CF



25

30

35

40

45

1880 1900 1920 1940 1960 1980 2000

YLE Current CF

Changes are now smaller. Av age of cons rises by only 4 years, and earning by 3 years. Less convergence.



25

30

35

40

45

1880 1900 1920 1940 1960 1980 2000

YLE Current CF

Also notice interesting pattern in age of earnings. Strange samples may affect this through 1935, but not after.

CPS data: Average Age of Earnings in the US, 1962-2005, using constant weights (Same constant age

weights as for the CEX)

40

41

42

43

1960 1970 1980 1990 2000

We see the same pattern: Av age1) Falls by about 1.5 years from 1962 to 19802) rises by 3.2 years from 1980 to 2002.

• What I expected– In 1910, median age at retirement for men in US was

74– By 1980 it had fallen to 63. – Since then flat, or very slightly rising.

• What I see here– Ignore early surveys; not comparable, perhaps.– Av age falling from 1960 to 1980, as expected.– But av age rises very strongly from 1980 to 2002,

despite roughly constant age at retirement for men.

• Try comparing to CPS data – larger, better labor.

Average Age of Earnings Over Time, Population Held Constant, CPS and CEX

40

41

42

43

44

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005

Here is a comparison of CEX and CPS. Stronger trends in CEX, but similar in CPS. I am very puzzled and very

Let’s link all this back to population aging and economic growth

• Slowing population growth, and resulting population aging, has two several effects on consumption:– Raises it, due to less capital dilution (-k/c)– May raise or lower it through First Dividend type

effects, depending on initial position in the demographic transition, and on age profiles c(x) and yl(x). (first dividend, sort of)

– Raises it, due to stronger life cycle saving, it effect is not eaten up by transfers (2nd dividend).

In historical US private consumption shifts strongly towards older ages. Why?

• Decline in coresidence? Could go either way.• How much of this is explained by rising private

health spending in old age?• Rise of public sector transfers, private pensions,

and improved financial institutions?• Decline in family solidarity, rise in selfishness?

• Will this happen in other countries? Any signs of it?

In historical US labor earning also shifts towards older ages.

• Can trends in age at retirement be so misleading? • Could this be related to cohort changes in educational

attainment and therefore age specific earnings? – When education is rising quickly, wages should be relatively

higher at younger ages.– When it rises in attainment slow, perhaps the average age rises?

• Something to do with women entering the LF?• This is a new trend, apparently unnoticed by labor

economists.• Maybe the elderly in the US aren’t so lazy and greedy

after all!

Next steps on the historical work

• Estimate the historical public accounts and combine them with the CEX private accounts.

• Use these historical data to calculate the time path of τ in the US, which can inform our development of the Constant τ model.

• Explore further the agreements and disagreements in the predictions of the various theories for how savings and capital accumulation should vary over the demographic transition.

Conclusion

• Through this project, we are all learning a lot, and the pace of progress seems to be accelerating.

• Today I have focused on the complex interplay of demographic change, mechanisms for reallocating income across age (or age and time), and economic growth.

• The glimpse historical trends in the US reinforces what we already know: institutions and private behavior change with economic growth and development

• We need to try to understand the proximate and deeper causes of the shifting age profiles of consumption and labor earnings in the US.

Documents

Transfers, Age Profiles, and Economic Growth: Contributions of NTA Ronald Lee, October 22, 2006 Tokyo