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
•
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•
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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.
  nx
C   e l  x  c  x  dx
0
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)
d ln  C 
dn
k
 Ac  Ayl 
c
NTA average ages of
consumption and
earning.
Golden rule steady states with age
structure (2): An Elegant Result
Proportional change in life time
• This result is due to
consumption when r changes.
Arthur and McNicoll
• The effect of a small
d ln C
k
variation in n on C is

A

A

c
y
l
found by differentiating
dn
c
across golden rule steady
states, and is:
• The effect on
consumption depends on
the balance of the capital
NTA average ages of
dilution effect and an
consumption and
intergenerational transfer
earning.
effect (actually, all
reallocations combined)
 
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
k
Ac  Ayl 
c
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.
Interpretation (cont.)
• After manipulation, the expression
k
Ac  Ayl 
c
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.
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 hyperrationality, 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
Max V  T 
  e   t N T  t  u  c T  t   dt

0
c t  
C t 


0
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
6
5
LC Model Results
Ratio
4
3
No Transfers
2
1
0
1900
1950
2000
2050
6
Simulated Capital/Income Ratio Under Life Cycle Savings for Taiwan
Demography, 1900 to 2050, Assuming NTA Style Familial Transfers to
Elderly with Co-Residence
5
LC Model Results
Ratio
4
3
No Transfers
2
1
0
1900
Family Transfers
1950
2000
2050
6
Simulated Capital/Income Ratio Under Fixed Tau
Model (.35, .65) Compared to Life Cycle Savings for
Taiwan Demography, 1900 to 2050
LC Model Results
Constant Tau Results
5
Ratio
4
3
Tau=0.35
No Transfers
2
1
0
1900
Tau=0.65
Family Transfers
1950
2000
2050
6
5
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
LC Model Results
Constant Tau Results
Actual Capital/Income Ratio
Actual Wealth/Income Ratio
4
Ratio
Tau=0.35
3
No Transfers
2
1
Tau=0.65
Family Transfers
0
1900
1950
2000
2050
Simulated Saving Rate Under Life Cycle Savings for Taiwan
Demography, 1900 to 2050, Assuming No Familial Transfers to Elderly
30
No Transfers
25
LC Model Results
Percentage
20
15
10
5
0
1900
-5
1950
2000
2050
30
Simulated Savings Rate Under Life Cycle Savings for Taiwan
Demography, 1900 to 2050, with NTA Style Transfers to Elderly and
Coresidence
No Transfers
25
LC Model Results
Percentage
20
Family
Transfers
15
10
5
0
1900
-5
1950
2000
2050
Simulated Savings Rate Under Fixed Tau Model (.35, .65) Compared
to Life Cycle Savings for Taiwan Demography, 1900 to 2050
30
No Transfers
25
LC Model Results
Constant Tau Results
Percentage
20
Family
Transfers
15
10
Tau=0.35
5
Tau=0.65
0
1900
-5
1950
2000
2050
Simulated Savings Rate Under Fixed Tau Model (.35, .65) Compared
to Life Cycle Savings for Taiwan Demography, 1900 to 2050
30
25
LC Model Results
Constant Tau Results
Actual Net Private Savings Rate
Actual Household Savings Rate
Percentage
20
No Transfers
Family
Transfers
15
10
Tau=0.35
5
Tau=0.65
0
1900
-5
1950
2000
2050
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?
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)
5000
4500
4000
3500
3000
2500
2000
1500
1000
500
0
0
20
Labor Earnings
40
60
Current Private Consumption
80
1917 (Industrial Workers and Their Children)
9000
8000
7000
6000
5000
4000
3000
2000
1000
0
0
20
Labor Earnings
40
60
Current Private Consumption
80
1935 (Urban Fam ilies w ith Native-Born Head)
12000
10000
8000
6000
4000
2000
0
0
20
Labor Earnings
40
60
Current Private Consumption
80
1960 (US Households)
20000
18000
16000
14000
12000
10000
8000
6000
4000
2000
0
0
20
Labor Earnings
40
60
Current Private Consumption
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
1980 (US Households)
35000
30000
25000
20000
15000
10000
5000
0
0
20
Labor Earnings
40
60
Current Private Consumption
80
1990 (US Households)
40000
35000
In 1990, we see that
consumption is rising
until age 60, and then is
flat until 80.
30000
25000
20000
15000
10000
5000
0
0
20
Labor Earnings
40
60
Current Private Consumption
80
2002 (US Households)
40000
35000
This pattern has become
even stronger in 2002.
Private consumption is
about 50% higher in old
age than in early 20s.
30000
25000
20000
15000
10000
5000
0
0
20
Labor Earnings
40
60
Current Private Consumption
80
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)
45
40
35
Av age of earnings
Av age of private cons
30
25
1880 1900 1920 1940 1960 1980 2000
Average Age of Earning and
Private Current Consumption
(Weighted by Actual National
Population in each year)
45
40
35
30
Av age of earnings
Av age of private
consumption rises by 12
years!
25
1880 1900 1920 1940 1960 1980 2000
Average Age of Earning and
Private Current Consumption
(Weighted by Actual National
Population in each year)
45
Av age of earnings
also rises by 8
years
40
35
Av age of private cons
30
25
1880 1900 1920 1940 1960 1980 2000
Average Age of Earning and
Private Current Consumption
(Weighted by Actual National
Population in each year)
Av age of consumption is above earnings in 1980
and 1990, then age of earnings rises more.
45
40
35
Av age of earnings
Av age of private cons
30
25
1880 1900 1920 1940 1960 1980 2000
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
Consum ption (w eighted by constant
population age distribution, survival for
e0=60)
45
40
35
30
25
1880 1900
1920 1940 1960
YLE
1980 2000
Current CF
Average Age of Earning and Private Current
Consum ption (w eighted by constant
population age distribution, survival for
e0=60)
45
40
35
30
Changes are now smaller. Av age of cons
rises by only 4 years, and earning by 3
years. Less convergence.
25
1880 1900
1920 1940 1960
YLE
1980 2000
Current CF
Average Age of Earning and Private Current
Consum ption (w eighted by constant
population age distribution, survival for
e0=60)
45
40
35
30
Also notice interesting pattern in age of earnings.
Strange samples may affect this through 1935, but
not after.
25
1880 1900
1920 1940 1960
YLE
1980 2000
Current CF
CPS data: Average Age of Earnings in the US, 19622005, using constant weights (Same constant age
weights as for the CEX)
43
42
We see the same pattern: Av age
1) Falls by about 1.5 years from 1962
to 1980
2) rises by 3.2 years from 1980 to
2002.
41
40
1960
1970
1980
1990
2000
• 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
44
43
Here is a comparison of CEX and
CPS. Stronger trends in CEX, but
similar in CPS.
I am very puzzled and very
42
41
40
1960
1965
1970
1975
1980
1985
1990
1995
2000
2005
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.