transfers, age profiles, and economic growth: contributions of nta ronald lee, october 22, 2006...
TRANSCRIPT
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
Constant Tau 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
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
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
Labor Earnings Current Private Consumption
1935 (Urban Families with Native-Born Head)
0
2000
4000
6000
8000
10000
12000
0 20 40 60 80
Labor Earnings Current Private Consumption
1960 (US Households)
0
2000
4000
6000
8000
10000
12000
14000
16000
18000
20000
0 20 40 60 80
Labor Earnings Current Private Consumption
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)
0
5000
10000
15000
20000
25000
30000
35000
0 20 40 60 80
Labor Earnings Current Private Consumption
1990 (US Households)
0
5000
10000
15000
20000
25000
30000
35000
40000
0 20 40 60 80
Labor Earnings Current Private Consumption
In 1990, we see that consumption is rising until age 60, and then is flat until 80.
2002 (US Households)
0
5000
10000
15000
20000
25000
30000
35000
40000
0 20 40 60 80
Labor Earnings Current Private Consumption
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
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 consumption rises by 12 years!
Av age of 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 also rises by 8 years
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
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
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
Changes are now smaller. Av age of cons rises by only 4 years, and earning by 3 years. Less convergence.
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
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.