Demography of Aging (1994) / Chapter Skim
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2 The Formal Demography of Population Aging, Transfers, and the Economic Life Cycle
2 The Formal Demography of Population Aging, Transfers, and the Economic Life Cycle
Pages 8-49
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From page 8... ...
Through each channel, resource reallocation takes one of three forms: capital formation, credit transactions, and interage transfers. As fertility and mortality decline, the population age distribution shifts toward older ages, which changes the terms on which these resource flows take place.
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From page 9... ...
Or is the desire to leave bequests responsible (Kotlikoff and Summers, 1981, 1988~? Do public sector pension systems undermine private saving (Feldstein, 19741?
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From page 10... ...
SOME ANALYTICS OF AGING IN STABLE POPULATIONS In a closed population, population aging can occur due either to decline in fertility or to decline in mortality, and these have quite different effects. Nonetheless, the distinction between the effects of changing fertility and changing mortality is not the most helpful one.
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From page 11... ...
Figure 2-1 depicts this decomposition. The Rate of Growth Effect Fertility Change Let us consider more formally the way that fertility and mortality affect the population age distribution through the rate of growth and individual Proportion of Population Age x= b e~nXp~xJ Rate of Growth Effect ~ Fertility Individual Aging Effect ,*
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From page 12... ...
Figure 2-2 plots anlai as calculated from Coale-De-meny model life tables, where i is scaled so that a unit change corresponds to a gain in eO by one year. Figure 2-2 shows how anlai changes, depending on the initial level of life expectancy, for life expectancy from 20 to 80 years.
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From page 13... ...
Figure 2-3 plots the number of person-years lived in each of the three stylized life-cycle stages for different mortality regimes indexed by eO, life expectancy at birth.2 When life expectancy is 2I have used the Coale-Demeny (1983) model life-table system, west female.
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From page 14... ...
The proportion of the life cycle spent in the working years changes little; the proportion spent in childhood declines markedly; and the proportion spent in old age increases dramatically. Recall that life expectancy is the sum over all ages of pax)
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From page 15... ...
when life expectancy changes by 1 year gives us an additive decomposition of that 1 year into gains in person-years lived at the various ages. Figure 2-5 plots dp~x~ldi for various initial levels of life expectancy, showing how these gains in personyears are distributed across the three life-cycle stages, and how that distribution varies from initially low to initially high levels of life expectancy.4 For example, by starting at a life expectancy of 20, if life expectancy were 4We could, for example, think of i as equaling 0.4 of one "level" in the Coale-Demeny model life-table system, since one level corresponds to an increment of 2.5 years of eO.
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From page 16... ...
When initial life expectancy is 75, however, as it is now in the United States, then a gain of 1 year in life expectancy would be distributed as only 0.04 year to children, only 0.34 year to the working ages, and 0.62 year to the elderly. We have now considered the effects of fertility and mortality on the population age distribution through the rate of growth effect and the lifecycle effect.
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From page 17... ...
However, the household framework also presents serious analytic difficulties: the dissolution and reconstitution of households over the life cycle, the presence of multiple adults of different ages in the household, and covariation of household headship propensities with earnings or wealth of individuals. Because of these difficulties with the household framework, I employ the individual accounting framework predominantly here, despite its occasional artificiality in dealing with children.
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From page 18... ...
Consequently this age profile can be used to calculate the aggregate quantity of labor in efficiency units as a weighted sum of the population age distribution. When the population age distribution changes, for example as a result of population aging, this age profile permits assessment of the consequences for aggregate production.
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From page 19... ...
Estimates of average net worth for age groups are available. For our purposes, it is helpful to extend this familiar concept of age-specific net worth or wealth to include transfer debt or transfer wealth for an age group.
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From page 20... ...
Third, under the golden rule assumption, the average person dies with zero wealth, and the constituent age profiles have been adjusted to ensure this. Fourth, it only includes wealth held for purposes of spreading consumption over the life cycle, not wealth held for purposes of leaving bequests or making other transfers.
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From page 21... ...
Consumer Expenditure Survey. specific wealth functions weighted by the entire population age distribution, then we find the aggregate demand for wealth in the population.8 Populations in which child dependency dominates tend to consume, on average, before they produce and therefore have a negative aggregate demand for wealth, that is, a demand for debt.
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From page 22... ...
, are fixed. The economy, which is closed, is on a golden rule steady-state growth path, so that the interest rate, r, equals the population growth rate, n, plus the rate of labor-augmenting technical progress, X, and aggregate consumption equals aggregate labor earnings.
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From page 23... ...
. It is~easily shown that Oc/On = -k across golden rule steady states, so population growth unambiguously reduces per capita consumption in neoclassical growth models of this typed However, this need not be true for life-cycle consumption, C: even while per capita consumption, c, is falling with more rapid growth, the present value of expected life-cycle consumption could be rising or could be falling even more rapidly than c.
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From page 24... ...
be sales of bonds, so that dad, their difference, is net sales of bonds and represents an inflow of funds to the individual's budget. In golden rule steady state, the aggregate value of outstanding government debt must grow at rate n, which is exactly the rate at which the value of the existing bonds at any moment grows.
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From page 25... ...
In a golden rule economy, this must equal income earned by capital, nK: 1 o e p~x~i~x~dx = nK Budget Constraint for Flows We can now gather together all these different flows into and out of the individual budget and relate them one to the other in an aggregate agespecific constraint on the flows: (~=yl~x)
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From page 26... ...
. Life-cycle wealth at age x can be held as capital, transfer wealth (including government debt)
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From page 27... ...
An alternative interpretation can be given in terms of the length of time the average dollar earned is held before being spent. As for transfer wealth, note that because the present value of transfers must integrate to zero over the expected life cycle, transfer wealth at age x is just the negative of the weighted integral of Sup to age x.
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From page 28... ...
I believe that this constellation was actually the typical case in high-mortality traditional societies. Let TF denote transfer wealth arising from familial transfers, TG denote transfer wealth arising from public sector transfers, and TD denote government debt.
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From page 29... ...
Indeed, since the life-cycle demand for wealth is met in good measure by holdings of public sector transfer wealth, Go, which is nearly twice the size of -TF, the comparison of -TF to K seems to me not to be very informative. An alternative comparison would be of -TF and W to K + 1< + TD.
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From page 30... ...
Is it possible that more rapid population growth, while reducing per capita consumption due to capital dilution, might nonetheless lead to higher life-cycle consumption? Here, I consider how the change in the population growth rate affects the present value of life-cycle consumption across golden rule steady states by differentiating the budget constraints developed above.
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From page 31... ...
Consider two stable populations with different total fertility rates of two and three children, and the same life expectancy of 75. Their annual growth rates will differ by 0.0142.
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From page 32... ...
Using the Mueller (1976) age profiles of consumption and earnings for a Third World agricultural population, together with a Coale-Demeny life table for a life expectancy of 20 years, and taking n = 0, we can also calculate Ac - Ay for a hypothetical high-mortality traditional society.
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From page 33... ...
suggested that because more rapid growth lowered life-cycle consumption through capital dilution, but also raised it by reducing the old age dependency burden, there might be an optimal rate of population growth at which the two effects were just offsetting. He called such an optimal rate of population growth for an economy with optimal saving, the "goldenest golden rule path." From the analysis above, we can conclude that when T = 0 on a golden rule path so that individuals willingly hold exactly the amount of capital that is socially optimal in the golden rule sense, then the population growth rate is optimal and the path is the goldenest golden rule.
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From page 34... ...
. Furthermore, the steady-state age distribution based on current rates (replacement level fertility, and a life expectancy of 75 years)
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From page 35... ...
Overall, it appears that on an individual accounting basis, the upward transfers through the public sector roughly offset the downward transfers within the family, so the net effect of slower growth is small. However, strong pressures obviously emerge in federal transfer programs, where households must either pay about $1,000 more per year in taxes ($690 + $350)
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From page 36... ...
o · - ~ in .~ ¢ 3 s° o .~ o 3 o so Ct au JO lo o JO au CQ o 50 au ' V)
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From page 38... ...
For this reason, we can view the age profiles of earning and consumption as functions, at every age, of the general level of mortality, indexed by i as above, just as we have viewed them earlier as functions of n. Mortality Decline, Consumption, and Earning: The Economic Life-Cycle Effect The basic strategy is to differentiate the golden rule life-cycle budget constraint with respect to the mortality level and set the derivative equal to zero.
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From page 39... ...
FIGURE 2-10 Person-years of life gained for 1-year increase in life expectancy versus labor earnings minus consumption, U.S. data, 1985.
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From page 40... ...
Person-years of life gained are predominantly in the working ages, as can be confirmed by reference to Figure 2-5, which shows that at a life expectancy of 20, 69 percent of the gain accrues to the ages 15-64. Mortality Decline and Transfers There is a corresponding equation constraining adjustments to the transfer system, which holds not only for the golden rule case, but for the general case as well: o ~ O .
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From page 41... ...
/di \ \ - - 1 - 0.06 - 0.04 - 0.02 o - -0.02 -- 0.04 100 20 40 60 80 Age (years) FIGURE 2-11 Annual net Social Security benefits and person-years of life gained (for a gain of 1 year in life expectancy)
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From page 42... ...
Finally, the life-cycle effect is relatively small and positive, since mortality decline adds years of life mainly during the working years. The net effect is that mortality decline in both high-mortality and low-mortality settings has similar consequences, but for very different reasons: a 1-year gain in life expectancy entails a 1- percent reduction in the present value of consumption or a corresponding increase in earnings.
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From page 43... ...
assume that the shapes of the age profiles of labor earnings and consumption are fixed, while allowing the levels of the profiles to vary by historical period based on estimated national aggregates for labor income and consumption. This is a partial synthetic cohort assumption.
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From page 44... ...
Most of these extensions would require further methodological research. Methodological Research Although the basic framework is quite general, its implementation here is confined to a doubly special case: first, to steady states, and second, to golden rule economies with r = n.
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From page 45... ...
But there are important related research literatures on why people make familial transfers, on the rationale for public sector transfer systems (Becker and Murphy, 1988) , and on the relations between public sector and familial transfers, as discussed earlier.
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From page 46... ...
This problem will be particularly acute in Third World settings. Second, household headship is typically not distributed randomly across individuals of a given age.
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From page 47... ...
Demeny 1983 Regional Model Life Tables and Stable Populations. New York: Academic Press.
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From page 48... ...
Oxford: Oxford Univer sity Press. In Population age structure, intergenerational transfers, and wealth: A new approach, press b with applications to the United States.
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From page 49... ...
Rodgers, eds., Economics of Changing Age Distributions in Developed Countries. Oxford: Clarendon Press.
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