why countries become wealthy: the effects of adult longevity on saving

World Development Vol. 35, No. 1, pp. 1–23, 2007� 2006 Elsevier Ltd. All rights reserved

0305-750X/$ - see front matter

doi:10.1016/j.worlddev.2006.09.002www.elsevier.com/locate/worlddev

Why Countries Become Wealthy: The Effects of

Adult Longevity on Saving

TOMOKO KINUGASAKobe University, Japan

and

ANDREW MASON *

University of Hawaii at Manoa, Honolulu, HI, USA

Summary. — We analyze steady-state and out-of-steady-state effects of the transition in adult lon-gevity on the national saving rate using historical data and international panel data. The rise inadult life expectancy has a large and statistically significant effect on aggregate saving. The effectshave been especially pronounced in East Asia because its mortality transition was very rapid. Gainsin life expectancy are much more important than declines in child dependency. Population agingmay not lead to lower saving rates in the future if life expectancy and the duration of retirementcontinue to increase.
� 2006 Elsevier Ltd. All rights reserved.
Key words — saving, investment, mortality, health, models, East Asia

* Mason’s research was supported by NIA R01AG-

025488. The authors appreciate useful suggestions from

Byron Gangnes, Sumner La Croix, Sang-Hyop Lee, Ilan

Noy, Robert Retherford, Xiaojun Wang, and three an-

onymous referees. We also thank Ann Takayesu for her

help with preparation of the manuscript.

1. INTRODUCTION

One of the most salient features of moderneconomic development is the increase in wealthand capital. In the United States, for example,the gross non-residential capital stock grew at4.1% per annum as compared with annualGDP growth of 3.6% during 1820–1992. Theexperience of the United Kingdom was quitesimilar, while in Japan over a shorter period,1890–1992, the annual rate of growth of capitalexceeded the annual rate of growth of GDP by1.4%. The ratio of the gross non-residentialcapital stock to GDP increased more thanfourfold, from 0.71 to 3.02 (Maddison, 1995).The extraordinary growth in wealth and capitalwas repeated, in a more condensed form, in theNewly Industrializing Economies. High rates ofsaving and investment in South Korea, Taiwan,Singapore, and in several other Asian countrieshave led to rapid capital deepening.

Why did this occur? The demand sideundoubtedly played an important role. Techno-logical innovation led to new and better equip-ment and machinery. Structural change led to

1

industrialization and the growth of the manu-facturing and service sectors with accompany-ing investment. The possibility explored inthis study, however, is that the modern rise inwealth was driven in large part by an importantsupply side factor—the increase in adult lifeexpectancy.

The proportion of adult life lived after age 60began to increase steadily in the West in the late19th century. In other parts of the world in-creases began much later—in the middle ofthe 20th century. Retirement emerged as a sig-nificant feature of the lifecycle creating a pow-erful saving incentive. Institutional responses,the emergence of funded employment-basedpension plans, the rise of the commercialfinancial service sector, the creation of tax

2 WORLD DEVELOPMENT

incentives, and, in some countries, the estab-lishment of funded public retirement systemsreinforced the effects of increased longevity.Other responses, particularly the creation oftransfer-based public pension programs inLatin America, Europe, and to a lesser extentin Japan and in the United States, undoubtedlyundermined the incentive effects of a longer lifespan.

That rising life expectancy leads to highersaving is not a new idea. Yaari’s (1965) seminalwork established the micro-level theoreticalfoundation. Since then other scholars have ex-plored the aggregate effects using steady-statemodels and simulation analysis (Lee et al.,2003). Previous empirical work supports theexistence of an important link between savingand life expectancy (Bloom et al., 2003;Borsch-Supan, 1996; Davies, 1981; Kageyama,2003; Kuehlwein, 1993; Leung, 1994; Schieber& Shoven, 1996; Yaari, 1965; Zilcha & Fried-man, 1985).

The theoretical analysis described briefly inSection 2 employs an overlapping generationsmodel which extends previous work to a dy-namic context. A unique implication of the mod-el is that the aggregate saving rate is influencedby both the level and the rate of change of adultlife expectancy. Given the current level of mor-tality, countries experiencing rapid mortalitytransitions will have higher saving rates. Theunderlying logic behind this result is straightfor-ward. If a rapid mortality transition country isplaying catch-up, the wealth required to supporta longer retirement must be accumulated over ashorter period of time. Thus, saving rates mustbe elevated during the catch-up period.

The empirical analysis relies on two differentapproaches. Section 3 takes a historical perspec-tive by looking at data for seven countries forwhich we can track saving and mortality trendsover all or a substantial part of the entire demo-graphic transition. In the sub-group of Westerncountries, adult life expectancy changed veryslowly or not at all until the middle or end ofthe 19th century. Thereafter, life expectancychanged at a pace that was remarkably constantand varied little from one country to the next.The sub-group of Asian countries began theirmortality transitions later, went through acatch-up period when adult longevity increasedrapidly, followed by a period of steady increaseat a rate similar to that found in the West.

The difference in the demographic transitionsbetween the West and East Asia offers a usefulopportunity to compare the implications of our

theoretical model with the experiences of thesetwo groups of countries. Some of the idiosyn-cratic features of the saving trends are notexplained by our model, but there is a broadconsistency. The increase in adult mortalitywas accompanied by a rise in aggregate savingrates in most countries. Rapid mortality transi-tion was clearly accompanied by elevated sav-ing rates.

In Section 4, we estimate the saving modelusing aggregate cross-national data. The evi-dence is consistent and robust in its supportof the hypothesis that an increase in old-agesurvival leads to higher saving rates. In a sub-sample consisting of Western and East Asiancountries, the rate of increase in old-age sur-vival also has a positive effect on saving. Inother parts of the developing world, however,we do not find evidence that the rate of changein old-age survival has an effect on saving. Whydifferent patterns persist is an issue requiringfurther exploration and some possibilities arediscussed below.

Two additional features of the analysis areimportant. First, several recent studies con-clude that changes in age structure, especiallythe decline in the youth dependency ratio, ac-counted for high saving rates especially in EastAsia (Higgins & Williamson, 1997; Kelley &Schmidt, 1996). Simulation studies (Lee et al.,2000, 2001a, 2001b) and empirical work basedon household survey data (Deaton & Paxson,2000) ascribe a substantially less important rolefor age structure. The empirical analysis pre-sented here offers some reconciliation of theseviews. Once we control for adult life expectancyand its rate of change, the youth dependencyratio has a smaller effect than previously esti-mated. The decline in youth dependency ac-counts for about one-quarter of the increasein saving rates in East Asia, while changes inadult survival account for about three-quartersof the increase.

Second, while some studies conclude thatpopulation aging will lead to substantial de-clines in aggregate saving rates, we do not findthis to be the case. So long as adult survivalcontinues to rise—as it has for many dec-ades—population aging will not drive savingrates lower.

2. THE THEORY 1

Changes in adult survival influence aggregatesaving in two ways in the lifecycle model

WHY COUNTRIES BECOME WEALTHY: THE EFFECTS OF ADULT LONGEVITY ON SAVING 3

employed here. First, there is a behavioraleffect. The expected duration of retirement risesas the survival rate increases. Thus, individualswill consume less and save more during theirworking years in order to support more ex-pected years of consumption and greater dis-saving during retirement. Second, there is acompositional effect as increases in the adultsurvival rate lead to an increase in the shareof retirees in the adult population. Given thatretirees are saving at a lower rate than workers,the compositional effect of an increase in adultsurvival is to reduce aggregate saving.

The net effect on saving is considered in stea-dy-state and in dynamic settings. We sum-marize the dynamics in two ways: first, byconsidering the effect of a one-time increase insurvival and, second, by considering the effectof continuing increases in survival. Consideringthese alternatives brings a clearer understand-ing of how the mortality transition—as it isactually evolving—will influence aggregatesaving rates.

The behavioral and compositional effects ofadult mortality are analyzed using a two-periodoverlapping generations model. The advantageof this approach is its relative simplicity. A dis-advantage is its neglect of another importantdemographic change—the change in youthdependency driven by trends in fertility andchild mortality. Previous theoretical work hasalready explored the effects of the number ofchildren on saving in a continuous-age, steady-state framework (Mason, 1987) and in a dy-namic OLG framework (Higgins, 1994). Theempirical analysis presented below considersthe effects of youth dependency relying on theHiggins OLG model. This allows a simplerand more focused theoretical analysis here onchanges in adult mortality.

Consider a population consisting of two gen-erations of adults. Each person lives for up totwo periods—the first period as a working,prime-age adult and the second period as a re-tiree. All individuals survive their working per-iod, and qt survive to the end of their retirementperiod. The remaining members of the popula-tion (1 � qt) die at the end of the first period oflife. In the OLG framework qt is the probabilityof reaching retirement age, the expected yearslived during retirement, and the ratio of retire-ment years to working years for the averagemember of the population. 2 Individuals cannotforesee whether they will survive, but theyknow the value of qt for the population. Cost-less annuities are available so that individuals

protect themselves against longevity risk bypurchasing an annuity. Individuals know theinterest rate that the annuity will pay.

The consumer’s optimization problem is tomaximize lifetime utility, assuming constant

relative risk aversion, V t ¼c1�h

1;t

1�h þ dqtc1�h

2;tþ1

1�h , given

the lifetime budget constraint: wtAt ¼ c1;tþqt

1þrtþ1c2;tþ1; c1,t is consumption while a prime-

age adult and c2,t+1 is consumption whileelderly; d is the discount factor, defined asd = 1/(1 + q), where q is the discount rate; 1/h is the intertemporal elasticity of substitution;rt+1 is the interest rate; At is labor-augmentingtechnology; and wt is the wage per unit of effec-tive labor.

Kinugasa (2004) shows that the per capitasavings of prime-age adults and retirees are

s1;t ¼ WtAtwt ¼qtd

1hAtwt

qtd1h þ ð1þ rtþ1Þ

h�1h

;

s2;t ¼ �s1;t�1 ¼ �Wt�1At�1wt�1

¼ qt�1d1hAt�1wt�1

qt�1d1h þ ð1þ rtÞ

h�1h

;

ð1Þ

where Wt is the share in wage income of savingby prime-age adults. An increase in the adultsurvival rate has an unambiguous positive effecton Wt and, hence, on per capita saving by prime-age adults. An increase in the adult survival ratehas an unambiguous negative effect on per capi-ta saving by retirees. The response of the com-bined saving of workers and retirees to changesin survival depends on additional features ofthe macro-economy to which we now turn.

Gross domestic product (Yt) is produced bya Cobb–Douglas production function withlabor-augmenting technological growth, thatis, Y t ¼ K/

t L1�/t , where / is the share of capital

in GDP, 0 < / < 1. Lt = AtN1,t is the aggre-gate labor supply measured in efficiency units.N1,t is the population of prime-age adults andAt is the technology index. The growth rate ofthe population of prime-age adults from timet � 1 to time t is nt � 1 and, hence, N1,t =ntN1,t�1. The technological growth rate fromtime t � 1 to time t is gt � 1. Hence, the rela-tionship between the total lifetime labor incomeof prime-age adults and pensioners is given bywt�1At�1N1,t�1 = wtAtN1,t/gtnt. Using lowercase letters to represent quantities per unit ofeffective worker, output per effective worker isyt ¼ k/

t and the capital–output ratio is k/�1t .

4 WORLD DEVELOPMENT

The depreciation rate (n) is assumed to be con-stant; hence, depreciation as a share of GDP isnk/�1

t .Total gross national saving is the sum of the

saving of adults (S1,t), the saving of the elderly(S2,t) and depreciation (nKt). Dividing by Yt

yields the gross national saving rate at time t:

St

Y t¼ ð1� /Þ Wðqt; ktÞ �Wðqt�1; kt�1Þ

1

gtnt

� �

þ nk1�/t : ð2Þ

The term (1 � /) is the share of labor incomein GNP, Wt(qt, kt) is saving by current workersas a share of current labor income,�Wðqt�1; kt�1Þ 1

gtntis saving by current retirees

as a share of current labor income, and nk1�/t

is depreciation as a share of current GNP.

(a) Steady-state rate of growth effects

The steady-state gross national saving rate is

SY

� ��¼ ð1� /ÞWðq�; k�Þ gn� 1

gn

� �þ nk�1�/;

ð3Þwhere the * superscript denotes equilibriumvalues. Standard and well-known implicationsof the lifecycle model (Modigliani & Brumberg,1954) follow directly from Eqn. (3). First, thenet saving rate is zero if the economy is notgrowing (gn = 1). If the economy is not grow-ing, the lifetime earnings of retirees and work-ers are equal and, hence, the dis-saving byretirees will exactly balance the saving by work-ers. Second, the partial effect of an increase inthe GDP growth rate is equal to the mean ageof earning less the mean age of consumption,as in the variable rate-of-growth model (Fry& Mason, 1982; Mason 1981, 1988). As shownin Kinugasa, w is the difference between themean ages of consumption and earning. 3

An important issue to clarify at this point isthat the effect of the rate of growth of the pop-ulation of children, not included in the theoret-ical model, will be very different than the rate ofgrowth of the population of prime-age adults.If the child population grows rapidly, then theworkers will be supporting many childrenand, hence, saving will be depressed. The effectsof child dependency are adequately addressedin the current literature (Higgins, 1994; Mason,1988). The effects of child dependency are dis-cussed more thoroughly and are estimatedbelow.

(b) The effect of adult survival in steady stateand in transition

The effect of changes in adult survival on sav-ing depends on whether or not the capital–labor ratio and interest rates are endogenous.In a small open economy, the equilibrium cap-ital–labor ratio and interest rates are deter-mined by global economic conditions. A risein domestic saving—and factors that influencethe saving rate—will have no effect on domesticinvestment nor on domestic interest rates. In aclosed economy, however, saving and invest-ment are equal and the rate of interest is endo-genously determined by the interplay of thesupply of capital by households and the de-mand for capital by firms. The effect on savingof an increase in adult survival in each of theseenvironments is considered in turn.

(i) Saving in a small open economyThe effect of an increase in adult survival on

the steady-state saving rate in a small openeconomy depends on the rate of growth of in-come. If the economy is growing, gn > 1, thesteady-state saving rate rises with adult sur-vival. In an economy with negative economicgrowth, the steady-state saving rate declineswith an increase in adult survival. The steady-state saving rate given by Eqn. (3) holds withk* exogenously determined. An increase inadult survival leads to a rise in the share oflabor income saved by prime-age adults, thatis, oW*/oq* > 0, but the dis-saving by retireesincreases, as well. In a growing economy, theincrease in saving by prime-age adults domi-nates the decline in saving by retirees and theaggregate saving rate rises with adult survival.In a declining economy, the decline in savingby retirees dominates and the aggregate savingrate declines as adult survival rises.

The response of saving rates in a dynamiccontext is more complex. The current savingrate is increasing at the rate of GDP growthduring the previous period, gt, because in aneconomy with a rapid aggregate economicgrowth during the preceding period the size ofthe current workers, measured in terms of totallifetime earnings, will be large relative to thecurrent retirees. The effect of the rate of eco-nomic growth will depend on adult survivalor, to be more precise, on the expected durationof retirement of those who are currently work-ing. In a dynamic context, however, adult sur-vival is also changing. Consider a small openeconomy that is in equilibrium, but experiences


an increase in the survival rate in period t.Prime-age adults respond by increasing theirsaving rates, while saving by retirees is unaf-fected. The aggregate saving rate must rise inperiod t. The transitory increase in saving isindependent of the rate of economic growthgn. In period t + 1, dis-saving by retirees risesand the aggregate saving rate declines. In theabsence of further changes in survival, a newequilibrium saving rate is established in periodt + 1. As shown above, the new equilibrium de-pends on the rate of economic growth. In agrowing economy, it will be higher than thesaving rate in period t � 1, but lower than thesaving rate in period t.

(ii) Saving in a closed economyIn a closed economy, an increase in the saving

rate leads to greater investment, capital deepen-ing, more rapid growth in wages, and a declinein the interest rate. The supply of capital followsdirectly from the saving model presented above,because the capital stock in period t + 1 is equalto total saving by prime-age adults in period t.Expressed as capital per effective worker, thesupply of capital in year t + 1 depends on thewage per effective worker in year t, the shareof that wage that is saved by prime-age adults,and the rate of growth:

ktþ1 ¼wðrtþ1; qtÞwtðktÞ

gtþ1ntþ1

¼ Stðrtþ1?

;wtþðktÞ; qt

þÞ;

ð4Þ

r

D

S

k* k2

r*

r2

r3

S*

S1S

Figure 1. Demand and supply o

where St is the supply function of capital. Theeffect of the interest rate on the supply of cap-ital is ambiguous. 4 The wage is equal to themarginal product of an effective worker, wt =f(kt) � ktf

0(kt), and is increasing in capital pereffective worker. An increase in the survivalrate leads to an increase in the share of labor in-come saved by prime-age adults and, hence,capital per effective worker and the supply ofcapital.

The demand for capital, D, is governed bythe marginal condition that the cost of capitalequals the net return, that is, rt+1 = f 0(kt+1) �n. That f 00 < 0 implies that the demand curveis downward sloping. The demand for capitalis independent of the survival rate.

The effect of an increase in the survival ratefrom q* to q 0 in period 1 is traced in Figure 1.The demand curve, DD, is unaffected. Workersin period 1 increase their saving because in per-iod 2 they expect to live longer and, perhaps,because they expect lower interest rates todepress the rate of return on annuities. Thus,the supply curve, SS, shifts to the right in per-iod 2. This leads to a rise in capital per workerand wages for the new generation of workers.As a result, the saving function shifts furtherto the right, in part, because of the expectedfurther decline in interest rates. The processcontinues until a new equilibrium is estab-lished. 5 Unless the decline in interest ratesleads to a substantial reduction in saving byprime-age adults—a possibility not born out

kt+1

* * * *( , , )r w q

*1 2( , , ')S r w q 2 3 1( , , ')S r w q

k3

2

D

f capital in a closed economy.

6 WORLD DEVELOPMENT

by empirical research—an increase in adultsurvival in period t leads to capital deepening.

The effect of survival on aggregate saving isreadily inferred from its effect on capital pereffective worker. In a closed economy, savingis equal to investment. Gross national savingis the sum of changes in asset holdings ofprime-age adults and the elderly and depreci-ation, so that St = S1,t + S2,t + nKt = S1,t �S1,t�1 + nKt. Gross investment is given byIt = Kt+1 � (1 � n)Kt. The national saving rateis

St

Y t¼ gtþ1ntþ1

ktþ1

kt� 1þ n

� �k1�/

t : ð5Þ

In steady state, the relationship simplifies to

SY

� ��¼ ðgn� 1þ nÞk�1�/: ð6Þ

From inspection of Eqn. (6) an increase in theequilibrium capital–labor ratio and, hence, thecapital–output ratio (k1�/), leads to an increasein the equilibrium net saving rate ((gn � 1)k*1�/) in a growing economy. The gross savingrate increases if the depreciation rate plus therate of growth is positive.

During transition, as is clear from Eqn. (5),the saving rate is elevated above the equilib-rium level depending on the rate of capitaldeepening (kt+1/kt). As with the open economycase, a one-shot increase in the survival rate

0.14

0.15

0.16

0.17

0.18

t-2 t-1 t

Figure 2. The effect of an increas

leads to a large increase in the saving rate forone generation followed by a decline in the sav-ing rate to a steady-state level as a new equilib-rium is established. In an economy withpositive labor-augmenting growth, the net sav-ing rate will be higher than in the initial equilib-rium, but lower than during the transitionperiod.

(c) Simulation results

Figure 2 compares the simulated saving ratesin a small open economy and a closed economyproduced by an increase in adult survival from0.4 in year t � 1 to 0.5 in year t. 6 The initialimpact is large in both cases. The response issomewhat muted in the closed economy be-cause the declines in interest rates lead to re-duced saving rates among prime-age adults. Anew equilibrium is established in period t + 1in the open economy, but the adjustment ismore gradual in the closed economy as de-scribed above. The equilibrium saving rate inthe closed economy is greater than in the openeconomy, because of capital deepening in theclosed economy. Higher net saving is requiredto sustain a higher capital–output ratio. Great-er depreciation leads to an increase in grosssaving beyond the increase in net saving.

One would not be likely to observe the simu-lated saving paths shown in Figure 2. Adultsurvival rates trend upward at a relatively

t+1 t+2 t+3

S/Y=I/Y, Closed S/Y Open I/Y, Open

e in the survival rate at time t.

0.14

0.15

0.16

0.17

0.18

0.19

0.20

0.21

0.22

t-2 t-1 t t+1 t+2 t+3

S/Y=I/Y, Closed S/Y Open I/Y, Open

Figure 3. The effect of a continuing increase in the survival rate.


constant rate in many countries—as we willshow below. Figure 3 presents simulated savingrates assuming that adult survival increases by0.1 per period starting from 0.4 in year t � 1.Otherwise, parameters are identical to thoseemployed in the simulations presented in Fig-ure 2. The onset of adult mortality decline leadsto a secular rise in saving rates that continuesas long as adult survival rates continue to in-crease. Saving rates appear to be very nearlylinear in adult survival after period t � 1 inthe open economy case and after period t inthe closed economy case.

3. HISTORICAL PERSPECTIVES ONOLD-AGE SURVIVAL AND SAVING

The modern mortality transition began in theWest. Early gains were concentrated at youngages, but by 1900 old-age survival rates wererising steadily in Sweden, the United Kingdom,Italy, and the United States—the four Westerncountries we examine below. The mortalitytransition began much later outside of theWest. The three Asian populations for whichwe have relatively complete historical data—Japan, Taiwan, and India—did not experiencesignificant gains in old-age survival until themiddle of the 20th century. When the mortalitytransition began, however, it was very rapid asthese Asian countries caught or, in the case ofJapan, surpassed the West.

Historical mortality transitions are of greatinterest here because of their implications forlong-run trends in national saving rates. Previ-ous empirical research—and the analysis pre-sented in Section 4—relies on data that cover arelatively small portion of the mortality transi-tion. This is unfortunate given the long-term nat-ure of the processes under consideration. Thedistinctive experiences of Asia and the West,however, provide an opportunity to assesslong-term effects of mortality change on saving.

We begin with an examination of the mortal-ity transitions of seven countries. The mostwidely available measures, life expectancy atbirth and the crude death rate, are inappropri-ate because, early in the mortality transition,they are driven by changes in infant and childmortality. Whether the resultant increase inchild dependency observed in many countriesaffected the accumulation of wealth is an issueconsidered below. The emphasis at this point,however, is on adult mortality.

The measure of mortality used here and inthe world panel analysis is the expected yearslived during old-age relative to the expectedyears lived during the working years. This mea-sures in a very direct fashion how mortalitydecline influences the expected duration ofretirement relative to the expected number ofworking years. It directly measures the influ-ence of mortality on population age structure.It also reflects mortality change that occursat any adult age. Ages 30 and 60 are used to

8 WORLD DEVELOPMENT

delineate the working ages (30–59) and the oldages (60+). This choice may be puzzling tosome, but it is based on recent empirical esti-mates of the economic lifecycle in a small groupof developing and industrialized countries thatfind that individuals do not begin to produceas much as they consume until their late 20sand that by their late 50s or early 60s they areconsuming more than they are producing (Leeet al., 2005). Thus, individuals are only begin-ning to save toward retirement in their 30sand later and are beginning to rely on accumu-lated wealth beginning at about age 60. 7

In six of the countries—all but India—we areable to construct an old-age survival index (q),also used in Section 4. 8 The old-age survivalindex is the expected years lived after age 60per expected year lived between the ages of 30and 60 given the age-specific death rates duringthe year of observation. The value of q rangesfrom less than 0.2 expected years lived afterage 60 per expected year lived between the agesof 30 and 60 in Taiwan circa 1900 to close to0.8 in current day Japan.

Historical data for Sweden allow us to tracethe transition in old-age survival from themid-18th century. The 250 years of data canbe described remarkably well as consisting ofa pre-transition period during which old-agesurvival was virtually stagnant and a transitionperiod during which old-age survival increasedsteadily. In 1751, adults could expect to liveabout one-third of a year after age 60 for everyyear lived between the ages of 30 and 60. Dur-ing 1761–1876, the old-age survival index in-creased at an annual rate of only 0.0006.During 1876–2001, the old-age survival indexincreased four times as rapidly—at an annualrate of 0.0026. Allowing for three short-runmortality crises—famine in 1772–73, the Fin-nish War in 1808–09, and the Spanish flu epi-demic of 1918—a piecewise linear regressionwith one break-point at 1876 explains 93% ofthe variance in adult mortality (Table 1). 9

The old-age survival transitions of the threeother Western countries can be characterizedin an equally simple fashion. For the UnitedKingdom, old-age survival increased at an an-nual rate of 0.0009 during 1841–1900 and at arate of 0.0024 during 1900–98, with 96% ofthe variance explained by the piecewise linearmodel with a single break point. The availabledata for Italy and the United States do not ex-tend into the pre-transition period. Old-age sur-vival in Italy from 1872 to 2000 and in theUnited States from 1900 to 2001 can be ex-

plained as consisting of a single transition per-iod with old-age survival increasing by 0.0029years per year in Italy and by 0.0033 yearsper year in the United States.

That the gains in these four countries havebeen remarkably constant during the 20th cen-tury has important—and unfortunate—impli-cations for testing the dynamic saving model.In the absence of time series variation in therate at which old-age survival is increasing,estimates of the effect of the rate of change inold-age survival will depend entirely on cross-country differences. Even though there aresmall year-to-year fluctuations and instancesof more significant fluctuations, for example,the flu epidemic of 1918, short-term fluctua-tions may have little or no effect on long-termexpectations. In our model, it is long-termexpectations that matter. To add to the difficul-ties, the cross-national differences among thefour Western countries are quite modest. Thehistorical experience of the West is useful, how-ever, to the extent that we explore the effect onsaving of the shift from pre-transition to transi-tion. We return to this issue below.

The mortality experience in East Asia is quitedistinctive judging from the relatively completedata for Japan and Taiwan. Their pre-transi-tion periods lasted until much later, but werefollowed by a significant catch-up period dur-ing which old-age survival increased quite rap-idly. Having closed the mortality gap with theWest, the gains in adult mortality have slowed.Recent mortality gains in Taiwan are similar tothose found in the West while Japan continuesto experience larger gains in old-age survival(Table 1).

Indian life expectancy at age 30 also in-creased very gradually until 1951. For the next40 years substantial gains were achieved. The1990s saw a marked slow-down. The patternis similar to that found in Japan and Taiwanalthough direct comparison is not possible.

To what extent are the saving trends in theseseven countries consistent with the predictionsof our saving model? Three implications ofthe model can be examined. First, prior to thetransition in old-age survival, saving rateswould have been relatively low. Second, con-stant increases in old-age survival during thetransition would have produced relatively con-stant increases in saving rates. Third, EastAsian countries would have experienced rela-tively elevated saving rates during their periodof rapid transition. Of course, these patternswould consistently emerge only if the trends

Table 1. Structural changes of the old-age survival index

Sweden United Kingdom Italy United States Japan Taiwan India1751–2002 1841–1998 1872–2000 1900–2001 1891–2001 1906–2002 1881–1997

t1 1876 1900 1947 1940 1951t2 1989 1983 1989

t 0.0006*** 0.0009*** 0.0029*** 0.0033*** 0.0010*** 0.0004 0.0392(0.0001) (0.0001) (0.0001) (0.0002) (0.0002) (0.0010) (0.0232)

(t � t1)d1 0.002*** 0.0024*** 0.0065*** 0.0056*** 0.3457***

(0.0001) (0.0001) (0.0004) (0.0011) (0.0599)

(t � t2)d2 �0.0014*** �0.0024*** �0.3075*

(0.0007) (0.0003) (0.1568)

Dm1773 �0.0231*** 0.0004*** �0.1231***

(0.0027) (0.0023)

Dm1808 �0.1625***

(0.0063)

Dm1918 �0.096***

(0.0040)

Constant 0.2869*** 0.3205*** 0.2518*** 0.2245*** 0.3250*** 0.2860*** 22.7955***

(0.0080) (0.0049) (0.0053) (0.0195) (0.0104) (0.0322) (0.8454)

Adjusted R2 0.9251 0.9587 0.9471 0.9585 0.9872 0.9944 0.9628

N 252 158 129 48 59 43 20

P-value 0.0000 0.0000 0.0000 0.0000 0.0000

DW 0.5765 0.7026 0.397 0.0958 0.3897 0.3651 0.0338

Note: Dependent variables are adult survival index except for India. The dependent variable for India is lifeexpectancy at age 30. The equation qt = b0 + b1t + b2d1(t � t1) + b3d2(t � t2) + et is estimated, where d1 = 1 ift P t1 and 0 otherwise, and d2 = 1 if t P t2 and 0 otherwise. Dm1773 is a dummy variable equal to 1 for year 1773.Dm1808, Dm1918 are defined in similar fashion. N is number of observations. ‘‘P-value’’ is the p-value of F-test forthe null hypothesis that b1, b2, and b3 are all zero. DW is Durbin–Watson statistics. The low Durbin–Watsonstatistics imply serial correlation. The augmented Dickey–Fuller test indicates that some variables are not trendstationary.* Significant at the 10% level.*** Significant at the 1% level.


in old-age survival dominated a myriad of otherpotentially important factors.

First, were pre-transition saving rates low?Estimates for five pre-transition populations

Table 2. Mean national saving rates in

Sweden United Kingdom Italy

Pre-transition 1751–1875 1841–99 <187Survival rate 0.31 0.34 naSaving rate 7.3 11.6 na

Transition 1876–2000 1900–98 1872–20Survival rate 0.53 0.49 0.47Saving rate 16.6 13 17.7

a Life expectancy at age 30 is presented instead of survival

are available and presented in Table 2. In allcases, the pre-transition saving rates are low ascompared with the saving rates that followed,but the UK saving rate during pre-transition is

pre-transition and transition periods

United States Japan Taiwan Indiaa

2 <1900 1891–1947 1906–39 1900–50na 0.35 0.24 24.0na 15.7 22.1 6.9

00 1900–2001 1947–2000 1940–99 1951–970.57 0.60 0.54 37.717.7 32.6 26.1 17.7

rate in India.

10 WORLD DEVELOPMENT

only slightly less than its transition saving rateand Taiwan’s pre-transition saving rate is quitehigh as compared with the other countries.

Second, are saving and old-age survival cor-related? The observed saving rates are plotted

(a) Sweden

r= 0.82

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0 0.2 0.4 0.6 0.8

q

S/Y

(c) Italy

r = 0.66

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0 0.2 0.4 0.6 0.8

q

S/Y

(e) Japan

r= 0.64

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0 0.2 0.4 0.6 0.8

q

S/Y

(g

r= 0.97

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0 20

Life Expec

S/Y

Figure 4. Adult survival index

against the observed survival values in Figure 4for each of the countries. 10 The United Statesstands out as an exception with a negativesimple correlation between saving rates andold-age survival. In the United Kingdom, the

(b) United Kingdom

r= 0.37

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0 0.2 0.4 0.6 0.8

qS/

Y

(d) United States

r = -0.53

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0 0.2 0.4 0.6 0.8

q

S/Y

(f) Taiwan

r = 0.66

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0 0.2 0.4 0.6 0.8

q

S/Y

) India

40 60

tancy at Age 30

and the national saving rate.

0

5

10

15

20

25

30

35

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

Change in Old Age Survival Index over 10 year period (Δq)

Nat

iona

l Sav

ing

Rat

e (S

/Y, %

)

q=0.4 q=0.5q=0.6 Linear (q=0.4)Linear (q=0.5) Linear (q=0.6)

r=0.58

r=0.72

r=0.59

Figure 5. Changes in old-age survival index and the national saving rate.


positive correlation is modest (0.37). In theother five countries, the correlation betweenthe two variables ranges from 0.64 upward.

With the exception of Sweden, the correla-tion between q and saving disappears or turnsnegative at higher survival rates. The theoreti-cal model offers two possible explanations forthis phenomenon. One is that a slowdown inthe rate of change in mortality, as occurred inJapan and in Taiwan, would cause saving ratesto drop below the regression lines. A second isthat a decline in the rate of economic growthwould have a similar effect. Institutionalchange—especially the adoption of pay-as-you-go pension programs—looms large as apotential explanation.

The third question is whether rapid changesin survival rates (observed mostly in the coun-tries of East Asia) were associated with highersaving rates. As a simple analytic device wecompare the countries at three benchmark old-age survival rates—0.4, 0.5, and 0.6—observedfor the six countries for which we have values(Figure 5). There is a clear positive associationbetween the national saving rate and the changein the old-age survival rates over the subsequentdecade. The simple correlation between thevariables ranges from 0.58 to 0.72. The effectsare essentially identical for q equal to 0.4 and0.5 and somewhat attenuated for 0.6. These re-sults provide modest but consistent support forthe dynamic model of adult survival and saving.

4. ANALYSIS OF WORLD PANELDATA 1965–99

Estimates of national saving rates, life expec-tancy at birth, and other variables that mayinfluence saving are available for 76 countriesin 1965–69 increasing to 94 countries in 1995–99. 11 In this section, we present the analysisof national saving rates employing these data.Using the world panel data offers advantagesover the historical analysis. First, we can moveto a multivariate framework that explicitlyincorporates the role of other factors in deter-mining national saving rates. Second, we canexplore whether the Western/East Asian dis-tinctions drawn in the historical analysis canbe generalized to other countries of the world.There are also disadvantages that are discussedbelow.

(a) Model specification

The empirical model incorporates the two ef-fects of old-age survival derived from the OLGmodel presented in Section 2: the steady-stateeffect, which interacts with the rate of economicgrowth, and the transitory effect, which de-pends on the rate at which old-age survival isincreasing. A linear approximation of theOLG model implies that both the steady-stateeffect (b1) and the transitory effect (b2) are posi-tive in Eqn. (7):


ðS=Y Þt ¼ b0 þ b1qt � Y gr;t þ b2Dqt

þ b3D1t � Y gr;t þ b4Y gr;t þ b5PRIt þ et

ð7Þ

where S/Y is the national saving rate, q is theold-age survival index, Ygr is the growth rateof GDP, Dq is the change in the old-age sur-vival index during the previous five year period,D1 is the youth dependency ratio, and PRI isthe relative price of investment goods, andsubscript t means year t. 12

The basic empirical model incorporates threeother saving determinants that have been ex-plored in previous studies. The first is the effectof youth dependency. As youth dependencyvaries over the demographic transition, aggre-gate saving can be influenced in a variety ofways of which two seem particularly important.First, an increase in the number of childrenmay have a direct effect on current householdconsumption because of the costs of additionalchildren. The direction of the effect will depend,however, on whether or not a decline in thenumber of children is associated with a declinein total consumption by children. If the price ofchildren relative to adults is rising and the de-mand for children is price inelastic, expendi-tures on children will increase as the numberof children declines. In this instance, youthdependency would have a positive effect on sav-ing. If the demand for children is price elastic orif the number of children is changing for rea-sons unrelated to changes in relative prices,youth dependency will have a negative effecton saving (Mason, 1987).

Changes in youth dependency may also influ-ence saving because children provide old-agesupport either through familial support systemsor through public pension and health care sys-tems. To the extent that children are seen as asubstitute for pension assets, youth dependencywill have a negative effect on saving. The spec-ification of the youth dependency effect followsthe variable rate-of-growth (VRG) model (Fry& Mason, 1982; Kelley & Schmidt, 1996; Ma-son, 1981, 1987).

The second effect included in the basic modelis the rate-of-growth effect, that is a feature ofthe OLG model presented in Section 2 andlife-cycle saving models in general (Modigliani& Brumberg, 1954). In an economy experienc-ing more rapid GDP growth, the lifetime earn-ings of young cohorts are greater relative to thelifetime earnings of older cohorts. To the extentthat lifecycle saving is used to shift resources

from younger to older ages, saving is concen-trated among younger cohorts. Hence, the rateof growth effect is typically positive, but canin principle be negative. 13 The effect of GDPgrowth is variable, equal to b1qt + b3D1t + b4,because the old-age survival rate and the youthdependency ratio influence the life-cycle profileof consumption. The coefficient b4 has no eco-nomic interpretation in isolation and, hence,may be positive or negative depending on theeffects of q and D1.

The third determinant included in the empir-ical model is the relative price of investmentgoods (PRI) following Taylor (1995) and Hig-gins and Williamson (1997). The PRI capturesthe effect of changing interest rates. An increasein the interest rate will lead to an increase or de-crease in saving by prime-age adults and by theelderly depending on the relative strengths ofthe substitution and wealth effects. Thus, the ef-fect of the PRI on the national saving rate is anempirical issue.

A potentially important extension of themodel, considered below, allows for a tran-sitory youth dependency effects followingHiggins (1994) and Williamson and Higgins(2001). A drop in youth dependency would in-duce prime-age adults to save more during theirworking years in anticipation that they wouldrely less on familial or public transfers duringtheir retirement years. Current retirees wouldbe unaffected as they are simply dis-saving the(small) assets they accumulated in the expecta-tion that they would be supported by the manychildren they chose to bear. Hence, aggregatesaving would rise steeply. In the next period,however, the higher saving by the new genera-tion of prime-age adults would be offset bythe higher dis-saving by the new generation ofretirees. Hence, saving would decline from thetransitory peak to a steady-state peak thatwould be higher than saving in period t, butlower than saving in period t + 1. Just as isthe case for survival, the saving rate would de-pend on the current level of youth dependencyand its rate of change.

(b) Variables, definitions, the sample,and estimation methods

Except as noted below, all variables are takendirectly from or constructed using data fromthe World Development Indicators (WDI,2003). The saving rate (S/Yt) is the averagegross national saving rate for the five-year per-iod t to t + 4. The rate of growth of income is


measured by the growth rate of real GDP dur-ing the preceding five-year period. The relativeprice of investment goods (PRIt) is taken di-rectly from the Penn World Table (PWT) andis the average value for the period t to t + 4.The youth dependency ratio (D1t) is the ratioof the population 0–14 to the population 15–64.

The old-age survival index (q) is the ratioof expected years lived after age 60 (T60) toexpected years lived between ages 30 and 60(T30–T60) given contemporaneous age-specificdeath rates. Tx, total number of years livedafter age x, is a standard life table value. Lifetables are not available for many countries inmany years. Hence, life expectancy at birthfrom the World Development Indicators(World Bank, 2003) were used in conjunctionwith Coale–Demeny model life tables (Coale& Demeny, 1983) to construct estimates ofq. 14 The change in the old-age survival indexis the average increase over the precedingfive-year period, that is, Dqt = qt � qt�5.

The full sample consists of 566 observationsfor 76 countries in 1965–69 increasing to 94countries in 1995–99. Estimates for Westernand East Asian countries and for Other Devel-oping Countries are presented separately.Because the national saving rates may affecteconomic growth, previous empirical studieshave relied on two-stage least squares (2SLS)method to deal with the endogeneity problem.We follow standard practice and present bothordinary least squares (OLS) and 2SLS esti-mates. OLS estimates are a useful complementto 2SLS estimates for two reasons. First, therate of economic growth is for the five-yearperiod preceding the saving rate rather than acontemporaneous measure. This may mitigate,although not eliminate, the endogeneity prob-lem. Second, it is difficult to find strong instru-ments for economic growth and using weakinstruments often does more harm than good(Bound, Jaeger, & Baker, 1995).

For the first stage variables we follow Higginsand Williamson (1997) and use the lagged val-ues of the national investment rate, the laborforce growth rate, the price of investmentgoods, the consumer price index, real GDPper worker, real GDP per capita, and a measureof openness. The rationale for including theinvestment rate and the labor force growth ratefollows directly from the neo-classical growthmodel. The price variables are included to cap-ture the effects of inflation on productivitygrowth. Per capita income measures are em-ployed to incorporate the possible effects of con-

vergence. Openness influences economic growthby creating a more competitive economic envi-ronment. All estimates include year and regio-nal dummies, as well. Below we report theresults of an over-identifying restriction test use-ful to judge the overall exogeneity of the instru-ments. We also use a Hausman test (Hausman,1978, 1983) to assess whether the OLS and 2SLSestimates are statistically distinguishable.

(c) Results

Estimates of the basic model (Eqn. (7)) arepresented in Table 3. OLS and 2SLS estimatesare both presented and they are generally simi-lar. The instrument variables in the first stageregression are jointly significant at the 1% levelin all cases. The Hausman test implies that theGDP growth rate is potentially endogenous.For the non-Western/non-East Asia sample,the overidentifying restriction test indicatesthat we cannot reject the hypothesis that theinstruments for economic growth are entirelyexogenous. But the other samples do not passthe overidentifying restriction test, and thusparameter estimates are influenced to some ex-tent by the endogeneity problem. The OLS and2SLS parameter estimates differ substantially inmagnitude as is evident in Table 3. The qualita-tive results are similar, however, and for thesake of brevity we will limit our discussion tothe 2SLS results.

Old-age survival consistently has a large, sta-tistically significant positive effect on nationalsaving rates for the full sample and for the twosub-samples. The change in survival has a statis-tically significant positive effect on national sav-ing in the West/East Asia (W/EA) sample, butnot in the other sub-sample. The youth depen-dency effect is not statistically significant forthe full sample or for the two sub-samples. Theeffect of PRI has a large positive effect in theW/EA and a smaller negative effect elsewhere,but the effects are only marginally significant.The rate of growth effect evaluated at the meanvalue of q and D1 is consistently positive with avalue that ranges from 1.4 in W/EA to 0.75 inthe non-W/EA sample. The regional dummyvariables are statistically significant—positivefor East Asia and negative for the non-West,non-East Asian countries. Thus, importantregional differences in saving rates remain aftercontrolling for demographic characteristics.

In analysis that is summarized only brieflyhere, we explored two other issues. First, were-estimated the models presented in Table 3

Table 3. Estimated saving equation with old-age survival index and youth dependency

(1) Whole world (2) West and East Asia (3) Non-West, Non-EastAsia

OLS 2SLS OLS 2SLS OLS 2SLS

q Æ Ygr 8.2055*** 14.8399*** 8.3714** 14.8129*** 9.1327*** 15.7251***

(1.8606) (2.6660) (3.7148) (3.5266) (1.9979) (2.9857)

Dq 0.8615 0.5104 1.7954** 1.8115** 0.3284 �0.2538(0.5266) (0.5752) (0.8192) (0.8519) (0.5962) (0.6823)

D1 Æ Ygr 0.7461 0.9319 �3.0912*** �1.7057 0.4379 1.0155(0.7639) (0.9345) (1.1164) (1.1246) (0.9871) (1.2978)

Ygr �3.7274*** �6.5927*** �2.9073 �6.4693*** �3.6892** �6.8701***

(1.3526) (1.9655) (2.4628) (2.3958) (1.5577) (2.4026)

PRI �0.0053* �0.0028 0.0422** 0.0350* �0.0084** �0.0064*

(0.0032) (0.0036) (0.0207) (0.0212) (0.0035) (0.0036)

y70 0.0100 0.0075 0.0093 0.0105 0.0069 0.0026(0.0181) (0.0184) (0.0161) (0.0159) (0.0251) (0.0253)

y75 �0.0175 �0.0253 �0.0280* �0.0250 �0.0261 �0.0373(0.0166) (0.0176) (0.0159) (0.0159) (0.0233) (0.0241)

y80 �0.0253 �0.0290 �0.0280 �0.0167 �0.0433* �0.0543**

(0.0165) (0.0188) (0.0198) (0.0238) (0.0222) (0.0234)

y85 �0.0031 �0.0013 0.0001 0.0184 �0.0272 �0.0345(0.0163) (0.0218) (0.0173) (0.0207) (0.0226) (0.0272)

y90 �0.0102 �0.0185 �0.0340* �0.0255 �0.0258 �0.0398(0.0161) (0.0197) (0.0175) (0.0191) (0.0225) (0.0257)

y95 �0.0009 �0.0086 �0.0039 0.0196 �0.0339 �0.0598**

(0.0168) (0.0235) (0.0197) (0.0231) (0.0235) (0.0285)

East Asia 0.0312** 0.0189 0.1073*** 0.0855***

(0.0137) (0.0175) (0.0165) (0.0202)

Other countries �0.1190*** �0.0915***

(0.0093) (0.0125)

Constant 0.1775*** 0.1487*** 0.1544*** 0.1267*** 0.0758*** 0.0855***

(0.0161) (0.0245) (0.0247) (0.0306) (0.0205) (0.0305)

N 566 566 189 189 377 377

Adjusted R2 0.4357 0.3945 0.4191 0.3848 0.1275 0.0852

P-values, Ygr 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

P-values, year dummies 0.2800 0.1160 0.0125 0.0006 0.2261 0.0954

Ygr effect 0.7203 1.1739 0.6967 1.4105 0.6177 0.7543

P-value, Hausman 0.0000 0.0037 0.0000

Note: The dependent variable is the national saving rate. q: Adult survival index, Ygr: GDP growth rate, D1: youngdependency rate, Dq: change in the adult survival rate, PRI: price of investment goods, yXX dummy variables foryear XX, N: number of observation. ‘‘P-value, Ygr’’ is the p-value of F-test of the null hypothesis that the bothcoefficients of q Æ Ygr and D1 Æ Ygr are zero. ‘‘P-value, year dummies’’ is the p-value of F-test of the null hypothesisthat all the year dummies are zero. ‘‘Ygr effect’’ is the partial effect of an increase in GDP growth. ‘‘P-valueHausman’’ is the p-value of Hausman test for the null hypothesis that economic growth rate is exogenous.Figures in parentheses are standard errors.* Significant at the 10% level.** Significant at the 5% level.*** Significant at the 1% level.



to capture any transitory effects of youthdependency on saving by including the changein the youth dependency ratio. We did not finda significant transitory effect of youth depen-dency, nor did the inclusion of the change inyouth dependency have any important effecton other aspects of the estimates. Old-age sur-vival has a strong positive effect in all estimates;the change in old-age survival has a positive ef-fect in W/EA but not elsewhere. The effects ofother variables are similar to those reportedin Table 3.

Second, we investigated the possibility thatthe effect of demographic variables dependedon whether the economy was open or closed.As shown in Figures 2 and 3, openness influ-ences the short-term and long-term effects of in-creased survival in a relatively complex fashion.Hence, the analysis was repeated (a) by sub-

(a) OL

0.15

0.17

0.19

0.21

0.23

0.25

0.27

0.29

0.31West East Asia

(b) 2S

0.15

0.17

0.19

0.21

0.23

0.25

0.27

0.29

0.31West East Asia

1955 1965 1975 1985 1995

1955 1965 1975 1985 1995

Figure 6. Projected saving rates of Western Countries and

dividing the sample into countries that were rel-atively open and those that were relativelyclosed; or (b) by interacting the demographicvariables with a measure of openness. Opennesswas measured using the Chinn and Ito (2005)de jure measure of financial openness. Wefound no statistically significant evidence thatthe effects of demographic variables were influ-enced by the degree of openness.

Two aspects of the results warrant emphasis.First, the results imply that the demographictransition has had an important effect on ag-gregate saving rates. Two different kinds ofexercises show this to be the case. The first exer-cise is to calculate that share of the actual in-crease in saving rates in East Asia explainedby demographic variables. We find that demo-graphic variables explain about half of the ac-tual increase in saving rates in East Asia.

S

LS

2005 2015 2025 2035 2045

2005 2015 2025 2035 2045

East Asia (Constant Youth Dependency, 1955–2050).


Although substantial, the estimated effects aresmaller than that found in recent aggregateanalyses. In the studies by Higgins and Wil-liamson and Kelley and Schmidt, changes inage structure explain virtually all of the increasein saving rates in East Asia (Higgins & William-son, 1997; Kelley & Schmidt, 1996). Here theage structure effects are of similar magnitudeto those found by Deaton and Paxson, whilethe effects of longevity would be part of the co-hort effect in the Deaton and Paxson (2000)analysis. These results bridge the gap, to someextent, between the large effects found in aggre-gate level analyses and the much smaller effectsfound in micro-level analyses.

The second exercise uses UN projections toproject saving rates. Projections for the Westand East Asia allowing only the old-age sur-vival ratio to change are presented in Figure6. Projections allowing both the old-age sur-

(a) O

0.15

0.17

0.19

0.21

0.23

0.25

0.27

0.29

0.31

1955 1965 1975 1985 1995

West East Asia

(b) 2S

0.15

0.17

0.19

0.21

0.23

0.25

0.27

0.29

0.31

1955 1965 1975 1985 1995

West East Asia

Figure 7. Projected saving rates of Western Countries and

vival ratio and the youth dependency ratio tovary, while holding all other variables constant,are presented in Figure 7.

The combined effect of the rise in adult mor-tality and the decline in youth dependency is toincrease the aggregate saving rate during 1955–60 and 2045 by 14.6% points in East Asia, by8.6% points in the West, and by 11.4% pointsin the remaining countries based on the 2SLSestimates. Improvements in adult mortality ac-counted for a little more than three-quarters ofthe increase in each region, while the decline inthe youth dependency ratio accounted for alittle less than one-quarter of the increase.

The second important feature of the resultsis the implication for population aging andaggregate saving. There is a widespread concern,though limited empirical support, that popula-tion aging will lead to a decline in aggregate sav-ing rates. The empirical results presented here

LS

2005 2015 2025 2035 2045

LS

2005 2015 2025 2035 2045

East Asia (Changing Youth Dependency, 1955–2050).


do not support that conclusion. If old-age sur-vival rates continue to increase, as is widely ex-pected, our empirical results imply that savingrates will continue to rise. This empirical findingis consistent with the Lee et al. (2003) simula-tions and suggests that economic growth maynot slow as much with population aging as isanticipated in some quarters.

5. RESERVATIONS

An important unanswered question in thisanalysis is why no dynamic effect of old-agesurvival is found in the non-W/EA sample.One possibility is that drawbacks with theworld panel data are responsible. The first lim-itation of the data is its relatively short timeframe. For most economic analyses 30 yearsof data are more than adequate, but 30 yearsis only the length of a single generation. In asense, we have a single observation of theOLG model presented in Section 2. The popu-lation of prime-age adults/workers of 1965 isthe old-age population of 1995.

A second difficulty, discussed in Section 3, isthat the 1965–99 period may not be well-suitedto testing our theoretical saving model. Thecountries of the West enjoyed similar and rela-tively constant increases in old-age survival;hence, analyzing variation across countries oracross time is unlikely to shed much light onthe role of increases in old-age survival. TheAsian experience may be more fertile groundto analyze as suggested in Section 3. Whatabout the rest of the developing world? Untilthe mid-1980s the gains in life expectancy wererelatively constant across the world. That thesimple correlation between life expectancy atbirth for the first half of the 1960s and the sec-ond half of the 1960s was 0.997 for the 176countries for which the UN reports estimatesillustrates the point.

Two groups of countries experienced signifi-cant departures from their historical trendsbeginning in the mid-1980s primarily becauseof two important events—the break-up of theSoviet empire and the emergence of the HIV/AIDS epidemic in sub-Saharan Africa. Regio-nal conflicts also played a role in the MiddleEast and Africa. If the saving model is applica-ble to these mortality crises, saving rates shouldhave declined. Evidence on this point is limited,but Gregory et al. (1999) conclude that the riseof mortality rates among middle-aged Russianmen depressed their saving rates.

A third and related issue is that the measuresof mortality in the international panel data arenot ideal. Although estimates of life expectancyat birth are reported by the World Bank, thesevalues are often based on very incompleteinformation. We rely on model life tables totransform life expectancy at birth into theold-age survival ratio described in the previoussection. Whether this is appropriate in all cir-cumstances and, in particular, is reliable undersevere mortality crises is a question to which wedo not have a satisfactory answer. Moreover,the measure of the speed of mortality declineis for five-year periods. It may be that expecta-tions about increases in old-age survival evolvemuch more slowly. Perhaps even generationlength changes in old-age survival—a measuremore consistent with our theoretical model—would be more appropriate.

It is not our intention to suggest that absenceof a dynamic effect in the non-W/EA samplemust surely be the fault of the data rather thanthe model. More fundamental explanations arepossible. Higher saving rates are not the onlypossible response to an increase in the numberof years lived at old age. One possibility is thatconsumption at old age may decline. Another isthat the elderly may choose to increase their la-bor force participation, although the oppositeis the case as an empirical matter with the re-cent exception of the United States and a fewother countries. Still another response is thattransfer systems, either public or familial, mayexpand to meet the needs of a growing elderlypopulation. Further work on these topics isclearly needed. 15

6. CONCLUSIONS

This is not the first paper to conclude that theincreased duration of life could lead to highersaving rates. At the individual or householdlevel, it is obvious that higher saving rates area likely response to an increased duration ofretirement. The effect on aggregate saving ismore complex, however, because there are bothbehavioral responses and age composition ef-fects at play. An important contribution of thispaper is to show that the aggregate saving ratedepends on both the level and the rate at whichadult survival is increasing.

The empirical results provide strong and con-sistent evidence that an increase in the portionof adult life lived at old ages leads to an in-crease in saving rates. This finding holds for


all samples and specifications. The historicalevidence suggests and the international paneldata confirm that the increase in adult survivalwas a major impetus to the rise in the wealth ofmany countries.

The evidence for the dynamic effect, that is,the effect of the rate of change in old-age sur-vival, is more fragile. When analysis is confinedto the West/East Asia sample, we find a statis-tically significant effect. Moreover, the long-runhistorical patterns available for countries fromEast Asia and the West are consistent withthe dynamic effect. In other parts of the con-temporary developing world, however, we donot find any support for a dynamic effect.

There are two additional important implica-tions of the empirical analysis. The first is thatthe demographic transition had a strong posi-tive effect on aggregate saving rates, but thatmost of the effect was a response to improve-ments in old-age survival rather than tochanges in youth dependency. This result mayhelp to reconcile the divergent findings of stud-ies based on the analysis of aggregate data andhousehold survey data. The second importantimplication is that population aging will notlead to a decline in saving rates. Any composi-tional effects associated with population agingare outweighed by the behavioral effects ofcontinued increases in longevity.

NOTES

1. Theoretical results are summarized here. Moredetails are available in Kinugasa (2004).

2. The interpretation of q becomes important in theempirical analysis.

3. In this model, the mean age of consumption is(c1,t + 2qtc2,t+1)/(c1,t + qtc2,t+1) and the mean age ofearning is 1.

4. In the simulation results presented below, we assumethat an increase in the interest rate leads to greatersaving. Qualitative results hold unless an increase ininterest rates has a large negative effect on saving—apossibility not supported by empirical evidence. Fordetails see Kinugasa (2004).

5. The economy converges in a non-oscillatory patternto the steady state under plausible parameter values. SeeKinugasa (2004) for details.

6. The parameters for the simulation model have beenchosen with an eye to maintaining consistency withprevious studies, for example, Barro and Sala-i-Martin(1995) and Higgins (1994). Productivity growth and therate of population growth are both set to 1.5% per year.The population growth rate for the world for 1820–1998was somewhat slower at 1.0% per year (Maddison, 1995).For the 1950–2000, the population growth rate wassomewhat faster at 1.75% per year (United NationsPopulation Division, 2005). We assume that the inter-temporal elasticity of consumption is 1.3, followingHiggins. This is an important parameter in the closedeconomy model because it implies that a higher interestrate will lead to a modest increase in saving rates. We haveused a discount rate of 0.02 per annum as have Barro and

Sala-i-Martin as compared with a discount rate of 0.025 inHiggins given our view that a low discount rate is moreconsistent with observed age-profiles of consumption thatare relatively flat in most countries. We use standardvalues for the depreciation rate (5%) and the elasticity ofoutput with respect to capital (1/3)—the same values usedby Barro and Sala-i-Martin and Higgins. We partcompany with Higgins by assuming that a generationlength is 30 years rather than 25. This assumption is basedon recent estimates of the economic lifecycle showing thata generation length of 30 years is a more realisticrepresentation (Lee et al., 2005).

7. Life tables used in the analysis here, and in otherstudies, are period tables based on current age-specificmortality rates. Thus, they describe the mortality expe-rience of a synthetic cohort that lives its life subject tocurrent mortality conditions. Using cohort specific lifetables would conform more closely to the theoreticalmodel. Projected cohort life tables are not generallyavailable, but they could be constructed using projectedage-specific survival rates from the United Nations, forexample. Given the simple methods used to project lifeexpectancy, it seems doubtful that projected valuescontain additional information beyond that alreadycaptured by the two measures of survival included inour analysis.

8. In India, we analyze life expectancy at age 30, whichis highly correlated with the old-age survival index.

9. The break points were assigned visually. A moreprecise iterative approach would improve the fit of thepiecewise linear approximations, but the analysis pre-sented below would not be affected in any importantway.


10. In the regression analysis in Figure 4, we checkedthe trend stationarity of the variables by AugmentedDickey–Fuller test and find that some variables are nottrend stationary.

11. In our world panel data, all variables are averagesfor the subsequent five-year period. So, the saving rate in1965 is calculated as the mean of saving rates from 1965to 1969 and a variable in 1995 is the mean of the variablefrom 1995 to 1999.

12. The effect of openness is explored below.

13. The saving mechanism can be used to shiftconsumption to younger ages, by accumulating creditcard debt, for example, but constraints on indebtednesslimit the importance of these transactions.

14. See Kinugasa (2004) for additional details. TheCoale–Demeny Model Life Table is an approximation

that does not fit certain countries very well, for example,countries with unusually high rates of mortality atprime-adult ages.

15. Our theoretical model and empirical analysisassume that demand side of capital is implicit. There-fore, the framework is more appropriate for capacity-constrained economies than demand-constrained econ-omies.

16. b oðStþ2=Y tþ2Þoqt

¼ k�/tþ2 gtþ3ntþ3

oktþ3

oktþ2� ktþ3

ktþ2/

� �� ð1� /Þ

hð1� nÞ� oktþ2

oktþ1

oktþ1

oqt, 0 < okt + 3/okt + 2 < 1, 0 < okt + 2/

okt+1 < 1, and okt+1/o qt > 0 hold, therefore, in theright hand side of this equation, the value inside thebracket is negative for plausible parameters, so that thesaving rate at time t has a negative effect on the savingrate at time t + 2. In the same way, the effects of thesurvival rate at time t on the saving rate after time t + 2can be derived. qt has a negative effect on the saving rateafter time t + 2.

REFERENCES

Barro, R., & Sala-i-Martin, X. (1995). Economic growth.Cambridge, MA: MIT Press.

Bloom, D. E., Canning, D., et al. (2003). Longevity andlife-cycle savings. Scandinavian Journal of Economics,105(3), 319–338.

Borsch-Supan, A. (1996). The impact of populationageing on savings, investment and growth in theOECD area. Future global capital shortages: Realthreat or pure fiction? Paris, France: Organisation-for-Economic-Co-operation and-Development. 103-41.

Bound, J., Jaeger, D. A., & Baker, R. M. (1995).Problems with instrumental variables estimationwhen the correlation between the instruments andthe endogenous explanatory variable is weak. Journalof the American Statistical Association, 90(430),443–450.

Chinn, M., & Ito, H. (2005). What matters for financialdevelopment? Capital controls, institutions, andinteractions, National bureau of economic researchworking paper, No. 11370.

Coale, A., & Demeny, P. (1983). Regional model lifetables and stable populations (2nd ed.). New York:Academic Press.

Davies, J. B. (1981). Uncertain lifetime, consumption,and dissaving in retirement. Journal of PoliticalEconomy, 89(3), 561–577.

Deaton, A., & Paxson, C. H. (2000). Growth, demo-graphic structure, and national saving in Taiwan. InR. Lee & C. Y. C. Chu (Eds.), Population andeconomic change in East Asia, a supplement topopulation and development review, vol. 26 (pp. 141–173). New York: Population Council.

Fry, M., & Mason, A. (1982). The variable rate ofgrowth effect in the life cycle model. EconomicInquiry, 20, 426–442.

Gregory, P. R., Mokhtari, M., & Wickfram, S. (1999).Do the Russians really save that much? Alternateestimates from the Russian longitudinal monitoringsurvey. Review of Economics and Statistics.

Hausman, J. A. (1978). Specification tests in economet-rics. Econometrica, 46, 1251–1271.

Hausman, J. A. (1983). Specification and estimation ofsimultaneous equations models. In Z. Griliches, &M. D. Intriligator (Eds.). Handbook of econometrics(Vol. 1, pp. 391–448). Amsterdam, Holland: NorthHolland.

Higgins, M. (1994). The demographic determinants ofsavings, investment and international capital flows.Ph.D. dissertation, Department of Economics, Har-vard University, Cambridge, MA.

Higgins, M., & Williamson, J. G. (1997). Age structuredynamics in Asia and dependence on foreign capital.Population and Development Review, 23(2), 261–293.

Kageyama, J. (2003). The effects of a continuousincrease in lifetime on saving. Review of Income andWealth, 49(2), 163–183.

Kelley, A. C., & Schmidt, R. M. (1996). Saving,dependency and development. Journal of PopulationEconomics, 9(4), 365–386.

Kinugasa, T. (2004). Life expectancy, labor force, andsaving, Ph.D. dissertation, Department of Eco-nomics. Honolulu, HI, University of Hawaii atManoa.

Kuehlwein, M. (1993). Life-cycle and altruistic theoriesof saving with lifetime uncertainty. Review of Eco-nomics and Statistics, 75(1), 38–47.

Lee, R., Mason, A., & Miller, T. (2000). Life cycle savingand the demographic transition in East Asia. Popu-lation and Development Review, 26(Suppl.).

20 WORLD DEVE

Lee, R., Mason, A., & Miller, T. (2003). From transfersto individual responsibility: Implications for savingsand capital accumulation in Taiwan and the UnitedStates. Scandinavian Journal of Economics, 105(3),339–357.

Lee, R. D., Lee, S.-H., & Mason, A. (2005). Charting theeconomic lifecycle. Mimeo.

Lee, R. D., Mason, A., & Miller, T. (2001a). Saving,wealth, and population. In N. Birdsall, A. C. Kelley,& S. W. Sinding (Eds.), Population does matter:Demography, poverty, and economic growth(pp. 137–164). Oxford: Oxford University Press.

Lee, R. D., Mason, A., & Miller, T. (2001b). Saving,wealth, and the demographic transition in East Asia.In A. Mason (Ed.), Population change and economicdevelopment in East Asia: Challenges met, opportuni-ties seized (pp. 155–184). Stanford, CA: StanfordUniversity Press.

Leung, S. F. (1994). Uncertain lifetime, the theory of theconsumer, and the life cycle hypothesis. Econome-trica, 62(5), 1233–1239.

Maddison, A. (1995). Monitoring the World economy1820–1992. Paris, France: OECD.

Mason, A. (1981). An extension of the life-cycle modeland its application to population growth and aggre-gate saving. East-West Population Institute WorkingPapers, Honolulu: East-West Center 4.

Mason, A. (1987). National saving rates and populationgrowth: A new model and new evidence. In D. G.Johnson, & R. D. Lee (Eds.), Population growth andeconomic development: Issues and evidence. Socialdemography series (pp. 523–560). Madison, WI:University of Wisconsin Press.

Mason, A. (1988). Saving, economic growth, anddemographic change. Population and DevelopmentReview, 14, 113–144.

Modigliani, F., & Brumberg, R. (1954). Utility analysisand the consumption function: An interpretation ofcross-section data. In K. K. Kurihara (Ed.), Post-Keynesian economics. New Brunswick, NJ: RutgersUniversity Press.

Schieber, S. J., & Shoven, J. B. (1996). Population agingand saving for retirement. In R. Landau, T. Taylor,& G. Wright (Eds.), The mosaic of economic growth(pp. 150–172). Stanford, CA: Stanford UniversityPress.

Taylor, A. (1995). Debt, dependence and the demo-graphic transition: Latin America in to the nextcentury. World Development, 869–879.

United Nations Population Division (2005). Worldpopulation prospects: The 2004 revision. New York:United Nations.

Williamson, J., & Higgins, M. (2001). The accumulationand demography connection in East Asia. In A.Mason (Ed.), Population change and economic devel-opment in East Asia: Challenges met, opportunitiesseized. Stanford: Stanford University Press.

Yaari, M. E. (1965). Uncertain lifetime, life insurance,and the theory of the consumer. The Review ofEconomics Studies, 32(2), 137–150.

Zilcha, I., & Friedman, J. (1985). Saving behavior inretirement when life horizon in uncertain. EconomicLetters, 17(1–2), 63–66.

APPENDIX A. DETAILS OF THEOVERLAPPING GENERATIONS

LOPMENT

MODEL

Individuals live at most for two periods. Withprobability 1 � qt they die at the end of period1 and with probability qt at the end of period 2.The probabilities are known but individualshave no information about their own survival.The consumer’s optimization problem is tomaximize lifetime utility, assuming constant

relative risk aversion, V t ¼c1�h

1;t

1�h þ dqtc1�h

2;tþ1

1�h , giventhe lifetime budget constraint. Consumption atage 1 in period t is c1,t and c2,t+1 is consumptionat age 2 during period t + 1; d is the discountfactor, defined as d = 1/(1 + q), where q is thediscount rate; and 1/h is the intertemporal elas-ticity of substitution. Prime-age adults of age 1earn Atwt. At is labor-augmenting technologyand wt is wage per unit of effective labor. Con-sumers divide their earnings between currentconsumption and saving for old age, so that:

c1;t þ s1;t ¼ Atwt; ðA:1Þwhere s1,t is the saving of prime-age adults.Elderly adults are retired and consume whatthey saved while young. Insurance against lon-gevity risk is available. An annuity is purchasedat the beginning of age 1. If insurance compa-nies are risk neutral and annuity markets areperfect, the rate of return to survivors is[(1 + rt+1)/qt], where rt+1 is the riskless interestrate on saving. The return to annuities is[(1 + rt+1)/qt]. In this situation, returns toinsurance are greater than a regular note. Thus,individuals save only in the form of insuranceand consume:

c2;tþ1 ¼1þ rtþ1

qt

s1;t: ðA:2Þ

From (A.1) and (A.2), the lifetime budgetconstraint of the individuals at age 1 is

wtAt ¼ c1;t þqt

1þ rtþ1

c2;tþ1: ðA:3Þ

The corresponding Lagrangian is

L ¼c1�h

1;t

1� hþ dqt

c1�h2;tþ1

1� h

� k c1;t þqt

1þ rtþ1

c2;tþ1 � Atwt

� �;

where k is a Lagrangian multiplier. First orderconditions are


oLoc1;t¼ c�h

1;t � k ¼ 0; ðA:4Þ

oLoc2;tþ1

¼ dqtc�h2;tþ1 �

qt

1þ rtþ1

k ¼ 0; ðA:5Þ

oLok¼ �c1;t �

qt

1þ rtþ1

c2;tþ1 þ Atwt ¼ 0: ðA:6Þ

Substituting (A.4) and (A.5) into the equationyields

k ¼1þ qtd

1hð1þ rtþ1Þ

1�hh

h ih

Aht wh

t

: ðA:7Þ

Substituting back for k yields

c1;t ¼ð1þ rtþ1Þ

1�hh Atwt


1�hh

; ðA:8Þ

c2;tþ1 ¼d

1hð1þ rtþ1ÞAtwt


1�hh

: ðA:9Þ

From the budget constraints in Eqns. (A.1) and(A.2) and Eqns. (A.8) and (A.9), we can cal-culate saving by prime-age adults (s1,t) andthe elderly (s2,t). Saving by prime-age adults is

s1;t ¼ WtAtwt ¼qtd

1hAtwt


h�1h

; ðA:10Þ

where Wt is the share of wage income saved byprime-age adults. The elderly consume assetsaccumulated while working plus interest in-come from the annuity. But the return on theannuity is part of their income, so s2;t ¼

1þrtqt� 1

� �s1;t�1 � c2;t ¼ �s1;t�1. Saving of the

elderly is

s2;t ¼ �s1;t�1 ¼ �Wt�1At�1wt�1

¼ qt�1d1hAt�1wt�1

qt�1d1h þ ð1þ rtÞ

h�1h

: ðA:11Þ

Eqns. (A.10) and (A.11) correspond to Eqn. (1)in the text. From Eqn. (A.11), the effect ofan increase in the survival rate at time t onthe share of wage income saved by prime-ageadults is

oWt

oqt

¼d

1h qtd

1h þ ð1þ rtþ1Þ

h�1h

h i� qtd

2h


h�1h

h i2

¼ d1hð1þ rtþ1Þ

h�1h


h�1h

h i2> 0:

Thus, an increase in survival rate increases theshare of saving by prime-age adults.

Gross domestic product (Yt) is produced by aCobb–Douglas production function with labor-augmenting technological growth, that is, Y t ¼K/

t L1�/t , where / is the share of capital in GDP,

0 < / < 1. Lt = AtN1,t is the aggregate laborsupply measured in efficiency units. N1,t is thepopulation of prime-age adults and At is thetechnology index. The population growth rateper generation is nt � 1 and, hence, N1,t =ntN1,t�1. The technological growth rate pergeneration is gt � 1. Hence, the relationshipbetween the total lifetime labor income ofprime-age adults and pensioners is given bywt�1At�1N1,t�1 = wtAt N1,t/gtnt. Using lowercase letters to represent quantities per unit ofeffective worker, output per effective worker isyt ¼ k/

t and the capital–output ratio is k/�1t .

The depreciation rate (n) is assumed to be con-stant; hence, depreciation as a share of GDP isnk/�1

t .

Total gross national saving is the sum of thesaving of adults (S1,t), the saving of the elderly(S2,t) and depreciation (nKt). Dividing by Yt

yields the gross national saving rate at time t:

St

Y t¼ ð1� /Þ Wðqt; ktÞ �Wðqt�1; kt�1Þ

1

gtnt

� �

þ nk1�/t : ðA:12Þ

This equation corresponds to Eqn. (2) in thetext. The term (1 � /) is the share of labor in-come in GNP, Wt(qt,kt) is saving by currentworkers as a share of current labor income,�Wðqt�1; kt�1Þ 1

gtntis saving by current retirees

as a share of current labor income, and nk1�/t

is depreciation as a share of current GNP.The steady-state gross national saving rate is

SY

� ��¼ ð1� /ÞWðq�; k�Þ gn� 1

gn

� �þ nk�1�/;

ðA:13Þwhere the * superscript denotes equilibriumvalues. This equation corresponds to Eqn. (3)in the text.

In a small open economy, capital is perfectlymobile. Residents can borrow and lend in theinternational capital market at the world inter-est rate. The assumption of a small open econ-omy implies that the country is sufficientlysmall not to influence the world interest rate.According to the arbitrage condition, the mar-ginal product of domestic capital is equal to the


world interest rate; thus, /k/�1t � n ¼ rw;t. The

capital stock per effective worker is

kt ¼/

rw;t þ n

� � 11�/

: ðA:14Þ

The aggregate capital stock is given byKt = AtN1,tkt. Eqn. (A.14) implies that capitalper effective worker is determined solely bythe world interest rate and the parameters ofthe production process. The rate of growthof the labor force does not affect kt, nor doesthe survival rate affect kt.

In the absence of international capital flows,domestic saving equals investment. Gross

dktþ1

dkt¼ ð1� /Þf 0ðktÞX tX

�1t

gtþ1ntþ1 þ ½gtþ1ntþ1ktþ1 � ð1� /Þf ðktÞ� 1�hh

� X tX

�1t ½1þ f 0ðktþ1Þ � n��1f 00ðktþ1Þ

: ðA:19Þ

national saving is the sum of changes in assetholdings of prime-age adults and the elderlyand depreciation, so that St = S1,t + S2,t +nKt = S1,t � S1,t�1 + nKt. Gross investment isgiven by It = Kt+1 � (1 � n)Kt. Because savingis equal to investment, S1,t = Kt+1. The savingof the young is equal to the capital stock inthe next period. Thus, the supply of capital is

Ktþ1 ¼ S1;t ¼ s1;tN 1;t: ðA:15ÞNoting that Kt+1 = At+1N1,t+1kt+1, Eqn. (A.15)can be rewritten as

ktþ1 ¼Wðrtþ1; qtÞwtðktÞ

gtþ1ntþ1

¼ Stðrtþ1;wtðktÞ; qtÞ;

ðA:16Þwhere St denotes the supply of capital per unitof effective labor. Eqn. (A.16) corresponds toEqn. (4) in the text.

Here, as a matter of convenience we set Xt

and Xt as Xt ¼ 1þ qtd1hð1þ rtþ1Þ

1�hh , and X t ¼

qtd1hð1þ rtþ1Þ

1�hh , where X�1 is the share of labor

income consumed in prime age and XX�1 is theshare saved by prime-age adults, so that W =XX�1. From Eqn. (A.16) the following equa-tion is obtained:

ð1� /ÞX tðqt; rðktþ1ÞÞk/t

¼ ktþ1gtþ1ntþ1Xtðqt; rðktþ1ÞÞ: ðA:17Þ

dk�

dq�¼ X��1d

1h½1þ f 0ðk�Þ � n�

1�h

gnþ ½gnk� � ð1� /Þf ðk�Þ� 1�hh

� X �X��1½1þ f

If the survival rate is constant, capital pereffective worker will approach the steadystate:

k� ¼ ð1� /ÞX ðq�; rðk�ÞÞgnXðq�; rðk�ÞÞ

� � 11�/

; ðA:18Þ

where k* and q* denote capital per unit ofeffective labor and the survival rate in steadystate, respectively. Assuming variables otherthan capital per effective worker at times tand t + 1 are constant in Eqn. (A.17), therelationship between kt and kt+1 is describedas

In Eqn. (A.19), gnkt+1 is saving and (1 � /)f(kt) is earning per prime-age adult at time t.Because saving is less than earning, gt+1nt+1

kt+1 < (1 � /)f(kt). Note that f 00 < 0 and that0 < XX�1 < 1 hold.

Substituting Eqn. (A.18) into Eqn. (A.19),the numerator of the right hand side of Eqn.(A.19) reduces to /gn in steady state. Thus,

0 < dktþ1

dkt< 1 is satisfied at least around the

steady state unless the intertemporal elasticityof substitution (1/h) is much less than 1. If

0 < dktþ1

dkt< 1 holds in Eqn. (A.19), the steady

state is stable. Also, if the intertemporal elastic-ity of substitution is much less than 1, it is pos-sible that the denominator of Eqn. (A.19) isnegative. For simplicity, we assume that 0 <dktþ1

dkt< 1 holds; in other words, the economy

converges in a non-oscillatory pattern.Suppose the survival rate is constant in stea-

dy state. Then, in steady state, the equilibriumof the capital market in Eqn. (A.17) is given by

ð1� /ÞX ðq�; rðk�ÞÞk�/ ¼ k�gnXðq�; rðk�ÞÞ:ðA:20Þ

Calculating total differentials of both sides ofEqn. (A.20) and simplifying the results yieldsthe following expression of the relationshipbetween capital per effective worker and thesurvival rate:

h

½ð1� /Þk�/ � k�gn�0ðk�Þ � n��1f 00ðk�Þ � X �X��1ð1� /Þf 0ðk�Þ

:

ðA:21Þ


Eqn. (A.18) and 0 < dktþ1

dkt< 1 imply that the

denominator of Eqn. (A.21) is positive. Becausesaving of prime-age adults is less than wage in-come, (1 � /)k*/ � k*gn > 0 holds, so that thenumerator is also positive. Therefore, ok�

oq� > 0holds.

Consider the effect of an anticipated one-timeincrease in life expectancy at time t and assumethat q stays at q* in subsequent periods. In Eqn.(A.17), assuming that all variables other thankt+1 and qt are constant, we can characterizethe relationship between the changes of qt andkt+1 as

dktþ1

dqt

¼ X�1t d

1h½1þ f 0ðktþ1Þ � n�

1�hh ½ð1� /Þk�/ � ktþ1gtþ1ntþ1�

gtþ1ntþ1 þ ½gtþ1ntþ1ktþ1 � ð1� /Þf ðktÞ� 1�hh

� X tX

�1t ½1þ f 0ðktþ1Þ � n��1f 00ðktþ1Þ

: ðA:22Þ

The denominator of the right hand side of Eqn.(A.22) is equal to that of Eqn. (A.19). We as-sume that 0 < dktþ1

dkt< 1 holds, so that the

denominator of Eqn. (A.22) is positive. As wediscussed above, (1 � /)k*/ is wage earningat time t, and kt+1gn is the saving per prime-age adult. Because saving of the young doesnot exceed earning, (1 � /)k*/ � kt+1gt+1

nt+1 > 0, the numerator is positive anddktþ1

dqt> 0 holds.

A greater survival rate brings capital deepen-ing (o k*/oq* > 0). If the GDP growth rate isgreater than the deprecation rate, the savingrate increases. If GDP is growing at a rate lessthan the rate of depreciation, an increase in q*

has a negative effect on the saving rate.Gross national saving is the sum of changes

in asset holdings of prime-age adults and theelderly and depreciation, so that St = S1,t +S2,t + nKt = S1,t � S1,t�1 + nKt. Gross invest-ment is given by It = Kt+1 � (1 � n)Kt. GDPis expressed as Y t ¼ K/

t ðAtN 1;tÞ1�/. Therefore,national saving rate is calculated as

St

Y t¼ gtþ1ntþ1

ktþ1

kt� 1þ n

� �k1�/

t : ðA:23Þ

Eqn. (A.23) corresponds to Eqn. (5) in the text.In steady state, the relationship simplifies to

SY

� ��¼ ðgn� 1þ nÞk�1�/: ðA:24Þ

Eqn. (A.24) corresponds to Eqn. (6) in the text.The effect of the national saving rate of a

one-time, anticipated increase of the survival

rate is oðSt=Y tÞoqt¼ gtþ1ntþ1

k�/dktþ1

dqt> 0. An anticipated

increase in the survival rate at time t leads toa higher national saving rate. At time t, saving

by prime-age adults increases, which causes anincrease in kt+1. The supply of capital increasesand the saving rate increases. The effect of anincrease in the survival rate at time t on the na-

tional saving rate at time t + 1 is oðStþ1=Y tþ1Þoqt

¼

k�/tþ1 gtþ2ntþ2

oktþ2

oktþ1� ktþ2

ktþ1/

� ��ð1�/Þð1�nÞ

h ioktþ1

oqt,

where 0 < o kt+2/okt+1 < 1 and okt+1/oqt > 0hold. For plausible parameter values, thisexpression is negative. The saving at timet + 1 is the difference between the wealth attime t + 2 and t + 1. An increase in qt inducescapital deepening at time t + 1, but the wealthof the previous period and depreciation are alsohigher than at time t. The net increase in wealthat time t + 1 is less than that at time t. In aclosed economy, the survival rate at time t alsoinfluences the saving rate at time t + 2. Thisstands in contrast to the case of small openeconomy. The survival rate at time t has anegative effect on the saving rate after timet + 2. 16

why countries become wealthy: the effects of adult longevity on saving

Documents