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WORKING PAPER no. 9

The Age-Saving Profile

and the Life-Cycle Hypothesis

Tullio Jappelli and Franco Modigliani

November 1998

DIPARTIMENTO DI SCIENZE ECONOMICHE - UNIVERSITÀ DEGLI STUDI DI SALERNO

Via Ponte Don Melillo - 84084 FISCIANO (SA)Tel. 089-96 3167/3168 - Fax 089-96 3169 – e-mail: csef@xcom.it

WORKING PAPER no. 9

The Age-Saving Profile

and the Life-Cycle Hypothesis

Tullio Jappelli* and Franco Modigliani**

Abstract

The life-cycle hypothesis posits that saving is positive for young households and negativefor the retired, so that wealth should be hump-shaped. Yet, if one looks at themicroeconomic evidence on saving by age, dissaving by the elderly is limited or absent.But the saving measures usually computed on cross-sections or panel data are based on aconcept of income that does not take into account the presence of pension arrangements. Infact, disposable income treats pension contributions as taxes, and pension benefits astransfers. But since contributions entitle the payer to receive a pension after retirement,contributions should be regarded as life-cycle saving and hence included back to income.Similarly, pension benefits accruing to the retired do not represent income produced, but adrawing from the pension wealth accumulated up to retirement. We use Italian repeatedcross-sectional data from 1984 to 1995 to show the importance of this adjustment for theevaluation of the saving behavior of the elderly.

We thank Arie Kapteyn and Chris Paxson for comments. This paper is part of a researchproject on “Structural Analysis of Household Savings and Wealth Positions over the Life-Cycle”. Financial support has been provided by The Training and Mobility of ResearchersNetwork Program (TMR) of the European Commission DGXII and by the Italian NationalResearch Council (CNR).

* CSEF, University of Salerno, and CEPR.** Sloan School of Management, MIT.

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Table of contents

1. Introduction

2. The repeated cross-sectional data

3. The age-profiles of consumption, income and saving

4. The age-wealth profile

5. Conclusions

References

APPENDIX

A1. The Survey of Household Income and Wealth

A2. Pension wealth

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1. Introduction

The life-cycle hypothesis posits that the main motivation for saving is toaccumulate resources do be drained down for later expenditure and inparticular during retirement. Saving should be positive for younghouseholds and negative for the retired, so that wealth should be hump-shaped (Modigliani, 1986). Yet, if one looks at the microeconomic evidenceon saving rates by age, dissaving by the elderly is seldom observed. To takejust one recent example, in the introductory essay of a collection of countrystudies on saving, Poterba (1994) reports that in virtually all nations themedian saving rate is positive well beyond retirement, concluding that “thecountry studies provide very little evidence that supports the life-cyclemodel”. Based on the country studies, Poterba also reports that the mediansaving rate in the age class 70-74 is 1.1 percent in the United States and 6percent in Canada. And in Italy and Japan the median saving rates for thoseaged 65 and greater exceeds 30 percent of disposable income (Table 3)!

These figures are inconsistent not only with the elementary version of thelife-cycle hypothesis, but also with elaborate versions of the model with lifeuncertainty, precautionary saving and accidental bequests. In its basicformulation, the life-cycle hypothesis posits that saving behavior is forwardlooking and driven by the desire to prepare for future expenditures abovelater income throughout life. The main foreseeable event in one’s life isretirement, when income may be expected on average to dwindle to a levelwell below active life consumption. This implies that an essentialobservable implication of the life-cycle hypothesis is that there must bephases of life - notably during the retirement period - when saving isnegative and wealth is reduced. Adding life uncertainty, precautionarysaving, and liquidity constraints, as in more elaborate versions of the model,affects the age after which one should start observing negative saving andwealth decumulation, but not the main implication of the theory thatindividual wealth must eventually fall with age. Thus, the widely reportedpositive saving rates at all ages represent a strong contradiction of thetheory, and are consistent only with alternative behavioral models ofconsumption, for instance models in which bequests represent a prominentrole, either because consumers are altruistic or because they derive utilityfrom terminal wealth.

Yet the saving rates that are often computed on microeconomic data arebased on a concept of disposable income that does not take into account thepresence of pension arrangements. In order to check the validity of the life-

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cycle hypothesis, saving should be defined as the difference between (net oftax) earnings plus capital income and consumption. We refer to this incomeconcept as earned income. This differs from disposable income asconventionally measured because the latter ignores pension arrangements.Thus, it should not come as a surprise that the implications of the theory arenot born out by the data if the theory is confronted with the wrong data.

Disposable income treats social security contributions as taxes, andpension benefits as transfers. But since contributions entitle the payer toreceive a pension after retirement, they should be regarded as life-cyclesaving and hence included back to income. On the other hand, pensionbenefits accruing to the retired do not represent income produced, but rathera drawing from the social security wealth accumulated up to retirement. Thesame issue arises when income from a private pension fund is treated as anordinary component of disposable income, rather than as wealth depletionduring retirement. The greater the amount of mandatory saving and thereplacement rate assured by the social security system, the greater is thedifference between earned income and disposable income.

Based on the two income concepts, we distinguish between total saving,the difference between earned income and consumption, and private saving,the difference between disposable income and consumption. Mandatorysaving is then the difference between total and private saving. Acorresponding break-down applies to total wealth, which is the sum ofpension wealth and private wealth. Except for capital gains and losses andmeasurement problems, the first difference of total wealth is total saving,and the first difference of private wealth is private saving. Our data allow usto check if the shape of the age-profile of these two saving concepts aremutually consistent.

It is well-known that age profiles of individual variables cannot beestimated using cross-sectional data. Following recent studies, we use atime-series of cross-sections of Italian households to control for cohorteffects, and to estimate consumption, income, saving and wealth profiles ofa representative individual. Given the features of its social security system,Italy provides the clearest example of the difference between theconventional definition of disposable income and our proposed measure ofearned income. But of course the adjustment affects the definition of savingin all countries in which part of saving occurs through mandatorycontributions to pension funds or pay-as-you-go social security.

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The exercise we perform in this paper is closely related to two strands ofliterature. The first dates back to Feldstein (1974), who first pointed out thatpension wealth should be counted as part of individuals’ resources,measured social security wealth and argued forcefully that the transition toan unfunded social security regime crowds out private saving. The second,more recent strand of literature, is the intergenerational accountingframework proposed by Auerbach, Gokhale and Kotlikoff (1991) whoseaim is to measure how much existing generations can be expected to pay tothe government over their remaining lifetimes. Generational accountsprovide measures of cohort-specific receipts (including pension transfers,health expenditures, etc.) and payments (including taxes and social securitycontributions) that can be used to evaluate the intergenerationalredistributive impact of fiscal policy. Our focus here is primarily thecomputation of cohort-adjusted mandatory saving profiles implied by thecurrent social security arrangements. Other types of transfers, such asmedical payments, are of course important, but are neglected in the presentanalysis.

In Section 2 we present our data, which are drawn from the 1984-1995Survey of Household Income and Wealth (SHIW), a total of sevenindependent cross-sections representative of the Italian population. InSection 3 we report the age-profile of total and private saving estimatedfrom cohort data. Apart for measurement errors and capital gains, totalsaving defined as earned income minus consumption should roughly equalthe change in total households’ wealth (the sum of private and pensionwealth). In Section 4 we thus add to private wealth an estimate of thepresent discounted value of future pension benefits, net of the present valueof social security contributions. We then compare the age-saving profilesobtained as difference of flow variables and change in stocks.

Our aim in this paper is mainly to perform an accounting exercise, but itis sometimes the case that accounting exercises shed light on empiricalpredictions of theoretical models. In Section 4 we also discuss theimplications of the estimated age-saving profiles for the interpretation of thedata and for the evaluation on the research on the saving behavior of theelderly. The data suggest that the private age-saving profile (obtained usingthe concept of disposable income) shows limited or no decumulation duringretirement. The profile of total saving (obtained using earned income)indicates instead that during retirement the elderly run down assets(inclusive of pension wealth) at substantial rates. We argue that total savingand total wealth are the relevant measures of saving that one should look at

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if one wants to confront the life-cycle hypothesis with the data. The bequestmotive can more appropriately be studied with reference to private savingand wealth. Even so, we argue that there is not much that can be learnt aboutbequest motives from private wealth trajectories. Section 5 concludes.

2. The repeated cross-sectional data

The age profile of variables like income, consumption or saving cannotbe constructed using purely cross-sectional data, because individuals invarious age classes belong to different generations (cohorts) which differ inmortality rates, preferences and productivity. It is only with panel data thatone can track individuals over time. If they are available, repeated cross-sectional data can partly overcame the absence of panel data. Although thesame individual is only observed once, a sample from the same generation isobserved in a later survey, so that one can track the income or consumptionnot of a same individual but of a sample of individuals born in the sameyear. Our aim is to purge age-saving and age-wealth profiles from cohorteffects, and repeated cross-sectional data are particularly useful in ourcontext. Since this amounts to construct averages of individuals grouped byyear of birth, cohort data can also reduce considerably the amount ofmeasurement error contained in the underlying microeconomic data.

We use a time-series of Italian surveys collected by the Bank of Italy (theSHIW, Survey of Household Income and Wealth). The purpose of thissurvey is to provide detailed data on demographics, consumption, incomeand households’ balance sheets. The data set used in this study includesseven independent cross-sections (1984, 1986, 1987, 1989, 1991, 993, and1995), a total of 52,930 observations. The Appendix describes the mainfeatures of the survey. Further details are reported by Brandolini andCannari (1994).

To gauge the quality of the data, it is useful to compare the SHIWmeasures of the private saving rate with the aggregate national accounts.1

1 In the aggregate defining saving as earned income minus consumption or as disposable incomeminus consumption does not make a great difference. As will be seen, it is the age-profile of thetwo saving measures that differs. The measure that is reported in the table is the conventionalprivate saving obtained using disposable income.

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Table 1 indicates that the survey measure of saving is substantially higherthan the national account measure in all years, because income in the SHIWis more accurately reported than consumption. In fact, Brandolini andCannari (1994) report that disposable income is under-reported by 25percent with respect to the national accounts data, while consumption isunder-reported by 30 percent. This could partly reconcile the level of theaggregate saving rate with the one obtained the microeconomic data. Thisshould be kept in mind when evaluating the saving profiles in the nextsections, especially when we compare the saving profiles obtained as thedifference between income and consumption with those obtained by first-differencing wealth.

Although the saving levels differ, the time pattern of the saving rate inthe SHIW is similar to that of the national accounts. Both measures report asaving decline of about 6 percentage points between 1984 and 1995, and inboth cases the bulk of decline occurs in the second half of the 1980s. Thedecline in saving is not peculiar to our sample period, but follows a trenddecline starting just after the period of high and sustained growth of the1950s and early 1960s.

From its peak in 1962 the Italian private saving rate declined by morethan 10 percentage points by the mid-1990s. Several explanations have beenproposed to explain the fall in the Italian private saving rate. In previouswork (Modigliani and Jappelli, 1990; Jappelli, Guiso and Terlizzese; 1994)we emphasize that the reduction in productivity growth is the main factorexplaining the trend decline in the Italian saving rate, particularly after the1973 oil shock.2 Rossi and Visco (1995) forcefully argue that theaccumulation of social security wealth due to the transition to an unfundedsocial security system and the increasing generosity of the system alsoexplains a substantial portion of the fall in household saving.3 Here we donot try to sort out these two explanations, that should be viewed ascomplementary. Rather, we limit ourselves to a description of the age-saving profiles of Italian households.

2 The positive relation between aggregate saving and productivity growth is one othe majorimplications of the life-cyle hypothesis. It has been recently documented by Modigliani (1990)using aggregate cross-country data.

3 Other explanations focus on the reduced need for precautionary saving due to the increasedavailability of social insurance schemes.

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Using the repeated cross-sections to sort the data by the year of birth ofthe head of the household and by the year in which the household wasinterviewed results in 12 generations. Generation 1 includes all householdswhose head was born between 1910 and 1914, generation 2 those bornbetween 1915 and 1919, and so on up to generation 12, including those bornbetween 1965 and 1969. For each cohort-age-year group we then computeaverage (or median) consumption, income, saving and wealth. The “age” ofthe household is then defined to be the median age within each cell, so that,for instance, generation 1 was 72 years old in 1984 (the year of the firstsurvey) and 83 years old in 1995 (the year of the last available survey).

Households headed by persons older than 80 or younger than 22(regardless of year of birth) are excluded from our analysis. Theseexclusions are motivated by concern over two sources of potential samplebias. The first arises because survival probabilities are generally thought tobe positively correlated with wealth, implying that rich households are over-represented in the oldest age groups. This correlation implies that one mayfind a low rate of decumulation after retirement simply because the poortend to disappear from the sample earlier than the rich. After droppinghouseholds headed by persons who would be over 80 years old, the residualcorrelation between wealth and mortality and between wealth or householdhead-ship should not seriously affect the estimates. But even if it does, theresidual presence of older households will bias the saving and wealthprofiles against the life-cycle model, rather than in its favor, due to thecorrelation between wealth and mortality and the finding that the poor thento decumulate more rapidly than the rich.

The second source of potential bias is a correlation between wealth andyoung household heads peculiar to our sample. In Italy young workingadults with independent living arrangements tend to be wealthier thanaverage, because most young working adults live with their parents.4 Forinstance, the fraction of income recipients below 30 years of age is about 20percent, while the fraction of household heads in that age bracket is less than10 percent. After the excluding few more observations with missing data forconsumption, income or wealth, our final sample covers 50,950 households(see Table 1).

4 The reasons for such behavior includes mortgage market imperfections, which prevent younghouseholds from borrowing, and imperfections in the rental market for housing (Guiso, Jappelliand Terlizzese, 1994).

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The first four columns in Table 2 report the year-of-birth intervals, therange over which the median age of each cohort is observed in 1984 and in1995, and the average cell size for each cohort. Columns (5) and (6) displayaverage disposable income and consumption. The difference between thetwo is reported in column (7) as private saving. The gap between mean andmedian saving (column 8) signals that the saving distribution is skewed. Alarge difference between means and medians characterizes also the wealthdistribution. The skewness suggests that means do not adequatelycharacterize the age-saving or age-wealth profiles. We have thusexperimented with other measures of location. Such experiments produceage-profiles of saving and wealth that are uniformly lower than the onesreported in the next sections. However, the shape of the profiles is notdramatically different, and for brevity they are not reported.

3. The age-profiles of consumption, income and saving

Figure 1 plots the age-consumption profile of the 12 cohorts.Consumption is the sum of durable and non-durable consumption.5 Thenumbers in the graph refer to the generation, going from 1 (the oldest) to 12(the youngest). Each generation is observed at seven different points intimes, one for each cross-section. Since the cross-sections run from 1984 to1995, each generation is observed for 12 years, and therefore each line isbroken (for instance, generation 11 is observed 7 times from age 22 to age33).

The figure shows the typical flat consumption profile predicted by thelife-cycle model. Cohort effects are clearly present in the data, as theconsumption profile for each generation lies below that of the previousgeneration. From the perspective of the life-cycle hypothesis, the best wayof combing the information contained in Figure 1 is to assume that the shapeof the age-consumption profile is the same for each generation, and that itslevel depends on cohort-specific intercepts, reflecting differences inproductivity across generations. This would in fact be the prediction of the

5 The main points of this paper do not depend on the definition of consumption (including orexcluding durables). We use total consumption expenditures because expenditure on durablegoods was not collected in the 1986 SHIW.

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life-cycle model in the absence of uncertainty. Common time effects alsoaffect the data in Figure 1. For instance, for several cohorts consumptionincreases between 1986 and 1987 (the second segment of each broken line),reflecting either measurement errors, or common business cycle shocks.6

The fitted line in Figure 1 is the estimated age-consumption profile of arepresentative individual. It is obtained by the fitted values of a regressionof consumption on a fourth-order polynomial in age, a full set of cohortdummies and a set of restricted time dummies. The latter requiresexplanation. Since age, cohort and time are perfectly collinear variables, anormalization is needed to estimate their effect on consumption. Here wefollow Deaton and Paxson (1994) and estimate the regression requiring thatthe year dummies be orthogonal to a time trend and sum to zero.7 Thisnormalization of time effects is useful, but it is important to keep in mindthat it rules out time-age or time-cohort interaction terms. In all otherfigures reported in this paper the age profiles are constructed in similarfashion.

The hump in consumption over the life-cycle is matched by a similarhump in family size. Figure 2 reports the life-cycle of family size, showingthe arrival and departure of children from the household. In this case cohorteffects are absent in our data, and the entire movements are due to ageeffects. It might be argued that the concave consumption profile in Figure 1reflects the age-profile of family size. Any adjustment that takes intoaccount the life-cycle of family size (e.g., deflating household consumptionby an equivalent scale) would make the age-consumption profile even flatterthan in Figure 1. Although we regard this as very important in manycontext, we do not pursue it here because adjusting for family size is notessential for our basic argument.

6 Two macroeconomic episodes characterize our sample period. The recovery from the 1981-1983recession started in early 1984 and grew in intensity in 1987-88: the average growth rate of GDPduring this expansion was 3 percent. The economy then went into a recession from the secondhalf of 1989 to 1993. Afterwards the Italian economy started a mild recovery.

7 The reason for the normalization of the time dummies is that “any trend in the real data can bearbitrarily reinterpreted as a year trend, or (since year equals age minus cohort plus a constant) astrends in ages and cohorts that are equal but of opposite sign [...] A steady growth in year effectssimply means that consumption is growing with age and declining with cohort, and it isappropriate to attribute the effects to age and cohort, not to time.” (Deaton and Paxson, 1993, p.18-19).

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In Figure 3 we plot earned income, the sum of after-tax earnings andcapital income. For reference, we also report the consumption profileestimated in Figure 1. It is important to stress that our definition of earnedincome does not treat contributions to pension funds and social securitycontributions as taxes, nor pension benefits as income. The reason is thatcontributions entitle the household to a stream of future income, while theaccrual of pension benefits is exactly offset by a decumulation of the stockpension wealth, which is by definition annuitized. Thus contributions arebest defined as mandatory saving, and pension benefits as mandatorydissaving.

It is not easy to estimate the relation between the flow of contributionsand the pension rights that they entitle the household. In a fully fundedsystem such relation depends on the real return of the pension fund. In anunfunded social security system, the relation depends on future legislationand on the implicit return of the social security system. For instance, if thereis neither population or productivity growth, if the social security system isin equilibrium, and if future legislation does not change, one dollar ofcontributions increases the stock of social security wealth by one dollar, andtherefore represents “true” saving. In practice, with productivity andpopulation growth the real return to one dollar of contribution can bepositive, as it has been the case in the Italian economy for the last highgrowth decades. On the other hand, the system may be structurallyunbalanced, with pension provisions that do not match contributions. If thenthe system is unable to pay its promises, the return of contributions isnegative.8

Thus, it should be recognized that the extent to which social securitycontributions should be counted as part of income depends on the extent towhich pension contributions actually increase the stock of wealth. In ourbaseline case we define mandatory saving as the total amount ofcontributions actually paid by each worker. In the SHIW earnings arereported net of taxes and contributions, and contributions are a flat tax forindividuals, increasing gradually from 24 percent of gross earnings in 1984

8 See Rossi and Visco (1995) and Jappelli (1995) for examples of calculations of social securitywealth in time series and cross-sectional data, respectively. Franco et al. (1994) provide similarcalculations in constructing Italian generational accounting.

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to 27 percent in 1995.9 It is therefore straightforward to rescale income inproportion.10 Pension benefits are easier to measure, being reported by allindividuals as part of their income.

The profile of income earned in Figure 3 peaks around the age of 50, andrapidly declines after age 55, a reflection of the increasing number of retiredin the older age groups. Retirement income is then provided mainly bycapital income (i.e, the return to private wealth). Cohort effects are againvery clearly seen affecting the resources of each generation, as the brokensegment for successive older generations lie below the ones of youngergenerations.

Figure 4 plots total saving, the difference between earned income andconsumption. The saving profile is clearly hump-shaped. Before retirementtotal saving is about 15 millions lire (or $9,000). Around age 65, saving fallsto zero. Households in the older age-groups dissave about 10 millions lireper year (roughly $6,000). But note that the region of positive saving ismuch larger than that of negative saving, indicating that either consumptionis underestimated, or that households do not consume all their wealth duringretirement. More on this below.

The conventional definition of disposable income is obtained bysubtracting mandatory saving from earned income (i.e. subtracting socialsecurity contributions and adding back pension benefits). The effect of thisadjustment is to obtain a much flatter age-income profile in Figure 5. Notethat disposable income is now fairly high even in old age, given thegenerous benefits provided by the Italian social security system. Contrary toFigure 4, disposable income exceeds consumption at all ages, a fact that hasbeen interpreted as being at variance with the life-cycle hypothesis.

In Figure 6 we plot private saving, or the difference between disposableincome and consumption. Removing from income all mandatory saving(whose purpose is precisely to smooth consumption) results in an incomeprofile that is very similar to the consumption profile, so that saving will be,

9 In Italy part of the contributions are paid by the employee, and part by the employer. But clearlythis is immaterial: in both cases it is the employee who actually has the burden of paying thecontributions (as well as of being entitled to a pension).

10 For the self-employed the contribution rates are actually different than for employed workers.Given that we work with large samples and aggregate over 5-year bands, excluding the self-employed does not change appreciably the graphs.

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by construction, relatively flat over the life-cycle. Note that the age behaviorof saving so calculated in Figure 3 is quite inconsistent with the age path ofprivate wealth discussed below, which is clearly more humped shaped, andwith the implied saving estimated from assets data (see Section 4).

Similar flat age-saving profiles for countries in which the amount ofmandatory saving is substantial have been noted by several studies. To takejust a few recent examples. Poterba (1994) summarizes the evidence for thegroup of most industrialized countries, Alessie et al. (1997) for theNetherlands, and Paxson (1996) for the US and the UK.11 One of thereasons for these flat age-saving profiles is that these studies neglect tocount mandatory saving, whose main purpose is in fact to smoothconsumption. Figure 7 shows that the size of mandatory saving anddissaving (the difference between total and private saving) is verysubstantial in the Italian economy: contributions average 6 or 7 millions upto retirement age, matched by generous pension provisions (about 15millions lire). The figure also points out that Italians retire relatively early(around age 60), given again generous early retirement rules.

Starting with Feldstein (1974), several studies have analyzed the effect ofsocial security on private saving. This effect is rather complex. In principle,an increase in contributions and benefits should reduce private saving andleave total saving unaffected. In practice, social security system tend toencourage early retirement, which would tend to increase private saving.Even though by definition total saving is the sum of private and mandatorysaving, it is not true that an increase in mandatory saving will reduce privatesaving in proportion. Most empirical studies suggest in fact that the offseteffect between private and mandatory saving is well below unity.

As mentioned, given the generosity of Italian social security system, andits actual and projected deficits, it is not likely that all contributions paid bycurrent workers truly represent saving. In Figure 7 it is assumed that only 20percent of gross earnings represents earned income, and treat the remainingportion of contributions as a flat income tax.12 The overall shape of saving

11 This latter study also presents flat age-saving profiles in Taiwan and Thailand, in which theamount of mandatory saving is much more limited. The evidence in these countries is thereforemuch less favorable to the life-cyle hypothsis than in other developed countries.

12 Conceptually, this is similar to the “old-age tax” computed by Gokhale, Kotlikoff and Sabelhaus(1996).

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by age is qualitatively unaffected, and therefore does not modify the basicinsights of this section.

In comparison with national account data, the SHIW consumption ismore severely underestimated than income (30 percent against 25 percent,respectively). One could thus compute total and private saving by “blowingup” income by 25 percent, and consumption by 30 percent. This adjustmentreduces the level of saving at all ages, but does not change the shape of theage-consumption profile, and therefore the shape of the age-saving profile.In particular, private saving is again flat over the life-cycle, and negativesaving in old age are not observed.

4. The age-wealth profile

It is useful to complement the analysis of saving by comparing the ageprofile of private wealth (real plus financial) and of total wealth (the sum ofprivate wealth and pension wealth). In principle, saving equals the change inassets. Private saving, as defined in the previous section, should be equal tothe change in private wealth. Similarly, total saving should correspond tothe change in total wealth. In practice, saving measures derived from flow orstock data may differ because of measurement errors and capital gains.

Total wealth is the sum of private wealth and pension wealth. Since thefraction of Italian households that contributes to private pension funds istiny, they can be safely neglected. Pension wealth is then defined as thedifference between the discounted value of social security benefits anddiscounted value of social security contributions. Constructing the latterrequires assumptions about expected benefits and expected contributions.As for mandatory saving, both depend on future legislation.

The 1995 pension reform of the social security system will graduallyimplement changes in eligibility rules, accrual rates and pension age. Ourestimate of social security wealth abstracts from most of these institutionaldetails, and aims only at providing a rough estimate of expectedcontributions and benefits, based on legislation prevailing at the end of the1980s (the mid-point of our sample). It is not our purpose here to constructprecise measures of social security wealth, but only to obtain a benchmark-indicator to be compared with private wealth. The assumptions needed tocompute social security wealth are described in the Appendix.

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Using the same cohort data in the previous figures, Figure 9 reports theage-profile of total wealth, the sum of pension wealth, financial wealth, realassets, net of liabilities. As in the previous figures, the fitted line shows theage-wealth profile of a representative individual, adjusted for cohort effects.Total wealth is clearly humped-shaped. Early in life wealth is 100 millionlire (about 5 times consumption), peaks at about 350 millions (about 16times consumption), and starts declining after age 60. For older households(aged 80) total wealth is considerably reduced, about 180 million lire (or 9times consumption).13

The role of pension wealth in providing for retirement is very important,as shown in Figure 10. Pension wealth starts roughly at zero (those whoenter the labor force have not yet accumulated for retirement). Theretirement peak is slightly less than 200 million lire, not very different thanprivate wealth.14 Thus through life about half of household wealth isannuitized. Given long life expectancies (about 10 years for the older agegroup) social security wealth is still about 100 million lire even at age 80.

The age-profile of total wealth (and of total saving) is useful to check ifwealth is hump-shaped, as predicted by the life-cycle model. However, theage-profile of private wealth reported in Figure 11 (obtained subtractingpension wealth from total wealth) is useful for a different purpose, i.e. toshed light on the importance of intergenerational transfers, which is thesubject of a very large literature. It has been sometimes argued that thedistinctive element of the life-cycle hypothesis is the absence ofintergenerational transfers. But this is a mistake. It is only a matter ofconvenience that in the elementary version of the life-cycle modelhouseholds start with zero assets, so that wealth increases only with savingsand is entirely consumed in life. In order to distinguish the life-cyclehypothesis from other theories (for instance, a model in which bequests arethe main motives for saving) one must show that wealth finances retirementconsumption, i.e. that wealth is hump-shaped (as in Figure 9).

But in order to assess the importance of intergenerational transfers, andof bequest motives in particular, one may want to look at the age-profile of

13 This pattern is even more evident for the age-profile of median wealth14 These numbers are broadly consistent with Rossi and Visco (1995) and Franco et al. (1994). The

latter, in particular, shows that pension wealth is about 200 million lire at retirement age (seeTable 4.5, p. 144).

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private (or bequeathable) wealth. This is the only component of total wealthwhich can be passed to future generations if it is not consumed before thehousehold dies. By definition, annuitized wealth disappears when the retireddies (even though part of wealth is transferred through survivors’ benefits,the survivors cannot transfer the capital to future generations).

Suppose one observes a hump in total wealth, but not in private wealthwhich increases after retirement. This must imply that part of pensionwealth is used to increase private wealth. If the retired continue toaccumulate bequeathable wealth, the most natural interpretation is that theyplan to leave a bequest. But the age-wealth profile in Figure 11 showsinstead that private wealth declines at least after the age of 60. Can we takethis as an indication that bequest motives are not important in our sample?The answer is no, and for at least three reasons: measurement error,presence of inter vivos transfers, and involuntary bequests.

First of all, there is an inconsistency between our wealth and savingmeasures. In principle, saving equals the first difference of wealth. This isactually reflected in the pattern in Figure 4 (total saving) and Figure 12(where we plot the change in total wealth). Note however that the commonpattern is entirely due to the fact that mandatory saving roughly equals thechange in pension wealth. Instead, the profile in Figure 6 (where privatesaving is defined as disposable income minus consumption) is ratherdifferent than in Figure 12 (where private saving is defined as the change inprivate wealth). While private wealth peaks in the age-group 55-60, privatesaving after that age-group is large and positive, even for the oldest age-groups.

The information available in the SHIW does not yet allow us to indicateif the saving profile computed on the basis of income and consumption ismore reliable than that obtained by first-differencing wealth. If the amountof under-estimation of wealth is constant between different surveys, anestimate of saving obtained subtracting wealth in year t from wealth in yeart+1 might be more reliable than an estimate based on flow variables in thesame survey. However, if the true saving profile is better approximated bythe wealth data, it should also be the case that the amount of measurementerror in consumption and income are age-dependent (for instance, thatconsumption is more severely under-estimated in old age). At the momentthis is a pure guess, and we have therefore no elements to claim that eitherone of the two measures of saving is superior to the other.

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The second reason why one cannot infer the importance of bequestmotives from the shape of the saving profile. In fact, even if private savingwas negative in old age, this would not be sufficient to reject the hypothesisof bequest motives. If a retired consumes part of his wealth to supplementhis pension, this does not imply that he or she does not plan to leave abequest. Wealth may also decline because people make inter vivos transfers.There is in fact very little that can be inferred about the size ofintergenerational transfers or the presence of bequest motives from Figure10. What we observe is that in the 25 years (from age 55 to age 80)bequeathable wealth is about halved, and private wealth at age 80 is about 5times consumption, certainly not a huge amount. But even this amount tellsus very little about bequests, because clearly bequests will be whatever willbe left after the survivor spouse dies (since the life-cycle hypothesis is atheory of household saving, infra-family transfers should not be counted asbequests).

Direct evidence on the importance of beqeusts and gifts is available inthe case of the Italian economy. A special section of the 1991 SHIW askseach member of the household to report the number and amount of bequestsand gifts received in the past from parents or other relatives. Thisinformation is used in Guiso and Jappelli (1996) to compute the aggregateshare of transfers in total wealth. On average, each household received 50.4million lire (equivalent to $31,500 in 1995), 24.3 percent of private wealth(20.2 percent in bequests plus 4.1 percent in gifts). Capitalizing bequestsand gifts at a net real interest rate of 2 percent, the share of intergenerationaltransfers in bequethable wealth comes to 35.8 percent (29.5 percent bequestsplus 6.3 percent gifts). Similar shares of transfer wealth in Italy is obtainedby Guiso and Cannari (1994) using different methods.

A final caveat why the wealth trajectory is not informative about bequestmotives is in order. The share of transfer wealth cannot be taken as ameasure of the importance of bequest motives for the obvious reason thatpart of bequeathed wealth was intended to finance consumption. Given lifeuncertain, risk averse consumers will always find optimal not to run downtheir assets to zero.

18

5. Conclusions

We use Italian cohort data to construct a measure of total saving, definedas the difference between earned income and consumption. Earned incomeincludes mandatory saving (in our case, social security contributions or aportion of such contributions), but excludes pension benefits. Since thelatter corresponds to a depletion of annuitized wealth they should not becounted as income. The second step of our analysis is to construct a measureof total wealth, the sum of pension and private (or bequethable) wealth.Since the age-profile of earned income is hump-shaped, and consumption isrelatively flat through life, both total saving and total wealth areconsiderably hump-shaped. The shape of this profile therefore agrees withthe prediction of the life-cycle model, which suggests that the youngaccumulate resources to be spent during retirement.

We also note that the hump-shape in saving and wealth depends mainlyfrom the fact that in modern societies a great deal of saving occurs throughmandatory retirement plans, such as social security and private pensionfunds, while dissaving occurs mainly through annuitized wealth. One mayquestion the fact that people cannot choose the amount of mandatory saving,which should therefore be ignored for understanding people’s behavior. Butsince people can change private saving in response to changes in mandatorysaving, total saving is the relevant measure of the change in assetsaccumulated for retirement. And after all, the existence of mandatory savingprograms and the widespread implementation of retirement plans should beinterpreted as the social approval of schemes designed to ensure people withadequate reserves to be spend during retirement.

Since private saving and private wealth (obtained subtracting mandatorysaving and pension wealth) are not relevant indicators of the retirementmotives for saving in modern societies, cross-country comparisons ofprivate saving (disposable income minus consumption) can be highlymisleading if proper account is not taken of the difference in mandatorysaving, especially for developed countries in which mandatory retirementprograms play a prominent role. The shape of one component of totalsaving, i.e. private saving, cannot therefore be cited as evidence against thelife-cycle model.

Even if private wealth and private saving, taken in isolation, are notinformative about the importance of saving for retirement, they might beuseful to evaluate the importance of bequest motives, because pension

19

wealth is not bequethable. In our sample we find that private saving ispositive and rather flat through age, but that private wealth is significantlyhump-shaped. The data do not allow us to be precise as to which indicator(first difference of stocks or flows) is more reliable. But even if they did,there is very little that can be learned from wealth trajectories about bequestmotives. Transfers may occur inter vivos. The size of transfers for the oldestage groups differs from the amount of bequeathed wealth. Finally, manybequests are involuntary.

Some studies erroneously focusing on private saving and wealth haveconcluded that the elderly continue to accumulate assets after retirement, orthat they decumulate at rates that are too low to be consistent with the life-cycle model. Our figures show instead that the elderly decumulate verysubstantial amounts of assets because a large portion of wealth is annuitized.We also find that in Italy private wealth for the oldest age group is aboutfive times consumption. Even though this is small fraction of lifetimewealth, it is still an open question to try to understand why do the elderlynot consume all their wealth before they die.

20

References

Alessie, Rob, Arie Kapteyn and Frank Klijn (1997), “Mandatory Pensions andPersonal Savings in the Netherlands”. CentER, Tilburg University, mimeo.

Auerbach, Alan, J., Gokhale, Jagadeesh, and Laurence J. Kotlikoff (1991),“Generational Accounts: a Meaningful Alternative to Deficit Accounting”,in D. Bradford (ed.), Tax Policy and the Economy, vol. V. Chicago:University of Chicago Press.

Brandolini, Andrea, and Luigi Cannari (1994), "Methodological Appendix: theBank of Italy's Survey of Household Income and Wealth", in Albert Ando,Luigi Guiso and Ignazio Visco (eds.), Saving and the Accumulation ofWealth. Essays on Italian Household and Government Saving Behavior.Cambridge: Cambridge University Press.

Deaton, Angus and Christina Paxson (1994) “Saving, Aging and Growth inTaiwan”, in David Wise (ed.), Studies in the Economics of Aging. Chicago:University of Chicago Press.

Feldstein, Martin (1976), "Social Security and Saving: the Extended Life-CycleTheory," American Economic Review 66, 77-87.

Daniele Franco, Jagadeesh Gokhale, Luigi Guiso, Laurence J. Kotlikoff and NicolaSartor (1994), “Generational Accounting: The Case of Italy”, in AlbertAndo, Luigi Guiso and Ignazio Visco (eds.), Saving and the Accumulationof Wealth. Essays on Italian Household and Government Saving Behavior.Cambridge: Cambridge University Press.

Gokhale, Jagadeesh, Laurence J. Kotlikoff and John Sabelhaus (1996),“Understanding the Postwar Decline in US Saving: a Cohort Analysis”,Brookings Papers on Economic Activity 1, 315-390.

Guiso, Luigi, Tullio Jappelli, and Daniele Terlizzese (1994), "Why is Italy's SavingRate so High?", in Albert Ando, Luigi Guiso and Ignazio Visco (eds.),Saving and the Accumulation of Wealth. Essays on Italian Household andGovernment Saving Behavior. Cambridge: Cambridge University Press.

Guiso, Luigi, and Tullio Jappelli (1996), "Intergenerational transfers, borrowingconstraints and the timing of home ownership", Temi di Discussione n.275. Rome: Bank of Italy.

Jappelli, Tullio (1995), "Does Social Security Reduce the Accumulation of PrivateWealth? Evidence from Italian Survey Data," Ricerche Economiche 49, 1-31.

21

Jappelli, Tullio, and Marco Pagano (1994), "Personal Saving in Italy", in JamesPoterba (ed.), International comparison of personal saving. Chicago:University of Chicago Press.

Modigliani, Franco (1986), "Life-Cycle, Individual Thrift, and the Wealth ofNations", American Economic Review 76, 297-313.

Modigliani, Franco (1990), “Recent Declines in Saving Rates: a Life-CyclePerspective”, Rivista di Politica Economica, December, 5-42.

Modigliani Franco, and Tullio Jappelli (1990), "Why Has the Italian NationalSaving Rate Declined?", in Salvatore Biasco, Alessandro Roncaglia, andMichele Salvati (eds.), Market and Institutions in Economic Development.London: MacMillan Press.

Paxson, Christina (1996), “Saving and Growth: Evidence from Micro Data”,European Economic Review 40, 255-88.

Poterba, James (1994), "Introduction", in James Poterba (ed.), InternationalComparison of Personal Saving. Chicago: The University of ChicagoPress.

Rossi, Nicola, and Ignazio Visco (1995), "National Saving and Social Security inItaly", Ricerche Economiche 49, 329-356.

22

APPENDIX

A1. The Survey of Household Income and Wealth

The Bank of Italy Survey of Household Income and Wealth (SHIW) wasconducted on a yearly basis from 1965 to 1987 (with the exception of 1985).Up to 1984 the number of participant households in a typical year wasaround 4,000. In 1986 the sample size was doubled, and since 1987 thesurvey has been run every other year. The most recent available survey isfor 1995. The survey is representative of the Italian population becauseprobability selection is enforced at every stage of sampling. The unit ofobservation is the family, which is defined to include all persons residing inthe same dwelling who are related by blood, marriage or adoption.Individuals selected as "partners or other common-law relationships" arealso treated as families. The interviews are conducted during the first threemonths of the year; thus flow variables refer to the previous calendar year,and stock variables are end-of period values. The use of sample weights isrecommended, particularly for 1987, a year in which the survey over-sampled wealthy households (Brandolini and Cannari, 1994). All statisticsreported in this paper use sample weights. Before 1980 the survey is notavailable on tape. Up to 1983 the age variable, which is central to thepresent analysis, is coded in 10-year bands, with an open interval forindividuals over 65 years of age. Since this precludes the construction of thecohort indicators, we use 1984 as the starting point for the analysis. The dataset includes the 1984, 1986, 1987, 1989, 1991, 1993 and 1995 SHIW.Wealth and consumption are converted into 1995 lire using the CPI deflator.

EARNED INCOME Sum of households earnings, transfers, pension benefits,capital income and income from financial assets, net of taxes and socialsecurity contributions. Earnings are the sum of wages and salaries, self-employment income, less income taxes and social security contributions.Wages and salaries include overtime bonuses, fringe benefits and paymentsin kind, and exclude withholding taxes. Self-employment income is net oftaxes and includes income from unincorporated businesses, net ofdepreciation of physical assets.

23

DISPOSABLE INCOME Earned income plus pension benefits minus socialsecurity contributions.

PRIVATE WEALTH Sum of household's net financial assets and real assets.Real assets are the sum of real estate, unincorporated business holdings andthe stock of durable goods less interest on household liabilities (consumercredit and mortgage loans).

A2. Pension wealth

Given that in Italy private pension funds are held by very few workers,pension wealth largely coincides with social security wealth. The stream ofsocial security benefits that will accrue to a person of age a expecting toretire at age n is equal to

S pyg

rnn

T n

τ

τ

ττ

τ

,>

−

∑+

+

1

1 (A.1)

where T is the maximum length of life, Sτ,n

the probability of surviving from

age τ to age n, p the expected replacement rate, yτ expected earnings atretirement, g

τ the rate of growth of pension benefits during retirement and r

the real rate of interest at which people discount future benefits.

Assuming that productivity growth before retirement is a constant rate g,so that y y ga

aτ

τ= +

−( )1 , the present discounted value of the social securitybenefits of an individual of age a is

SSW S pyg

rS

g

ra a a

a

nn

T n

=+

+

+

+

−

>

−

∑, ,ττ

τ

τ

τ

τ

τ1

1

1

1, (A.2)

where SSW is social security wealth and Sa,t

the survival probability from

age a to age τ.

24

To construct SSW we need to make assumptions about each of the aboveparameters. We do not distinguish between men and women and assumethat the household retires at age 60. The replacement rate is assumed to be70 percent, in line with 1980s figures. We use mortality tables for women toimpute the survival probabilities Sa,τ and Sτ,n. The sum is truncated at age100. The probabilities refer to the year 1989. The source is ISTAT,Annuario Statistico Italiano, Table 2.19.

Earnings ya use to compute SSW are estimated by the fitted value of a

regression of earnings on a fifth-order age polynomial, a set of cohortdummies and a set of restricted time dummies (as explained in the text).Using the fitted values form this regression, we project for each age-year-cohort group the earnings at the assumed retirement age of 60.

SSW is constructed on the assumptions that g=0.03, r=0.03 and gτ =0.The latter implies that pensions are fully indexed to the cost of living but notto current wages. The ratios (1+g)/(1+r) and (1+gτ)/(1+r) are, respectively,the net discount factors of pension benefits for pre- and post-retirementyears. Net social security wealth (NSSW) is computed as the differencebetween the discounted value of benefits and the discounted value ofcontributions:

NSSWa = SSW

a - SST

a (A.3)

where social security contributions are assumed to be 25 percent in all years.Contributions to private pension funds are not included in our calculation;however, they account for a tiny portion of Italians' total assets and can besafely neglected. For pension recipients (the retired) social security wealth isgiven by:

SSW S bg

ra n an a

T n a

=+

+

>

−

∑ ττ

,

1

1(A.4)

where ba is the current pension andd the other symbols are defined above.

Pension benefits ba include all types of pension (old-age, social and

disability pensions). Survival probabilities refer again to women.

25

TABLE 1

A COMPARISON BETWEEN MEASURES OF AGGREGATE SAVING DERIVED

FROM NATIONAL ACCOUNTS AND SURVEY DATA

Year Nationalaccounts data

Survey data

(SHIW)

Total number ofobservations

Observations used

(1) (2) (3) (4)

1984 20.2 31.5 4,172 3,878

1986 17.6 30.3 8,022 7,593

1987 17.6 25.6 8,027 7,602

1989 16.3 26.4 8,297 8,040

1991 16.5 24.0 8,188 7,947

1993 14.5 25.0 8,089 7,931

1995 14.0 23.4 8,135 7,959

Note: The aggregate saving rate in column (1) is the private saving rate as computed on thebasis of the 1995 Annual Report of the Bank of Italy. The aggregate saving rate in column(2) is computed using the SHIW dividing the total private saving by total disposableincome. The estimates in column (2) use sample weights and the entire data set for eachsurvey.

26

TABLE 2

CELL SIZE, INCOME, CONSUMPTION AND SAVING

BY YEAR OF BIRTH OF THE HOUSEHOLD HEAD

Year ofbirth

Medianage in1984

Medianage in1995

Averagecell size

Disposable

income

Totalconsumption

Privatesaving(mean)

Privatesaving

(median)

(1) (2) (3) (4) (5) (6) (7) (8)

1910-14 72 83 383 23.5 16.6 6.8 3.4

1915-19 67 78 398 26.0 18.5 7.5 4.4

1920-24 62 73 675 31.0 21.9 9.1 4.8

1925-29 57 68 751 37.6 26.2 11.5 6.6

1930-34 52 63 795 41.7 29.5 12.2 7.6

1935-39 47 58 865 43.7 31.4 12.3 7.7

1940-44 42 53 793 42.8 31.7 11.0 7.5

1945-49 37 48 867 41.0 30.9 10.1 7.3

1950-54 32 43 697 38.0 29.1 8.6 6.2

1955-59 27 38 596 34.3 26.7 7.6 5.1

1960-64 22 33 357 30.6 25.0 5.6 4.6

1965-69 17 28 203 29.7 24.9 4.8 3.4

Note Income, consumption and saving are expressed in millions of 1995 lire. Samplestatistics are computed using sample weights. Households headed by individuals older than80 and younger than 22 are excluded.

Figure 1

Consumption

20 30 40 50 60 70 80

0

10

20

30

40

50

60

11

1 11

22

22 2 2

2

33

33 3 3

3

44

4

44 4

4

5

5

5

55

556 6

66 6

6 6

7 7

7 7 7 7 7

8 8

88 8 8 8

9 9

9 9 9 9 9

10 10

10 10 10 10 10

11 11

1111

1111 11

1212

12 12

Figure 2

Family size

20 30 40 50 60 70 80

0

1

2

3

4

5

11 1 1 1

22

2 2 2 22

33 3

33

3 3

44 4

44

44

55 5

5

5

5 5

66 6

6 66

6

7 7 7 7 77

78 8 8 8 8 8 8

9

9 9 99 9 9

10

101010

1010 10

11

1111 11

1111 11

1212

12 12

Figure 3

Earned income Consumption

20 30 40 50 60 70 80

0

10

20

30

40

50

60

1 1 11

1

22 2

2 2 2 2

3

3

3

3

33 3

4

4

4

4

4

44

5

5

5

5

5

5

5

6

6

6

6

6

6

6

7

7

77

7 7

7

8 8

8

88 8

8

99

99

9 99

1010

1010 10 10 10

11 11

11 11 11 11 11

12 12 12 12

Figure 4

Total saving

20 30 40 50 60 70 80

-20

-10

0

10

20

30

40

1 11

1 1

2 22 2 2 2 2

33

3

3

33 3

4

44

4

4

4 4

5

5

5

5

5

5

5

6

66

6

6

6

6

77

77

7 7

7

88

88

8 88

9

99

99 9

910 1010 10 10 10

10

1111

11 11 1111 11

12 1212 12

Figure 5

Disposable income Consumption

20 30 40 50 60 70 80

0

10

20

30

40

50

60

11

1 11

22

22

2 22

33

33

33

3

44

4

4

44

4

5

5

5

5

55

566

6

66

6 6

77

7 7 77

7

8 8

88

8 8 8

99

99 9 9

9

1010

10 10 10 10 10

11 11

1111 11 11 11

12 1212

12

Figure 6

Private saving

20 30 40 50 60 70 80

-20

-10

0

10

20

30

40

1 1 1 1 12

2 2 2 2 2 2

3 3 3 33

3 3

4 44

44 4 4

5

55

55 5 56

6 6 66 6 6

7 7 7 7 77

78 8

88

88 8

99 9 9

9 99

101010 10 10 10

1011

1111 11 1111 11

12 12

1212

Figure 7

Mandatory saving

20 30 40 50 60 70 80

-20

-10

0

10

20

30

40

11

1 1 12

2

2 22 2 2

33

3

33 3 3

44 4

44

4 4

55

5

5

5

55

66

6

6

6

6

6

77

77

77

7

8 88

8 8 8 899

99 9 9 9

10 1010 10 10 10 10

11 1111 11 11 11 11

12 1212 12

Figure 8

Total saving (contr.=20%)

20 30 40 50 60 70 80

-20

-10

0

10

20

30

40

11

11 1

2 22 2 2 2 2

33

3

3

33 3

4

44

4

44 4

5

5

5

5

5

55

6

66

6

6

6

6

77

77

7 7

7

88

88

8 889

99

99 9

910

1010 10 10 10

10

1111

11 11 1111 11

12 1212

12

Figure 9

Total wealth

20 30 40 50 60 70 80

0

100

200

300

400

500

1

1

1 11

2

2

22

22

2

3

3

33 3

3

3

44

4

4 4

4

4

5

5

5

55

55

6 6

6

6

66

6

7 7

7

7

7

7

7

8 8

88

8

8

8

9 9

99

9

9

9

10 10

1010

10

10

10

1111

1111

11

1111

12 12

1212

Figure 10

Pension wealth

20 30 40 50 60 70 80

0

100

200

300

1

1

11

1

2

2

2

2 2

2

2

33

33

3

3

3

4 4

4

44 4

4

55

5

5 5

55

6 6

6

66 6

6

7 7

7

77

7

7

8 8

88

8 8

8

9 9

99

9 9

9

1010

10

1010 10

10

11 11

11

11 1111

11

1212 12

12

Figure 11

Private wealth

20 30 40 50 60 70 80

0

100

200

300

1

1

1 11

22

2 2

2

2

23

3

3 33 3

34

4

4

44

44

5

5

5

55

5

5

6 6

6

6

66

6

7 7

77

7

7 7

88

88

8

8 8

9 9

9

9

9

99

1010

10

1010

1010

11

11

1111

11

1111

12 12

1212

Figure 12

Change in private wealth Change in total wealth

20 30 40 50 60 70 80

-20

-10

0

10

20

30

40