The Age-Saving Profile and the Life-Cycle Hypothesis

Transcription

1 CENTRO STUDI IN ECONOMIA E FINANZA CENTRE FOR STUDIES IN ECONOMICS AND FINANCE WORKING PAPER no. The Age-Saving Profile and the Life-Cycle Hypothesis Tullio Jappelli and Franco Modigliani November 8 DIPARTIMENTO DI SCIENZE ECONOMICHE - UNIVERSITÀ DEGLI STUDI DI SALERNO Via Ponte Don Melillo FISCIANO (SA) Tel. 08- /8 - Fax csef@xcom.it

2 WORKING PAPER no. 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 negative for the retired, so that wealth should be hump-shaped. Yet, if one looks at the microeconomic 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 a concept of income that does not take into account the presence of pension arrangements. In fact, disposable income treats pension contributions as taxes, and pension benefits as transfers. 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 a drawing from the pension wealth accumulated up to retirement. We use Italian repeated cross-sectional data from 8 to to show the importance of this adjustment for the evaluation of the saving behavior of the elderly. We thank Arie Kapteyn and Chris Paxson for comments. This paper is part of a research project on Structural Analysis of Household Savings and Wealth Positions over the Life- Cycle. Financial support has been provided by The Training and Mobility of Researchers Network Program (TMR) of the European Commission DGXII and by the Italian National Research Council (CNR). * CSEF, University of Salerno, and CEPR. ** Sloan School of Management, MIT.

3 Table of contents. Introduction. The repeated cross-sectional data. The age-profiles of consumption, income and saving. The age-wealth profile. Conclusions References APPENDIX A. The Survey of Household Income and Wealth A. Pension wealth

4 . Introduction The life-cycle hypothesis posits that the main motivation for saving is to accumulate resources do be drained down for later expenditure and in particular during retirement. Saving should be positive for young households and negative for the retired, so that wealth should be humpshaped (Modigliani, 8). Yet, if one looks at the microeconomic evidence on saving rates by age, dissaving by the elderly is seldom observed. To take just one recent example, in the introductory essay of a collection of country studies on saving, Poterba () reports that in virtually all nations the median saving rate is positive well beyond retirement, concluding that the country studies provide very little evidence that supports the life-cycle model. Based on the country studies, Poterba also reports that the median saving rate in the age class 0- is. percent in the United States and percent in Canada. And in Italy and Japan the median saving rates for those aged and greater exceeds 0 percent of disposable income (Table )! These figures are inconsistent not only with the elementary version of the life-cycle hypothesis, but also with elaborate versions of the model with life uncertainty, precautionary saving and accidental bequests. In its basic formulation, the life-cycle hypothesis posits that saving behavior is forward looking and driven by the desire to prepare for future expenditures above later income throughout life. The main foreseeable event in one s life is retirement, when income may be expected on average to dwindle to a level well below active life consumption. This implies that an essential observable implication of the life-cycle hypothesis is that there must be phases of life - notably during the retirement period - when saving is negative and wealth is reduced. Adding life uncertainty, precautionary saving, and liquidity constraints, as in more elaborate versions of the model, affects the age after which one should start observing negative saving and wealth decumulation, but not the main implication of the theory that individual wealth must eventually fall with age. Thus, the widely reported positive saving rates at all ages represent a strong contradiction of the theory, and are consistent only with alternative behavioral models of consumption, for instance models in which bequests represent a prominent role, either because consumers are altruistic or because they derive utility from terminal wealth. Yet the saving rates that are often computed on microeconomic data are based on a concept of disposable income that does not take into account the presence of pension arrangements. In order to check the validity of the life-

5 cycle hypothesis, saving should be defined as the difference between (net of tax) earnings plus capital income and consumption. We refer to this income concept as earned income. This differs from disposable income as conventionally measured because the latter ignores pension arrangements. Thus, it should not come as a surprise that the implications of the theory are not born out by the data if the theory is confronted with the wrong data. Disposable income treats social security contributions as taxes, and pension benefits as transfers. But since contributions entitle the payer to receive a pension after retirement, they should be regarded as life-cycle saving and hence included back to income. On the other hand, pension benefits accruing to the retired do not represent income produced, but rather a drawing from the social security wealth accumulated up to retirement. The same issue arises when income from a private pension fund is treated as an ordinary component of disposable income, rather than as wealth depletion during retirement. The greater the amount of mandatory saving and the replacement rate assured by the social security system, the greater is the difference 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. Mandatory saving is then the difference between total and private saving. A corresponding break-down applies to total wealth, which is the sum of pension wealth and private wealth. Except for capital gains and losses and measurement problems, the first difference of total wealth is total saving, and the first difference of private wealth is private saving. Our data allow us to check if the shape of the age-profile of these two saving concepts are mutually consistent. It is well-known that age profiles of individual variables cannot be estimated using cross-sectional data. Following recent studies, we use a time-series of cross-sections of Italian households to control for cohort effects, and to estimate consumption, income, saving and wealth profiles of a representative individual. Given the features of its social security system, Italy provides the clearest example of the difference between the conventional definition of disposable income and our proposed measure of earned income. But of course the adjustment affects the definition of saving in all countries in which part of saving occurs through mandatory contributions to pension funds or pay-as-you-go social security.

6 The exercise we perform in this paper is closely related to two strands of literature. The first dates back to Feldstein (), who first pointed out that pension wealth should be counted as part of individuals resources, measured social security wealth and argued forcefully that the transition to an unfunded social security regime crowds out private saving. The second, more recent strand of literature, is the intergenerational accounting framework proposed by Auerbach, Gokhale and Kotlikoff () whose aim is to measure how much existing generations can be expected to pay to the government over their remaining lifetimes. Generational accounts provide measures of cohort-specific receipts (including pension transfers, health expenditures, etc.) and payments (including taxes and social security contributions) that can be used to evaluate the intergenerational redistributive impact of fiscal policy. Our focus here is primarily the computation of cohort-adjusted mandatory saving profiles implied by the current social security arrangements. Other types of transfers, such as medical payments, are of course important, but are neglected in the present analysis. In Section we present our data, which are drawn from the 8- Survey of Household Income and Wealth (SHIW), a total of seven independent cross-sections representative of the Italian population. In Section we report the age-profile of total and private saving estimated from cohort data. Apart for measurement errors and capital gains, total saving defined as earned income minus consumption should roughly equal the change in total households wealth (the sum of private and pension wealth). In Section we thus add to private wealth an estimate of the present discounted value of future pension benefits, net of the present value of social security contributions. We then compare the age-saving profiles obtained as difference of flow variables and change in stocks. Our aim in this paper is mainly to perform an accounting exercise, but it is sometimes the case that accounting exercises shed light on empirical predictions of theoretical models. In Section we also discuss the implications of the estimated age-saving profiles for the interpretation of the data and for the evaluation on the research on the saving behavior of the elderly. The data suggest that the private age-saving profile (obtained using the concept of disposable income) shows limited or no decumulation during retirement. 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 saving and total wealth are the relevant measures of saving that one should look at

7 if one wants to confront the life-cycle hypothesis with the data. The bequest motive can more appropriately be studied with reference to private saving and wealth. Even so, we argue that there is not much that can be learnt about bequest motives from private wealth trajectories. Section concludes.. The repeated cross-sectional data The age profile of variables like income, consumption or saving cannot be constructed using purely cross-sectional data, because individuals in various age classes belong to different generations (cohorts) which differ in mortality rates, preferences and productivity. It is only with panel data that one can track individuals over time. If they are available, repeated crosssectional data can partly overcame the absence of panel data. Although the same individual is only observed once, a sample from the same generation is observed in a later survey, so that one can track the income or consumption not of a same individual but of a sample of individuals born in the same year. Our aim is to purge age-saving and age-wealth profiles from cohort effects, and repeated cross-sectional data are particularly useful in our context. Since this amounts to construct averages of individuals grouped by year of birth, cohort data can also reduce considerably the amount of measurement error contained in the underlying microeconomic data. We use a time-series of Italian surveys collected by the Bank of Italy (the SHIW, Survey of Household Income and Wealth). The purpose of this survey is to provide detailed data on demographics, consumption, income and households balance sheets. The data set used in this study includes seven independent cross-sections (8, 8, 8, 8,,, and ), a total of,0 observations. The Appendix describes the main features of the survey. Further details are reported by Brandolini and Cannari (). To gauge the quality of the data, it is useful to compare the SHIW measures of the private saving rate with the aggregate national accounts. In the aggregate defining saving as earned income minus consumption or as disposable income minus consumption does not make a great difference. As will be seen, it is the age-profile of the two saving measures that differs. The measure that is reported in the table is the conventional private saving obtained using disposable income.

8 Table indicates that the survey measure of saving is substantially higher than the national account measure in all years, because income in the SHIW is more accurately reported than consumption. In fact, Brandolini and Cannari () report that disposable income is under-reported by percent with respect to the national accounts data, while consumption is under-reported by 0 percent. This could partly reconcile the level of the aggregate saving rate with the one obtained the microeconomic data. This should be kept in mind when evaluating the saving profiles in the next sections, especially when we compare the saving profiles obtained as the difference between income and consumption with those obtained by firstdifferencing wealth. Although the saving levels differ, the time pattern of the saving rate in the SHIW is similar to that of the national accounts. Both measures report a saving decline of about percentage points between 8 and, and in both cases the bulk of decline occurs in the second half of the 80s. The decline in saving is not peculiar to our sample period, but follows a trend decline starting just after the period of high and sustained growth of the 0s and early 0s. From its peak in the Italian private saving rate declined by more than 0 percentage points by the mid-0s. Several explanations have been proposed to explain the fall in the Italian private saving rate. In previous work (Modigliani and Jappelli, 0; Jappelli, Guiso and Terlizzese; ) we emphasize that the reduction in productivity growth is the main factor explaining the trend decline in the Italian saving rate, particularly after the oil shock. Rossi and Visco () forcefully argue that the accumulation of social security wealth due to the transition to an unfunded social security system and the increasing generosity of the system also explains a substantial portion of the fall in household saving. Here we do not try to sort out these two explanations, that should be viewed as complementary. Rather, we limit ourselves to a description of the agesaving profiles of Italian households. The positive relation between aggregate saving and productivity growth is one othe major implications of the life-cyle hypothesis. It has been recently documented by Modigliani (0) using aggregate cross-country data. Other explanations focus on the reduced need for precautionary saving due to the increased availability of social insurance schemes.

9 Using the repeated cross-sections to sort the data by the year of birth of the head of the household and by the year in which the household was interviewed results in generations. Generation includes all households whose head was born between 0 and, generation those born between and, and so on up to generation, including those born between and. For each cohort-age-year group we then compute average (or median) consumption, income, saving and wealth. The age of the household is then defined to be the median age within each cell, so that, for instance, generation was years old in 8 (the year of the first survey) and 8 years old in (the year of the last available survey). Households headed by persons older than 80 or younger than (regardless of year of birth) are excluded from our analysis. These exclusions are motivated by concern over two sources of potential sample bias. The first arises because survival probabilities are generally thought to be positively correlated with wealth, implying that rich households are overrepresented in the oldest age groups. This correlation implies that one may find a low rate of decumulation after retirement simply because the poor tend to disappear from the sample earlier than the rich. After dropping households headed by persons who would be over 80 years old, the residual correlation between wealth and mortality and between wealth or household head-ship should not seriously affect the estimates. But even if it does, the residual presence of older households will bias the saving and wealth profiles against the life-cycle model, rather than in its favor, due to the correlation between wealth and mortality and the finding that the poor then to decumulate more rapidly than the rich. The second source of potential bias is a correlation between wealth and young household heads peculiar to our sample. In Italy young working adults with independent living arrangements tend to be wealthier than average, because most young working adults live with their parents. For instance, the fraction of income recipients below 0 years of age is about 0 percent, while the fraction of household heads in that age bracket is less than 0 percent. After the excluding few more observations with missing data for consumption, income or wealth, our final sample covers 0,0 households (see Table ). The reasons for such behavior includes mortgage market imperfections, which prevent young households from borrowing, and imperfections in the rental market for housing (Guiso, Jappelli and Terlizzese, ). 8

10 The first four columns in Table report the year-of-birth intervals, the range over which the median age of each cohort is observed in 8 and in, and the average cell size for each cohort. Columns () and () display average disposable income and consumption. The difference between the two is reported in column () as private saving. The gap between mean and median saving (column 8) signals that the saving distribution is skewed. A large difference between means and medians characterizes also the wealth distribution. The skewness suggests that means do not adequately characterize the age-saving or age-wealth profiles. We have thus experimented with other measures of location. Such experiments produce age-profiles of saving and wealth that are uniformly lower than the ones reported in the next sections. However, the shape of the profiles is not dramatically different, and for brevity they are not reported.. The age-profiles of consumption, income and saving Figure plots the age-consumption profile of the cohorts. Consumption is the sum of durable and non-durable consumption. The numbers in the graph refer to the generation, going from (the oldest) to (the youngest). Each generation is observed at seven different points in times, one for each cross-section. Since the cross-sections run from 8 to, each generation is observed for years, and therefore each line is broken (for instance, generation is observed times from age to age ). The figure shows the typical flat consumption profile predicted by the life-cycle model. Cohort effects are clearly present in the data, as the consumption profile for each generation lies below that of the previous generation. From the perspective of the life-cycle hypothesis, the best way of combing the information contained in Figure is to assume that the shape of the age-consumption profile is the same for each generation, and that its level depends on cohort-specific intercepts, reflecting differences in productivity across generations. This would in fact be the prediction of the The main points of this paper do not depend on the definition of consumption (including or excluding durables). We use total consumption expenditures because expenditure on durable goods was not collected in the 8 SHIW.

11 life-cycle model in the absence of uncertainty. Common time effects also affect the data in Figure. For instance, for several cohorts consumption increases between 8 and 8 (the second segment of each broken line), reflecting either measurement errors, or common business cycle shocks. The fitted line in Figure is the estimated age-consumption profile of a representative individual. It is obtained by the fitted values of a regression of consumption on a fourth-order polynomial in age, a full set of cohort dummies and a set of restricted time dummies. The latter requires explanation. Since age, cohort and time are perfectly collinear variables, a normalization is needed to estimate their effect on consumption. Here we follow Deaton and Paxson () and estimate the regression requiring that the year dummies be orthogonal to a time trend and sum to zero. This normalization of time effects is useful, but it is important to keep in mind that it rules out time-age or time-cohort interaction terms. In all other figures reported in this paper the age profiles are constructed in similar fashion. The hump in consumption over the life-cycle is matched by a similar hump in family size. Figure reports the life-cycle of family size, showing the arrival and departure of children from the household. In this case cohort effects are absent in our data, and the entire movements are due to age effects. It might be argued that the concave consumption profile in Figure reflects the age-profile of family size. Any adjustment that takes into account the life-cycle of family size (e.g., deflating household consumption by an equivalent scale) would make the age-consumption profile even flatter than in Figure. Although we regard this as very important in many context, we do not pursue it here because adjusting for family size is not essential for our basic argument. Two macroeconomic episodes characterize our sample period. The recovery from the 8-8 recession started in early 8 and grew in intensity in 8-88: the average growth rate of GDP during this expansion was percent. The economy then went into a recession from the second half of 8 to. Afterwards the Italian economy started a mild recovery. The reason for the normalization of the time dummies is that any trend in the real data can be arbitrarily reinterpreted as a year trend, or (since year equals age minus cohort plus a constant) as trends in ages and cohorts that are equal but of opposite sign [...] A steady growth in year effects simply means that consumption is growing with age and declining with cohort, and it is appropriate to attribute the effects to age and cohort, not to time. (Deaton and Paxson,, p. 8-). 0

12 In Figure we plot earned income, the sum of after-tax earnings and capital income. For reference, we also report the consumption profile estimated in Figure. It is important to stress that our definition of earned income does not treat contributions to pension funds and social security contributions as taxes, nor pension benefits as income. The reason is that contributions entitle the household to a stream of future income, while the accrual of pension benefits is exactly offset by a decumulation of the stock pension wealth, which is by definition annuitized. Thus contributions are best defined as mandatory saving, and pension benefits as mandatory dissaving. It is not easy to estimate the relation between the flow of contributions and the pension rights that they entitle the household. In a fully funded system such relation depends on the real return of the pension fund. In an unfunded social security system, the relation depends on future legislation and on the implicit return of the social security system. For instance, if there is neither population or productivity growth, if the social security system is in equilibrium, and if future legislation does not change, one dollar of contributions increases the stock of social security wealth by one dollar, and therefore represents true saving. In practice, with productivity and population growth the real return to one dollar of contribution can be positive, as it has been the case in the Italian economy for the last high growth decades. On the other hand, the system may be structurally unbalanced, with pension provisions that do not match contributions. If then the system is unable to pay its promises, the return of contributions is negative. 8 Thus, it should be recognized that the extent to which social security contributions should be counted as part of income depends on the extent to which pension contributions actually increase the stock of wealth. In our baseline case we define mandatory saving as the total amount of contributions actually paid by each worker. In the SHIW earnings are reported net of taxes and contributions, and contributions are a flat tax for individuals, increasing gradually from percent of gross earnings in 8 8 See Rossi and Visco () and Jappelli () for examples of calculations of social security wealth in time series and cross-sectional data, respectively. Franco et al. () provide similar calculations in constructing Italian generational accounting.

13 to percent in. It is therefore straightforward to rescale income in proportion. 0 Pension benefits are easier to measure, being reported by all individuals as part of their income. The profile of income earned in Figure peaks around the age of 0, and rapidly declines after age, a reflection of the increasing number of retired in the older age groups. Retirement income is then provided mainly by capital income (i.e, the return to private wealth). Cohort effects are again very clearly seen affecting the resources of each generation, as the broken segment for successive older generations lie below the ones of younger generations. Figure plots total saving, the difference between earned income and consumption. The saving profile is clearly hump-shaped. Before retirement total saving is about millions lire (or $,000). Around age, saving falls to zero. Households in the older age-groups dissave about 0 millions lire per year (roughly $,000). But note that the region of positive saving is much larger than that of negative saving, indicating that either consumption is underestimated, or that households do not consume all their wealth during retirement. More on this below. The conventional definition of disposable income is obtained by subtracting mandatory saving from earned income (i.e. subtracting social security contributions and adding back pension benefits). The effect of this adjustment is to obtain a much flatter age-income profile in Figure. Note that disposable income is now fairly high even in old age, given the generous benefits provided by the Italian social security system. Contrary to Figure, disposable income exceeds consumption at all ages, a fact that has been interpreted as being at variance with the life-cycle hypothesis. In Figure we plot private saving, or the difference between disposable income and consumption. Removing from income all mandatory saving (whose purpose is precisely to smooth consumption) results in an income profile that is very similar to the consumption profile, so that saving will be, 0 In Italy part of the contributions are paid by the employee, and part by the employer. But clearly this is immaterial: in both cases it is the employee who actually has the burden of paying the contributions (as well as of being entitled to a pension). For the self-employed the contribution rates are actually different than for employed workers. Given that we work with large samples and aggregate over -year bands, excluding the selfemployed does not change appreciably the graphs.

14 by construction, relatively flat over the life-cycle. Note that the age behavior of saving so calculated in Figure is quite inconsistent with the age path of private wealth discussed below, which is clearly more humped shaped, and with the implied saving estimated from assets data (see Section ). Similar flat age-saving profiles for countries in which the amount of mandatory saving is substantial have been noted by several studies. To take just a few recent examples. Poterba () summarizes the evidence for the group of most industrialized countries, Alessie et al. () for the Netherlands, and Paxson () for the US and the UK. One of the reasons for these flat age-saving profiles is that these studies neglect to count mandatory saving, whose main purpose is in fact to smooth consumption. Figure shows that the size of mandatory saving and dissaving (the difference between total and private saving) is very substantial in the Italian economy: contributions average or millions up to retirement age, matched by generous pension provisions (about millions lire). The figure also points out that Italians retire relatively early (around age 0), given again generous early retirement rules. Starting with Feldstein (), several studies have analyzed the effect of social security on private saving. This effect is rather complex. In principle, an increase in contributions and benefits should reduce private saving and leave total saving unaffected. In practice, social security system tend to encourage early retirement, which would tend to increase private saving. Even though by definition total saving is the sum of private and mandatory saving, it is not true that an increase in mandatory saving will reduce private saving in proportion. Most empirical studies suggest in fact that the offset effect between private and mandatory saving is well below unity. As mentioned, given the generosity of Italian social security system, and its actual and projected deficits, it is not likely that all contributions paid by current workers truly represent saving. In Figure it is assumed that only 0 percent of gross earnings represents earned income, and treat the remaining portion of contributions as a flat income tax. The overall shape of saving This latter study also presents flat age-saving profiles in Taiwan and Thailand, in which the amount of mandatory saving is much more limited. The evidence in these countries is therefore much less favorable to the life-cyle hypothsis than in other developed countries. Conceptually, this is similar to the old-age tax computed by Gokhale, Kotlikoff and Sabelhaus ().

15 by age is qualitatively unaffected, and therefore does not modify the basic insights of this section. In comparison with national account data, the SHIW consumption is more severely underestimated than income (0 percent against percent, respectively). One could thus compute total and private saving by blowing up income by percent, and consumption by 0 percent. This adjustment reduces the level of saving at all ages, but does not change the shape of the age-consumption profile, and therefore the shape of the age-saving profile. In particular, private saving is again flat over the life-cycle, and negative saving in old age are not observed.. The age-wealth profile It is useful to complement the analysis of saving by comparing the age profile of private wealth (real plus financial) and of total wealth (the sum of private wealth and pension wealth). In principle, saving equals the change in assets. Private saving, as defined in the previous section, should be equal to the change in private wealth. Similarly, total saving should correspond to the change in total wealth. In practice, saving measures derived from flow or stock data may differ because of measurement errors and capital gains. Total wealth is the sum of private wealth and pension wealth. Since the fraction of Italian households that contributes to private pension funds is tiny, they can be safely neglected. Pension wealth is then defined as the difference between the discounted value of social security benefits and discounted value of social security contributions. Constructing the latter requires assumptions about expected benefits and expected contributions. As for mandatory saving, both depend on future legislation. The pension reform of the social security system will gradually implement changes in eligibility rules, accrual rates and pension age. Our estimate of social security wealth abstracts from most of these institutional details, and aims only at providing a rough estimate of expected contributions and benefits, based on legislation prevailing at the end of the 80s (the mid-point of our sample). It is not our purpose here to construct precise measures of social security wealth, but only to obtain a benchmarkindicator to be compared with private wealth. The assumptions needed to compute social security wealth are described in the Appendix.

16 Using the same cohort data in the previous figures, Figure reports the age-profile of total wealth, the sum of pension wealth, financial wealth, real assets, net of liabilities. As in the previous figures, the fitted line shows the age-wealth profile of a representative individual, adjusted for cohort effects. Total wealth is clearly humped-shaped. Early in life wealth is 00 million lire (about times consumption), peaks at about 0 millions (about times consumption), and starts declining after age 0. For older households (aged 80) total wealth is considerably reduced, about 80 million lire (or times consumption). The role of pension wealth in providing for retirement is very important, as shown in Figure 0. Pension wealth starts roughly at zero (those who enter the labor force have not yet accumulated for retirement). The retirement peak is slightly less than 00 million lire, not very different than private wealth. Thus through life about half of household wealth is annuitized. Given long life expectancies (about 0 years for the older age group) social security wealth is still about 00 million lire even at age 80. The age-profile of total wealth (and of total saving) is useful to check if wealth is hump-shaped, as predicted by the life-cycle model. However, the age-profile of private wealth reported in Figure (obtained subtracting pension wealth from total wealth) is useful for a different purpose, i.e. to shed light on the importance of intergenerational transfers, which is the subject of a very large literature. It has been sometimes argued that the distinctive element of the life-cycle hypothesis is the absence of intergenerational transfers. But this is a mistake. It is only a matter of convenience that in the elementary version of the life-cycle model households start with zero assets, so that wealth increases only with savings and is entirely consumed in life. In order to distinguish the life-cycle hypothesis from other theories (for instance, a model in which bequests are the main motives for saving) one must show that wealth finances retirement consumption, i.e. that wealth is hump-shaped (as in Figure ). But in order to assess the importance of intergenerational transfers, and of bequest motives in particular, one may want to look at the age-profile of This pattern is even more evident for the age-profile of median wealth These numbers are broadly consistent with Rossi and Visco () and Franco et al. (). The latter, in particular, shows that pension wealth is about 00 million lire at retirement age (see Table., p. ).

17 private (or bequeathable) wealth. This is the only component of total wealth which can be passed to future generations if it is not consumed before the household dies. By definition, annuitized wealth disappears when the retired dies (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 wealth which increases after retirement. This must imply that part of pension wealth is used to increase private wealth. If the retired continue to accumulate bequeathable wealth, the most natural interpretation is that they plan to leave a bequest. But the age-wealth profile in Figure shows instead that private wealth declines at least after the age of 0. Can we take this 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 saving measures. In principle, saving equals the first difference of wealth. This is actually reflected in the pattern in Figure (total saving) and Figure (where we plot the change in total wealth). Note however that the common pattern is entirely due to the fact that mandatory saving roughly equals the change in pension wealth. Instead, the profile in Figure (where private saving is defined as disposable income minus consumption) is rather different than in Figure (where private saving is defined as the change in private wealth). While private wealth peaks in the age-group -0, private saving after that age-group is large and positive, even for the oldest agegroups. The information available in the SHIW does not yet allow us to indicate if the saving profile computed on the basis of income and consumption is more reliable than that obtained by first-differencing wealth. If the amount of under-estimation of wealth is constant between different surveys, an estimate of saving obtained subtracting wealth in year t from wealth in year t+ might be more reliable than an estimate based on flow variables in the same survey. However, if the true saving profile is better approximated by the wealth data, it should also be the case that the amount of measurement error in consumption and income are age-dependent (for instance, that consumption is more severely under-estimated in old age). At the moment this is a pure guess, and we have therefore no elements to claim that either one of the two measures of saving is superior to the other.

18 The second reason why one cannot infer the importance of bequest motives from the shape of the saving profile. In fact, even if private saving was negative in old age, this would not be sufficient to reject the hypothesis of bequest motives. If a retired consumes part of his wealth to supplement his pension, this does not imply that he or she does not plan to leave a bequest. Wealth may also decline because people make inter vivos transfers. There is in fact very little that can be inferred about the size of intergenerational transfers or the presence of bequest motives from Figure 0. What we observe is that in the years (from age to age 80) bequeathable wealth is about halved, and private wealth at age 80 is about times consumption, certainly not a huge amount. But even this amount tells us very little about bequests, because clearly bequests will be whatever will be left after the survivor spouse dies (since the life-cycle hypothesis is a theory of household saving, infra-family transfers should not be counted as bequests). Direct evidence on the importance of beqeusts and gifts is available in the case of the Italian economy. A special section of the SHIW asks each member of the household to report the number and amount of bequests and gifts received in the past from parents or other relatives. This information is used in Guiso and Jappelli () to compute the aggregate share of transfers in total wealth. On average, each household received 0. million lire (equivalent to $,00 in ),. percent of private wealth (0. percent in bequests plus. percent in gifts). Capitalizing bequests and gifts at a net real interest rate of percent, the share of intergenerational transfers in bequethable wealth comes to.8 percent (. percent bequests plus. percent gifts). Similar shares of transfer wealth in Italy is obtained by Guiso and Cannari () using different methods. A final caveat why the wealth trajectory is not informative about bequest motives is in order. The share of transfer wealth cannot be taken as a measure of the importance of bequest motives for the obvious reason that part of bequeathed wealth was intended to finance consumption. Given life uncertain, risk averse consumers will always find optimal not to run down their assets to zero.

19 . Conclusions We use Italian cohort data to construct a measure of total saving, defined as the difference between earned income and consumption. Earned income includes mandatory saving (in our case, social security contributions or a portion of such contributions), but excludes pension benefits. Since the latter corresponds to a depletion of annuitized wealth they should not be counted as income. The second step of our analysis is to construct a measure of total wealth, the sum of pension and private (or bequethable) wealth. Since the age-profile of earned income is hump-shaped, and consumption is relatively flat through life, both total saving and total wealth are considerably hump-shaped. The shape of this profile therefore agrees with the prediction of the life-cycle model, which suggests that the young accumulate resources to be spent during retirement. We also note that the hump-shape in saving and wealth depends mainly from the fact that in modern societies a great deal of saving occurs through mandatory retirement plans, such as social security and private pension funds, while dissaving occurs mainly through annuitized wealth. One may question the fact that people cannot choose the amount of mandatory saving, which should therefore be ignored for understanding people s behavior. But since people can change private saving in response to changes in mandatory saving, total saving is the relevant measure of the change in assets accumulated for retirement. And after all, the existence of mandatory saving programs and the widespread implementation of retirement plans should be interpreted as the social approval of schemes designed to ensure people with adequate reserves to be spend during retirement. Since private saving and private wealth (obtained subtracting mandatory saving and pension wealth) are not relevant indicators of the retirement motives for saving in modern societies, cross-country comparisons of private saving (disposable income minus consumption) can be highly misleading if proper account is not taken of the difference in mandatory saving, especially for developed countries in which mandatory retirement programs play a prominent role. The shape of one component of total saving, i.e. private saving, cannot therefore be cited as evidence against the life-cycle model. Even if private wealth and private saving, taken in isolation, are not informative about the importance of saving for retirement, they might be useful to evaluate the importance of bequest motives, because pension 8

20 wealth is not bequethable. In our sample we find that private saving is positive and rather flat through age, but that private wealth is significantly hump-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 bequest motives. Transfers may occur inter vivos. The size of transfers for the oldest age groups differs from the amount of bequeathed wealth. Finally, many bequests are involuntary. Some studies erroneously focusing on private saving and wealth have concluded that the elderly continue to accumulate assets after retirement, or that they decumulate at rates that are too low to be consistent with the lifecycle model. Our figures show instead that the elderly decumulate very substantial 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 about five times consumption. Even though this is small fraction of lifetime wealth, it is still an open question to try to understand why do the elderly not consume all their wealth before they die.

21 References Alessie, Rob, Arie Kapteyn and Frank Klijn (), Mandatory Pensions and Personal Savings in the Netherlands. CentER, Tilburg University, mimeo. Auerbach, Alan, J., Gokhale, Jagadeesh, and Laurence J. Kotlikoff (), 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 (), "Methodological Appendix: the Bank of Italy's Survey of Household Income and Wealth", in Albert Ando, Luigi Guiso and Ignazio Visco (eds.), Saving and the Accumulation of Wealth. Essays on Italian Household and Government Saving Behavior. Cambridge: Cambridge University Press. Deaton, Angus and Christina Paxson () Saving, Aging and Growth in Taiwan, in David Wise (ed.), Studies in the Economics of Aging. Chicago: University of Chicago Press. Feldstein, Martin (), "Social Security and Saving: the Extended Life-Cycle Theory," American Economic Review, -8. Daniele Franco, Jagadeesh Gokhale, Luigi Guiso, Laurence J. Kotlikoff and Nicola Sartor (), Generational Accounting: The Case of Italy, in Albert Ando, Luigi Guiso and Ignazio Visco (eds.), Saving and the Accumulation of Wealth. Essays on Italian Household and Government Saving Behavior. Cambridge: Cambridge University Press. Gokhale, Jagadeesh, Laurence J. Kotlikoff and John Sabelhaus (), Understanding the Postwar Decline in US Saving: a Cohort Analysis, Brookings Papers on Economic Activity, -0. Guiso, Luigi, Tullio Jappelli, and Daniele Terlizzese (), "Why is Italy's Saving Rate so High?", in Albert Ando, Luigi Guiso and Ignazio Visco (eds.), Saving and the Accumulation of Wealth. Essays on Italian Household and Government Saving Behavior. Cambridge: Cambridge University Press. Guiso, Luigi, and Tullio Jappelli (), "Intergenerational transfers, borrowing constraints and the timing of home ownership", Temi di Discussione n.. Rome: Bank of Italy. Jappelli, Tullio (), "Does Social Security Reduce the Accumulation of Private Wealth? Evidence from Italian Survey Data," Ricerche Economiche, -. 0

22 Jappelli, Tullio, and Marco Pagano (), "Personal Saving in Italy", in James Poterba (ed.), International comparison of personal saving. Chicago: University of Chicago Press. Modigliani, Franco (8), "Life-Cycle, Individual Thrift, and the Wealth of Nations", American Economic Review, -. Modigliani, Franco (0), Recent Declines in Saving Rates: a Life-Cycle Perspective, Rivista di Politica Economica, December, -. Modigliani Franco, and Tullio Jappelli (0), "Why Has the Italian National Saving Rate Declined?", in Salvatore Biasco, Alessandro Roncaglia, and Michele Salvati (eds.), Market and Institutions in Economic Development. London: MacMillan Press. Paxson, Christina (), Saving and Growth: Evidence from Micro Data, European Economic Review 0, -88. Poterba, James (), "Introduction", in James Poterba (ed.), International Comparison of Personal Saving. Chicago: The University of Chicago Press. Rossi, Nicola, and Ignazio Visco (), "National Saving and Social Security in Italy", Ricerche Economiche, -.

23 APPENDIX A. The Survey of Household Income and Wealth The Bank of Italy Survey of Household Income and Wealth (SHIW) was conducted on a yearly basis from to 8 (with the exception of 8). Up to 8 the number of participant households in a typical year was around,000. In 8 the sample size was doubled, and since 8 the survey has been run every other year. The most recent available survey is for. The survey is representative of the Italian population because probability selection is enforced at every stage of sampling. The unit of observation is the family, which is defined to include all persons residing in the same dwelling who are related by blood, marriage or adoption. Individuals selected as "partners or other common-law relationships" are also treated as families. The interviews are conducted during the first three months 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 is recommended, particularly for 8, a year in which the survey oversampled wealthy households (Brandolini and Cannari, ). All statistics reported in this paper use sample weights. Before 80 the survey is not available on tape. Up to 8 the age variable, which is central to the present analysis, is coded in 0-year bands, with an open interval for individuals over years of age. Since this precludes the construction of the cohort indicators, we use 8 as the starting point for the analysis. The data set includes the 8, 8, 8, 8,, and SHIW. Wealth and consumption are converted into 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 social security contributions. Earnings are the sum of wages and salaries, selfemployment income, less income taxes and social security contributions. Wages and salaries include overtime bonuses, fringe benefits and payments in kind, and exclude withholding taxes. Self-employment income is net of taxes and includes income from unincorporated businesses, net of depreciation of physical assets.

24 DISPOSABLE INCOME Earned income plus pension benefits minus social security contributions. PRIVATE WEALTH Sum of household's net financial assets and real assets. Real assets are the sum of real estate, unincorporated business holdings and the stock of durable goods less interest on household liabilities (consumer credit and mortgage loans). A. 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 of social security benefits that will accrue to a person of age a expecting to retire at age n is equal to T n> τ S τ, n py τ + + gτ r n τ (A.) where T is the maximum length of life, S τ,n the probability of surviving from age τ to age n, p the expected replacement rate, y τ expected earnings at retirement, 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, τ a so that y = ya ( + g), the present discounted value of the social security τ benefits of an individual of age a is SSW = S py + gτ r τ a T a a, τ a τ, n + n> τ S + + gτ r n τ, (A.) where SSW is social security wealth and S a,t the survival probability from age a to age τ.