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http://www.jstor.org Life Cycle, IndividualThrift, and the Wealth of Nations
This paper provides a review of the theory Yet, there was a brief but influential inter- of the determinants of individual and na- val in the course of which, under the impact tional thrift that has come to be known as of the Great Depression, and of the interpre- the Life Cycle Hypothesis (LCH) of saving. tation of this episode which John Maynard Applications to some current policy issues Keynes suggested in the General Theory are also discussed. (1936), saving came to be seen with suspi- Section I deals with the state of the art on cion, as potentially disruptive to the econ- the eve of the formulation of the LCH some omy and harmful to social welfare. The thirty years ago. Section II sets forth the period in question goes from the mid-1930's theoretical foundations of the model in its to the late 1940's or early 1950's. Thrift original formulation and later amendment, posed a potential threat, as it reduced one calling attention to various implications, dis- component of demand, consumption, without tinctive to it and, sometimes, counterintui- systematically and automatically giving rise tive. It also includes a review of a number of to an offsetting expansion in investment. It crucial empirical tests, both at the individual might thus cause "inadequate" demand and the aggregate level. Section III reviews and, hence, output and employment lower some applications of LCH to current policy than the capacity of the economy. This failure issues, though only in sketchy fashion, as was attributable to a variety of reasons in- space constraints prevent fuller discussion. cluding wage rigidity, liquidity preference, fixed capital coefficients in production, and I. Antecedents to investment controlled by animal spirits rather than by the cost of capital. A. The Role of Thriftand the Not only was oversaving seen as having Keynesian Revolution played a major role in the Great Depression, but, in addition, there was widespread fear The study of individual thrift and aggre- that the problem might come back to haunt gate saving and wealth has long been central the postwar era. These fears were fostered by to economics because national saving is the a widely held conviction that, in the future, source of the supply of capital, a major there would not be too much need for ad- factor of production controlling the produc- ditional accumulation of capital while saving tivity of labor and and its growth over time. would rise even faster than income. This It is because of this relation between saving combination could be expected to result, and productive capital that thrift has tradi- sooner or later, in saving outstripping the tionally been regarded as a virtuous, socially "(need" for capital. These concerns were at beneficial act. the base of the "stagnationist" school which was prominent in the 1940's and early 1950's.
B. Early Keynesian Theoriesof the * Sloan School of Management, Massachusetts In- Determinants of Saving stitute of Technology, Cambridge, MA 02139. This article is the lecture Franco Modigliani delivered It is interesting and somewhat paradoxical in Stockholm, Sweden, December 9, 1985, when he that the present day interest and extensive received the Nobel Prize in Economic Sciences. The behavior owes article is copyright (0 The Nobel Foundation 1985, and research activity about saving published here with the permission of The Nobel its beginnings to the central role assigned by Foundation. Keynesian economics to the consumption
297 298 TIIE A MERICAN ECONOMIC REVIEW JUNE 1986 function as a determinant of aggregate de- having saved first or without exceeding their mand, and to the concern with oversaving as means. a source of both cyclical fluctuations and long-run stagnation. It is for this reason that C. Three Landmark Empirical Studies the early endeavor to model individual and aggregate saving behavior was dominated by In the second half of the 1940's, three the views expressed on this subject by Keynes important empirical contributions dealt a in the General Theory, and in particular by fatal blow to this extraordinarily simple view his well-known "fundamental psychological of the saving process. First, the work of [rather that 'economic'] law" (p. 96) to the Simon Kuznets (1946) and others provided effect that an increase in income can be clear evidence that the saving ratio had not counted on to lead to a positive but smaller changed much since the middle of the nine- change in consumption. Even when the anal- teenth century, despite the large rise in per ysis followed the more traditional line of capita income. Second, a path-breaking demand theory, it relied on a purely static contribution of Dorothy Brady and R. D. framework in which saving was seen as one Friedman (1947) provided a reconciliation of of the many "goods" on which the consumer Kuznets' results with budget study evidence could spend his income. Thus, income was of a strong association between the saving seen as the main systematic determinant of rate and family income. They demonstrated both individual and national saving, and, in that the consumption function implied by line with Keynes' "law," it was regarded as a family data shifted up in time as mean in- superior commodity (i.e., one on which "ex- come increased, in such a way that the saving penditure" rises with income) and most likely rate was explained not by the absolute in- a luxury, for which expenditure rises faster come of the family but rather by its income than income. Also, in contrast to other goods, relative to overall mean income. the "expenditure" on saving could be nega- Ways of reconciling these findings with the tive-and, accordingly, dissaving was seen as standard linear consumption function were typical of people or countries below some soon provided by James Duesenberry (1949) "break-even" level of income. All these fea- and me (1949), though within the empirical tures could be formalized by expressing con- tradition of the earlier period. Duesenberry's sumption as a linear function of income with "relative income hypothesis" accounted for a substantial positive intercept. This formu- the Brady-Friedman results in terms of im- lation appeared to be supported by the find- itation of the upper classes. This is an ap- ings of numerous budget studies, and even pealing explanation, though it fails to come by the newly developed National Income to grips with the budget constraint in the Accounts, spanning the period of the Great case of would-be dissavers below mean in- Depression, at the bottom of which saving come. Similarly, the " Duesenberry-Modig- turned small or even negative. liani" consumption function tried to recon- As is apparent, in this early phase the cile the cyclical variations of the saving ratio dominant approach could best be char- with its long-run stability by postulating that acterized as crudely empirical; little attention current consumption was determined not just was given to why rational consumers would by current income but also by its highest choose to "allocate" their income to saving. previous peak, resulting in a ratchet-like up- The prevailing source of substantial saving ward creep in the short-run consumption was presumably the desire of the rich to function. In my own formulation, primary bequeath an estate (Keynes' "pride" motive, stress was placed on reasons why the saving p. 108). Accordingly, the main source of the rate should move procyclically and on the existing capital stock could be traced to in- consideration that in an economy with stable heritance. Similarly, there was little evidence long-run growth, the ratio of the current of concern with how, and how long, "poor" to highest previous income could be taken people, or countries, could dissave without as a good measure of cyclical conditions. VOL. 76 NO. 3 MODIG,IA NI: LIFE CYCLE AND INDI VIDUA L T'IIRIFT 299
Duesenberry, on the other hand, put more that a representative consumer allocates to stress on consumers explicitly anchoring their consumption at any age, t, will depend only consumption on the previous peak. This for- on his life resources (the present value of mulation was brought to its logical conclu- labor income plus bequests received, if any) sion by Tillman Brown (1952) when he pro- and not at all on income accruing currently. posed that the highest previous income When combined with the self-evident propo- should be replaced by the highest previous sition that the representative consumer will consumption. choose to consume at a reasonably stable The third fundamental contribution was rate, close to his anticipated average life the highly imaginative analysis of Margaret consumption, we can reach one conclusion Reid (unpublished) which pointed to a total- fundamental for an understanding of indi- ly different explanation for the association vidual saving behavior, namely that the size between the saving ratio and relative income, of saving over short periods of time, like a namely that consumption was controlled by year, will be swayed by the extent to which normal or "permanent," rather than current, current income departs from average life re- income. sources. This contribution was an important source This conclusion is common to LCH and to of inspiration, both for the life cycle and for Friedman's PIH which differs from LCH the roughly contemporaneous Permanent In- primarily in that it models rational consump- come Hypothesis (PIH) of Milton Friedman tion and saving decisions under the "sim- (1957). plifying" assumption that life is indefinitely long. Accordingly, the notion of life re- II. The Life CycleHypothesis sources is replaced by that of "permanent income," while the discrepancy between cur- Between 1952 and 1954, Richard Brum- rent and permanent income is labeled " tran- berg and I wrote two essays, "Utility Analy- sitory" income. sis and the Consumption Function: An In- The notion that saving largely reflects terpretation of Cross-Section Data" (1954), transitory income has a number of implica- and "Utility Analysis and the Aggregate tions which have been made familiar by the Consumption Function: An Attempt at In- contributions of Friedman and by our own tegration" (published in 1979) which provide 1954 paper, and which have received ample the basis for the Life Cycle Hypothesis of empirical support, even with some occasional Saving (LCH). They will be referred to controversy. Among these implications, the hereafter as MB-C and MB-A, respectively. best known and well established is that relat- Our purpose was to show that all the well- ing to the upward bias arising in estimating established empirical regularities could be the slope of a saving-income relation from accounted for in terms of rational, utility- budget data, when, as is usual, the individual maximizing, consumers allocating optimally observations are classified by current income their resources to consumption over their classes. Because of the correlation between life, in the spirit of Irving Fisher (1930). (For transitory and current income (relative to an earlier and extensive, but strictly theoreti- mean income), the regression line tends to be cal, application of utility maximization to the steeper than the underlying true relation be- theory of saving by households, see U. Ricci, tween the (permanent) saving rate and 1926.) permanent income. Thus, the estimated sav- ing function departs from the true one by A. Utility Maximization and the Role being rotated counterclockwise around the of Life Resources (Permanent Income) mean, to an extent that is greater the greater the variability of transitory income, for ex- The hypothesis of utility maximization ample, more for a sample of farmers than for (and perfect markets) has, all by itself, one one of government employees. It is this very powerful implication-the resources phenomenon that accounts for the finding of 300 TFIE AMERICAN ECONOMIC REVIEW JUNE 1986
Brady-Friedman cited above, to the effect Y,C, A that the saving ratio, estimated from budget (L-N)N - studies at different points of time, appears to L depend on the income not in absolute terms A(T) but rather relative to overall mean income. This same consideration provides an ex- planation for a famous counterintuitive em- ,' Y(T) C(T) = Y pirical finding first observed in a large survey conducted in the United States in 1936, ,' ~~~~~~~~~~DISSAVIG namely that black families appeared to , . \\\\4 >~~~~~~~~~~~--T (age ) save 0 N L more (or dissave less) than white families at INCOME, CONSUMPTION, SAVINGAND WEALTH AS A FUNCTIONOF AGE any level of income. The reason, of course, is that black families tend to have a much FIGURE 1 lower average level of permanent income, and, therefore, at any given level of current income the transitory component, and hence saving, tended to be larger (see, for example, cle path of household opportunities and Fisher and Brown). tastes, in order to draw out succinctly the The extent of bias in the cross-sectional essential implications of the LCH approach. saving function should tend to decline if the These were: 1) opportunities: income con- households are classified by some criterion stant until retirement, zero thereafter; zero less positively correlated with transitory in- interest rate; and 2) preferences: constant come, and this prediction too has been ex- consumption over life; no bequests. tensively verified (see, for example, my paper For this "basic" or "stripped down" with Albert Ando, 1960). model, the life cycle path of saving and However, I do not intend to pursue here wealth is described in the, by now familiar, any further the implications of the relation graph of Figure 1. Because the retirement between saving and transitory income since, span follows the earning span, consumption as already noted, these implications are basi- smoothing leads to a humped-shaped age cally the same for LCH as for PIH. I con- path of wealth holding, a shape that had centrate, instead, on those aspects that are been suggested earlier by Roy Harrod (1948) specific to LCH. under the label of hump saving (though "hump wealth" would seem like a more de- B. LCH The "StrippedDown" Version scriptive label). In MB-A, it was shown that this basic By explicitly recognizing the finite life of model led to a number of implications which households, the LCH could deal with varia- were at that time quite novel and surprising tions in serving other than those resulting -almost counterintuitive. They included the from the transitory deviations of income from following: life resources of PIH. In particular, it could 1. The saving rate of a country is en- focus on those systematic variations in in- tirely independent of its per capita income. come and in "needs" which occur over the 2. Differing national saving rates are life cycle, as a result of maturing and retir- consistent with an identical individual life ing, and of changes in family size-hence the cycle behavior. name Life Cycle Hypothesis. In addition, the 3. Between countries with identical indi- LCH was in a position to take into account vidual behavior, the aggregate saving rate bequests and the bequest motive, which were will be higher the higher the long-run growth not amenable to analysis within the ap- rate of the economy. It will be zero for zero proximation of infinite life. growth. In MB-C and in the first two parts of the 4. The wealth-income ratio is a decreas- MB-A, we made a number of simplifying, ing function of the growth rate, thus being stylized, assumptions concerning the life cy- largest at zero growth. VOL. 76 NO. 3 MODIGLIANI: LIFE CYCLE A ND INDI VIDUA L TIIRIFT 301
5. An economy can accumulate a very the large stock of wealth-Proposition 3. substantial stock of wealth relative to income The explanation is that, in stationary state, even if no wealth is passed on by bequests. the dissaving of the retired, from wealth 6. The main parameter that controls the accumulated earlier, just offsets the accumu- wealth-income ratio and the saving rate for lation of the active population in view of given growth is the prevailing length of re- retirement. Saving could occur only tran- tirement. siently if a shock pushed W away from To establish these propositions, we begin (M/2)Y, where Y is the stationary level of by considering the case of a stationary econ- income; then, as long as Y remained at Y, omy, and then that of steady growth. wealth would gradually return to the equi- librium level (M/2)Y. 1. The Case of a Stationary Economy. Sup- pose that there is neither productivity nor 2. The Case of a Steadily Growing Economy. population growth, and assume, convenient- In this case, the behavior of the saving rates ly, that mortality rate is 1 at some age L and can be inferred from that of aggregate private Obefore. Then, clearly, Figure 1 will repre- wealth, W, through the relation S = AW, im- sent the age distribution of wealth, saving, plying: consumption, and income, up to a factor representing the (constant) number of people S AW W (2) s-= -- =pw in each age bracket. Hence, the aggregate Y W Y wealth-income ratio, W/Y, is given by the ratio of the sum of wealth held at each ds/dp = w + p(dw/dp) age-the area under the wealth path-to the area under the income path. This has a num- where w is the wealth-income ratio and p is ber of significant implications. the rate of growth of the economy which in (a) It is apparent from the graph that steady state equals the rate of growth of WIY depends on a single parameter, the wealth,, AW/W. Since w is positive and is length of retirement, M-which establishes based on a level life cycle consumption and Proposition 6. The relation between M and earnings, which insures that it is independent WIY turns out to be extremely simple, to of the level of income, we have established wit: Propositions 1 and 2. If, in addition, the age profile of the wealth-income ratio could be (1) W/ Y-=M/2, taken as independent of growth, then the saving rate would be proportional to growth (see MB-A, fn. 38). with a proportionality factor equal to M/2, (b) In MB-A, for illustrative purposes, substantiating Proposition 3. Actually, the we conservatively took the average length of model implies that w is, generally, a declin- retirement as 10 years, implying a wealth- ing function of p -Proposition 4-though income ratio of 5. This result was an exciting with a small slope, so that the slope of the one in that this value was close to the income relation between s and p tends to flatten out ratio suggested by preliminary estimates of as p grows. Raymond Goldsmith's (1956) monumental When the source of growth is population, study of U.S. savings. It implied that one the mechanism behind positive saving may could come close to accounting for the entire be labelled the Neisser effect (see his 1944 wealth holding of the United States without article): younger households in their accumu- any appeal to the bequest process-Proposi- lation phase account for a larger share of tion 5-a quite radical departure from con- population, and retired dissavers for a smaller ventional wisdom. share, than in the stationary society. How- (c) With income and population sta- ever, w also falls with p because the younger tionary, aggregate wealth must remain con- people also are characterized by relatively stant in time and, therefore, the change in lower levels of wealth holding. Thanks to the wealth or rate of saving must be zero, despite simplifying assumptions of the basic model, 302 TIlE A MERICAN ECONOMIC RE VIE W JUNE 1986 it was possible to calculate explicitly values somewhat earlier by Gardner Ackley (1951), for w and s: for p = 2 percent, w = 4, s = 8 though both the functional form and the percent; for p = 4 percent, w = 3-1/4, s = 13 presumed stability of the coefficients rested percent. on purely heuristic considerations. By con- When the growth is due to productivity, trast, it was shown in MB-A that, if income the mechanism at work may be called the followed closely the steady growth path, then Bentzel (1959) effect (who independently the parameters a and 8 could be taken as called attention to it). Productivity growth constant in time and determined by the implies that younger cohorts have larger length of life (L), of retirement (M), and the lifetime resources than older ones, and, rate of growth (MB-A, p. 135). For the therefore, their savings are larger than the standard assumption L = 50, M =10 and p dissaving of the poorer, retired cohorts. It =.03, 8 comes to .07 (see MB-A, p. 180). was shown in MB-A that, if agents plan their Furthermore, the parameters could be well consumption as though they did not antic- approximated by the same constant even if ipate the future growth of income, then w(p) income moved around the trend line, as long and s(p) for productivity growth are just as the departures were not very long lasting about the same as for population growth, for and deep, except that YL should be interpre- values of p in the relevant range. ted as long-run expected rather than current It should be noted that this conclusion is income. The short-run equation (3) is, of diametrically opposite to that reached by course, consistent with the long-run proper- Friedman, namely that productivity growth ties 1 to 6, as one can readily verify. should tend to depress the saving ratio on the ground that a rise in income "expected to 3. Empirical Verifications. None of these continue tends to raise permanent income long- and short-run implications of the basic relative to measured income and so to raise model could be explicitly tested at the time consumption relative to measured income" they were established. There were no data on (p. 234). This difference in the implications Private Net Worth to test equation (3), ex- of the two models-one of the very few of cept for some indirect estimates pieced to- any significance-can be traced to the fact gether by W. Hamburger (1951) and some that, if life is infinite, there cannot be a preliminary Goldsmith figures for a few Bentzel effect. To be sure, to the extent that selected years. Similarly, information on agents anticipate fully future income, they Private National Saving were available only will tend to shift consumption from the fu- for a couple of countries. We could only take ture to the present and this will tend to encouragement from the fact that the model reduce the path of wealth and perhaps even seemed to fit the single observation available, generate negative net worth in early life (see, namely the United States. Both the wealth- for example, James Tobin, 1967). But this income ratio, 4 to 5, and the saving rate, S, effect must be overshadowed by the Bentzel "between 1/7 and 1/8" (Goldsmith) were effect, at least for small values of p which, broadly consistent with the prediction of the realistically, is what matters. (This follows model, for a 3 percent growth rate, namely from the continuity of ds/dp in equation 4-1/3 for w and 13 percent for s. (2).) But the availability of data improved The model also implies that the short-run dramatically in the next decade. For the behavior of aggregate consumption could be United States an annual time-series of Private described by a very simple aggregate con- Wealth was put together in the early 1960's sumption function, linear in aggregate (labor) (Ando et al., 1963), and equation (3) was income (YL), and wealth (W): tested (my article with Ando, 1963). It was found to fit the data quite well, and with (3) C = aYL + SW. parameter estimates close to those predicted by the model. By now the consumption func- An equation of this type had been proposed tion (3) has become pretty much standard, VOL. 70 NO. 3 MODIGI,IANI. LIFE CYCLEEANDINDIVIDLIAI, THRIFT 303
25% Japan 0 E the basic nature of the results, and, in par- Q ticular, the validity of Propositions I to 5. 0. E. C.D. Norm 8 - 20 ?
C 1. Nonzero Interest. Allowing for a nonzero Italy W Germany *
4. Liquidity Constraint. Imperfections in the D. The Role of Bequests and credit markets as well as the uncertainty of the Bequest Motive future income prospects may, to some extent, prevent households from borrowing as much Obviously bequests exist in market econo- as would be required to carry out the uncon- mies (and not only in market economies). strained optimum consumption plan. Such a How does their presence affect the relevance constraint will have the general effect of and usefulness of the model, and, in particu- postponing consumption and increase w as lar, the validity of Propositions 1 to 5? In well as s. But, clearly, these are not essential attacking this problem, one must distinguish modifications, at least with respect to the the issue of principle from the empirical one aggregate implications-on the contrary, of how important a role bequests may play they contribute to insure that productivity in the accumulation of wealth. growth will increase the saving rate. How- ever, significant liquidity constraints could 1. How Important are Bequests in the Accu- affect quantitatively certain specific conclu- mulation of Wealth? This is an interesting sions, for example, with respect to temporary question. The traditional approach took it tax changes (see Section III, Part 1, below). for granted that bequests are a major source of the existing wealth, while the LCH sug- 5. Myopia. The LCH presupposes a substan- gested that they might not contribute appre- tial degree of rationality and self-control to ciably. make preparations for retired consumption I recently (1985) reviewed a substantial needs. It has been suggested-most recently body of information on inherited wealth by H. M. Shefrin and Richard Thaler (1985) based on direct surveys of households and -that households, even if concerned in on various sources of estimates on the flow principle with consumption smoothing, may of bequests. This review yields a fairly con- be too myopic to make adequate reserves. To sistent picture suggesting that the proportion the extent that this criticism is valid, it should of existing wealth that has been inherited is affect the wealth-income ratio in the direc- around 20 percent, with a margin of some- tion opposite to the liquidity constraint, thing like 5 percentage points. though the effect of transitory changes in This conclusion is at odds with that pre- income from any source would go in the sented in a provocative paper of Kotlikoff same direction. However, such myopia is not and Lawrence Summers (1981, hereafter supported empirically. The assets held at the K-S). They endeavor to estimate the share of peak of the life cycle are found to represent a bequests by two alternative methods: 1) from substantial multiple of average income (in an estimated flow of bequests, as above, and the order of 5, at least for the United States) 2) by subtracting from an independent and an even larger multiple of permanent estimate of private wealth in a given year, income which, in a growing economy, is less their own estimate of the amount of life cycle than current income. Such a multiple ap- wealth, accumulated by every cohort present pears broadly consistent with the mainte- in that year. Using the first method, K-S nance of consumption after retirement. This reach an estimate of inherited wealth of over inference is confirmed by recent studies which one-half, while using the second-which they have found very little evidence of myopic regard as more reliable- their estimate rises saving behavior. In particular, both Laurence even higher, to above four-fifths. In the 1985 Kotlikoff et al. (1982) and Blinder et al. paper, I have shown that the difference be- (especially Figure 4.1), working with data on tween my estimate and their much higher 306 TIIE AMERICAN ECONOMIC REVIEW JUNE 1980 ones can be traced (i) to some explicit errors the wealth-income ratio actually continues to of theirs, for example, their treatment of the rise in retirement. (Note, however, that his purchase of durable goods, and (ii) to un- estimate is biased as a result of including conventional definitions, both of inherited education in his regression. Given the steady wealth of life cycle saving. I have shown that historical rise in educational levels, there will when one corrects the error and uses the be a strong association between age, educa- accepted definitions, one of the K-S mea- tional attainment, and socioeconomic status sures-that based on bequest flows-coin- relative to one's cohort if one holds constant cides very closely with all other estimates. the absolute level of education. Thus, his Their alternative measure remains somewhat results could merely reflect the association higher, but I show it is subject to an appre- between bequests, wealth, and relative in- ciable upward bias which could easily ac- come discussed below.) Most other recent count for the difference. analysts have found that the wealth of a Kotlikoff and Summers have suggested an given cohort tends to decline after reaching alternative operational criterion of "impor- its peak in the 60-65 age range (A. F. Shor- tance" which should be independent of def- rocks 1975; King and Dicks-Mireaux; initional differences, namely: by what per- Diamond and Hausman; Avery et al.; Ando, centage would aggregate wealth decline if the 1985; Hurd, 1986), though there are excep- flow of bequests declined by 1 percent? The tions- for example, Paul Menchik and suggestion is sound but is very hard to im- Martin David (1983) discussed below. To be plement from available observations. None- sure, the results depend on the concept of theless, it would appear this effect, measured saving and wealth used. If one makes proper in terms of its impact through inherited allowance for participation in pension funds, wealth, can be taken as approximately equal then the dissaving (or the decline in wealth) to the observed share of bequeathed wealth, of the old tends to be more apparent, and it when wealth is measured according to the becomes quite pronounced if one includes an conventional definition. Thus, with either estimate of Social Security benefits. But, when measure, bequeathed wealth can be put at the saving and wealth measures include only less than 25 percent. cash saving and marketable wealth, the dis- The only other country for which the rele- saving and the decline appears weaker or vant information is available seems to be the even absent. Also, those studies which pro- United Kingdom (see Royal Commission, vide median as well as mean values (for 1977). The estimated share of inherited example, Ando, 1985), suggest that the pic- wealth is, again, close to 20 percent. ture of a steady decline in wealth is clearer for the median than for the mean which has 2. The Behavior of Saving and the Wealth of a more erratic behavior, reflecting the ex- the Aged. A quite different ground for ques- treme variability of the data. tioning whether the accumulation of wealth There are several considerations that can can be better accounted for by a life cycle account, at least partly, for the above finding parable than by a bequest motive is to be within an LCH framework. In particular, the found in the behavior of saving and assets of survey data may give an upward biased pic- elderly households, especially after retire- ture of the true behavior of wealth during ment. The basic LCH implies that, with re- old age for two reasons. First, as Shorrocks tirement, saving should become negative, and has argued, one serious bias arises from thus assets decline at a fairly constant rate, the well-known positive association between reaching zero at death. The empirical evi- longevity and (relative) income. This means dence seems to reveal a very different pic- that the average wealth of successively older ture: dissaving in old age appears to be at age classes is the wealth of households with best modest (for example, see J. Fisher, 1950; higher and higher life resources, hence the Harold Lydall, 1955; T. W. Mirer, 1979, and age profile of wealth is upward biased. Sec- Ando and Kennickell). According to Mirer, ond, in a similar vein, Ando and Kennickell VOL. 70 NO. 3 MODIGLIANI: LIFE CYCLE AND INDIVIDUA I,TIIRIFT 307 have found evidence that aged households and the result labelled LCH cum precaution- which are poor tend to double up with ary bequests. younger households and disappear from the These considerations may go part way to- sampled population so that the wealth of ward explaining the slow decumulation. Still, those remaining independent is again an up- this phenomenon may also reflect, in part, ward biased estimate of average wealth. the working of an explicit bequest motive and life planning for it. We may, therefore, 3. Bequests and Uncertainty of the Length of ask whether there is any intrinsic incon- Life. While it is difficult to assess the extent sistency between a significant amount of be- of these biases, the decumulation, at least of quests induced by a bequest motive and the the marketable assets, would seem to be too LCH view of the world, in particular, impli- slow to be explained by the basic LCH. A cations I to 5. possible partial reconciliation is provided by giving explicit recognition to the existence of 4. Bequest Motive in the LCH. First, it is uncertainty about the length of life. Indeed, obvious that no inconsistency arises if in view of the practical impossibility of hav- planned bequests are, on average, propor- ing negative net worth, people tend to die tional to life resources. However, this possi- with some wealth, unless they can manage to bility is uninteresting. The most casual ob- put all their retirement reserves into life an- servation suggests that the planning and nuities. However, it is a well-known fact that leaving of bequests is concentrated in the annuity contracts, other than in the form of upper strata of the distribution of life re- group insurance through pension systems, sources, by which we now mean the sum of are extremely rare. Why this should be so is (discounted) lifetime labor income and be- a subject of considerable current interest. It quests received. This observation suggests the is still ill-understood. "Adverse selection," following hypothesis, first proposed in MB-A causing an unfavorable payout, and the fact (pp. 173-74): that some utility may be derived from be- quests (Andre Masson, 1986)-see below- HYPOTHESIS I: The share of its resources are, presumably, an important part of the that a household earmarks, on the average, answer. for bequests is a (nondecreasing) stable func- In the absence of annuities, the wealth left tion of the size of its life resources relative to behind will reflect risk aversion and the cost the average level of resourcesof its age cohort. of running out of wealth. This point has been elaborated in particular by J. B. Davies (1981) We might expect the share to be close to who has shown that, for plausible parameters zero until we reach the top percentiles of the of the utility function including a low inter- distribution of resources, and then to rise temporal elasticity of substitution, the extent rapidly with income. to which uncertainty of life depresses the One can readily demonstrate (cf. my 1975 propensity to consume increases with age. As article) that this assumption assures that a result, "uncertain life time could provide Propositions 1 to 5 will continue to hold, at the major element in a complete explanation least as long as: of the slow decumulation of the retired" (relative to what would be implied by a HYPOTHESIS II: The frequency distribution standard LCH model). This conclusion is of the ratio of life resources to mean life reinforced by allowing for the uncertainty of resources for each age group is also stable in major medical expenses. Note also that the time. wealth bequeathed as a result of a precau- tionary motive, related to uncertainty of Indeed, under these conditions, if income death, must tend, on the average, to be pro- is constant, wealth will also tend to be con- portional to life resources. Hence, it can be stant and, therefore, saving to be zero, even readily incorporated into the basic model in the presence of bequests. To see this, note 308 THE A MERICAN ECONOMIC RE VIE W JUNE 1986 first that Hypothesis I insures that bequests receives strong support from a recent test by left (BL) are a fraction, say y, of life re- Menchik and David. In this imaginative con- sources, y', BL = y(Y+ BR), where BR is tribution, the authors have assembled, from bequests received. Hypothesis II in turn in- probate records, a large body of data on sures that y is constant in time (and pre- individual bequests which they have matched sumably less than one). Next, note that life with income data from tax returns. Their savings, LS, is given by sample covers persons born since 1880 (in- cluding a few before) and deceased between (5) LS=BL-BR=yY-(l-y)BR. 1947 and 1978. They find striking evidence that (a) bequests depend on the position of Thus, LS increases with Y and decreases the household's life resources in the distri- with BR, and is zero if BR = [y/(l - y)]Y. bution of life resources of its cohort, (b) that But this last condition must hold in long-run they are small for people whose estimated equilibrium since, if BR is smaller, then there life resources fall below the 80th percentile in will be positive saving which will increase that distribution but that, (c) beyond the BR, and reduce LS toward zero; and vice 80th percentile, they rise rapidly with (per- versa if BR is larger. manent) income. This generalization of the basic model has a number of implications, a few of which 5. The Individual Bequests and the Share of may be noted here. Bequeathed Wealth- A Reconciliation.There (i) The age patterns of Figure 1 for a remains one serious puzzle. If something like stationary society are modified, as bequests two-thirds of peak wealth is passed on at raise the average wealth path by a constant, death, be this "unintentional" transmission equal to BR, beginning at the age at which through precautionary saving or the con- bequests are received. The new path remains scious result of a desire to bequeath, how can parallel to the old so that at death it has the share of wealth received by bequests height BL = BR. amount to less than 25 percent of the total? (ii) If labor income is growing at some Recent contributions of Kennickell (1984) constant rate, then average BR will tend to and Ando and Kennickell have pointed the grow at this same rate and so will BL, but way to a satisfactory resolution, by demon- BL will exceed BR by a factor ePT, where T strating that, in the presence of significant is the average age gap between donor and growth, the share of wealth inherited is not a recipient. Thus, with positive growth, and satisfactory indication of the importance of then only, the existence of bequests involves bequests. To understand their argument, life saving, on top of hump saving. In other suppose, conveniently, that all wealth ever words, bequests result in a higher wealth- accumulated is passed on at death, there income ratio, depending on y, and a higher being therefore no life cycle (hump) saving. saving ratio, to an extent that is proportional If the economy is stationary, and thus saving to p. is zero, it will be true that all wealth is due to (iii) The share of life resources left as the bequest motive. It will also be true that bequests could be an increasing function of all existing wealth is inherited so that, in this the household's resources relative to the re- case, the share of bequeathed wealth will sources of his cohort. This, in turn, implies provide a valid measure of the importance of that at any age, the saving-income and bequests. But suppose there is growth. Then wealth-income ratio for individual families there is also saving and, therefore, a portion could be an increasing function of relative of the existing wealth will be held by those (not absolute) income. who are accumulating it on its way to be This last proposition, which is clearly in- bequeathed. And that portion rises rapidly consistent with PIH,is supported by a good with growth: for example, at 3 percent deal of empirical evidence, beginning with growth, bequests left are, on the average, Brady and Friedman. As for the first part of some 2-1/2 times larger than those received, (iii), and the underlying Hypothesis I, it and, correspondingly, the share of wealth VOL. 76 NO. 3 MODIGLIANI. LIFE CYCLE AND INDIVIDUAL THRIFT 309 received by bequests falls to just below 40 version-a deterministic length of life and percent (Kennickell), even though all wealth the absence of a bequest motive appear, in would again disappear in the absence of the the light of presently available information, bequest motive. to be conspicously counterfactual. There is The empirical relevance of this conclusion substantial evidence that wealth declines has been confirmed by an interesting calcula- slowly in old age-even after correcting for tion carried out by Ando and Kennickell various sources of bias-implying that (A-K). Starting from estimates of national households, on the average, leave substantial saving and allocating them by age, using the bequests relative to peak wealth. saving-age relation derived from a well- This evidence can be readily accommo- known budget study (the Bureau of La- dated within the generalized LCH frame- bor Statistics' Consumer Expenditure Sur- work. That portion of bequests that arises vey, 1972-73), they are able to estimate the from the precautionary motive can be han- aggregate amount of wealth accumulated dled by a straightforward relaxation of the through life saving by each cohort living in a assumptions to allow for a stochastic length given year. They then compare this with of life and risk-averse behavior. The holding aggregate wealth to obtain an estimate of the of wealth arising from this mechanism can shares of wealth that are, respectively, self- be rightfully regarded as life cycle wealth accumulated and inherited. since it reflects the optimum allocation of Even though the age pattern of saving they resources to consumption over life. Further- use involves relatively little dissaving in old more, the expected size of bequests relative age, their estimate of the share of inherited to life resources should be largely indepen- wealth turns out to be rather small. For the dent of resources. The remaining bequests years after 1974, it is around 25 percent, arising from a genuine bequest motive can which agrees well with, and thus supports, also be accommodated within the generalized the findings of my 1985 paper. For the years LCH provided that motive satisfies Hy- 1960 to 1973, the share they compute is pothesis I above-and the limited evidence somewhat larger, fluctuating between 30 and available appears to support this assumption. 40 percent. But this higher figure may at The generalized LCH still implies the basic least partly reflect an upward bias in the A-K Propositions 1 to 5. On the other hand, estimate of inherited wealth. The bias arises Proposition 6 must be released: the general- from the fact that the change in overall ization of the basic model points to a num- real wealth includes capital gains, while ber of variables that could affect wealth and the change in the self-accumulated portion saving. These include demographic char- largely excludes them. In the period before acteristics like the dependency ratio, the rate 1974, capital gains were unquestionably sig- of return on wealth, household access to nificantly positive, and hence self-accumula- credit, and the strength of the bequest mo- tion is underestimated and the share of be- tive. Another potentially important variable quests overestimated. In the years from 1973 is Social Security, though its systematic effect to 1980, depressed conditions in the stock on saving has so far proven elusive, a failure market reduce the significance of this effect, not convincingly accounted for by its having though this is partially offset by the boom in two offsetting effects on private saving (cf. real estate values. Section II, Part C, subsection 3, above). Allowing for a significant bequest motive E. A Summing Up raises the issue of its importance. How large a portion of wealth can be traced to this We have found that the basic version of motive, as against true life cycle saving (i.e., the LCH has proved quite helpful in under- hump plus precautionary)? Unfortunately, it standing and predicting many aspects of seems impossible at present to give a well- individual and aggregate saving and wealth- founded answer to the question. We know holding behavior. However, two of the as- that the share of wealth received through sumptions embodied in the stripped down inheritance can be placed at 1/5 to 1/4 for 310 TIIE AMERICAN ECONOMIC REVIEW JUNE 1986 the United States (and presumably the function or refinements thereof. I will, how- United Kingdom), but this information is of ever, list some of the major areas of applica- little help. On the one hand, we know that in tions with a brief statement of the LCH a growing economy, if all the inheritance implications: resulted from the bequest motives, the share would tend to underestimate its "impor- 1. SHORT-RUN STABILIZATION POLICY tance." On the other hand, the observed share is upward biased to the extent that it (i) The Monetary Mechanism: The fact reflects not just the bequest motive, but also that wealth enters importantly in the short- that portion of bequests which arise from the run consumption function means that mone- precautionary motive. We do not know how tary policy can affect aggregate demand not total bequests are split between the two. only through the traditional channel of in- There is evidence suggesting that the bequest vestment but also through the market value motive is not very important. Thus, in a 1962 of assets and consumption. (See my 1971 survey (Projector and G. Weiss, 1964), only 3 article.) percent of the respondents gave as a reason (ii) Transitory Income Taxes: Attempts for saving, "To provide an estate for the at restraining (or stimulating) demand family." However, the proportion rises with through transitory income taxes (or rebates) wealth, reaching 1/3 for the top class (1/2 can be expected to have small effects on million 1963 dollars and over). Similar, consumption and to lower (raise) saving be- though somewhat less extreme, results are cause consumption depends on a life re- reported in a Brookings study (R. Barlow sources which are little affected by a transi- et al., 1966). Thus, the bequest motive seems tory tax change (empirically supported). (See to be limited to the highest economic classes. the literature cited in my paper with Charles This hypothesis is supported by the finding Steindel, 1977, and my paper with Sterling, of Menchik and David that for (and only 1986.) for) the top 20 percent, bequests rise pro- portionately faster than total resources, some- 2. LONG-RUN PROPOSITIONS thing which presumably cannot be explained by the precautionary motive. Furthermore, it (i) Consumption Taxes: A progressive is consistent, incidentally, with the observa- tax on consumption is more equitable than tion that the decline in wealth with age tends one on current income because it more nearly to be more pronounced and systematic in taxes permanent income (quite apart from its terms of the median than of the mean. But, incentive effects on saving.) then the top fifth of the income distribution (ii) Short and Long-Run Effects of Def- can be expected to account for substantially icit Financing: Expenditures financed by def- more than 1/5 of all bequests. Thus, there is, icit tends to be paid by future generations; at present, no basis for estimating, or even those financed by taxes are paid by the cur- placing bounds on, the importance of the rent generation. The conclusion rests on the bequest motive. My hunch, based on pre- proposition that private saving, being con- liminary analysis, is that hump plus precau- trolled by life cycle considerations, should be tionary wealth is likely to account for well (nearly) independent of the government over half-but this is only conjecture, to be budget stance (myself and Sterling), and probed by future research. therefore private wealth should be indepen- dent of the national debt (my 1984 paper). It III. PolicyImplications follows that the national debt tends to crowd out an equal amount of private capital at a Limitations of space make it impossible to social cost equal to the return on the lost pursue a systematic analysis of policy issues capital (which is also approximately equal to for which the LCH has implications that are the government interest bill). significantly different from those derivable This conclusion stands in sharp contrast to by the standard Keynesian consumption that advocated by the so-called Ricardian OL. 7(, NO. 3 MODIGLIANI: LIFE CYCLE AND INDIIDUAL TIIRIFT 311
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