Chapter 1
In this chapter I present the life-cycle hypothesis (LCH) or life-cycle model developed by Franco Modigliani. The study of individual thrift and aggregate saving and wealth has long been central to economics because national saving is the source of the supply of capital, a major factor of production controlling the productivity of labor and its growth over time. It is because of this relation between saving and productive capital that thrift has traditionally been regarded as a virtuous and socially beneficial act. Yet, saving came to be seen with suspicion, as potentially disruptive to the economy and harmful to social welfare. The period in question goes from the mid '30s to the late '40s or early '50s. Thrift posed a potential threat, as it reduced one component of demand, consumption, without systematically and automatically giving rise to an offsetting expansion in investment and production.
It might thus cause “inadequate” demand and, hence, output and employment lower than the capacity of the economy. This failure was attributable to a variety of reasons including wage rigidity, liquidity preference, fixed capital coefficients in production and to investment controlled by animal spirits rather than by the cost of capital. In the second half of the ’40s two important empirical contributions dealt a fatal blow to this extraordinarily simple view of the saving process. First, the work of Kuznets (1946) and others provided clear evidence that the saving ratio had not changed much since the middle of the 19th century, despite the large rise in per capita income.
Second, a path breaking contribution of Brady and Friedman (1947) provided a reconciliation of Kuznets' results with budget study evidence of a strong association between the saving rate and family income.
They demonstrated that the consumption function implied by family data shifted up in time as mean income increased, in such a way that the saving rate was explained not by the absolute income of the family but rather by its income relative to overall mean income. In the first formulation primary stress was placed on reasons why the savings rate should move procyclically and on the consideration
that in an economy with stable long run growth, the ratio of the current to highest previous income could be taken as a good measure of cyclical conditions. These empirical studies have inspired several authors in subsequent years; among these F. Modigliani’s work represents one of the most relevant contribution
The chapter is organized as follows: in the first section will be presented the ”stripped down version” of the LCH ; in the second we will analyze some
extension made to the model about consumption, saving and wealth;
1.1 Life cycle hypothesis: overview
Modigliani and Brumberg formalized the idea that people maximize utility of their future consumption, presuming that the principal motivation for saving is to accumulate resources for later expenditure and especially to support consumption at the habitual standard during retirement. The LCH represented a fundamental shift in the economic debate of the post-war period and in the way of thinking about saving. The LCH was developed three years before the publication of Friedman’s theory of saving; the difference between LCH and Friedman’s Permanent Income Hypothesis refers to the length of the planning period. For Friedman, this period is infinite, i.e. people save not only for themselves but also for their descendants. In the Modigliani-Brumberg version of the theory, the planning period is finite. In some cases, PIH and LCH share similar predictions about individual behavior, for example according to both theories transitory income shocks (transitory taxes and rebates) and capital gains or losses can be expected to have small effects on consumption. But the most part of LCH’ implications about individual and aggregate saving rates are unique, and differ from the infinite horizon version of the model.
When we look at the aggregate implications, the distinction between LCH and infinite horizons is more evident; in fact horizons models have few aggregate predictions and Modigliani always explained that LCH is a theory about individual saving and wealth that behave differently from the corresponding aggregate. If in
the original LCH model the income profile of each generation is constant, and productivity growth is generation specific, this implies the proposition that an increase in productivity growth raises the income of those who save relative to those who dissave, and therefore the aggregate saving rate, a central prediction for LCH. Other implications are the following. First, that the aggregate saving rate depends on the demographic structure of a nation and life expectancy, but is independent from per capita income. Second, that a country can accumulate a large amount of wealth even in the absence of any bequest motive. Third, for this capacity to explain individual and aggregate data the LCH has represented for decades the reference framework for analyzing intertemporal consumption decisions. For the same reason many of the empirical implications of the Modigliani-Brumberg original work have been explored and validated in studies conducted by Modigliani and Albert Ando between 1957 and the early 1970s; and due to this life-long association in the study of saving the LCH has sometimes been termed the M-B-A model and the parameter that controls the aggregate wealth-income ratio is the expected length of retirement. On the theoretical front, the original LCH provided the main inspiration for the development of finite live and overlapping generations models in macroeconomics. On the empirical front, the LCH provided the reference framework of empirical tests of the Keynesian structure.
Even today, the consumption function used by central banks and international institutions to forecast aggregate demand is clearly based on those contributions. When instead microeconomic data became available, the LCH has been the subject of countless empirical scrutiny. The simplest formulation of the model – which Modigliani used to call the “stripped-down” and sometimes the “elementary” or “standard” version of LCH – has been extended to consider many other variables influencing saving decisions, such as changes in family size during the life-cycle, income and other risks, labour supply, habits, bequests, the interaction with insurance and credit markets. The LCH has proved to be a very flexible framework to import each of these additional features, without changing
the basic insights. Modigliani was part of this debate, through important contributions concerning the effect of changes in family size (Modigliani and Ando, 1957), intertemporal choice in the presence of interest and income risk (Drèze and Modigliani, 1974), the role of bequests and other intergenerational transfers (Modigliani, 1988). The LCH could deal with variations in serving other than those resulting from the transitory deviations of income from life resources of PIH. In particular, it could focus on systematic variations in income and in needs which occur over the life cycle, as a result of maturing and retiring, and of changes in family size.
1.2 The hypothesis of the stripped down version
In the M.-B. life cycle model it is assumed that agents maximize a utility function with respect to their own lifetime consumption(that will depend only from his life resources), so their utility is assumed to be a function of his own aggregate consumption in current and future periods. Consumption must be continuous, even if income through the life-cycle is discontinuous and saving is main or even exclusively done to finance consumption during the retirement period. The pure version of the life cycle theory does not allow consumption of current or future heirs to enter parent’s (or household’s) utility function. The hypotheses underlying the M.-B. stationary economy model are the following:
1) population and labour productivity are constant;
2) agents work, with certainty, N years and live, again with certainty, L years;
3) during their working life workers get a constant yearly income, Y, and this income is the same for all workers;
4) during their retirement period, lasting L-N years, workers do not receive any income and, thus, can only consume if, during their working life, they have
accumulated a certain amount of wealth
5) the real interest rate is zero;
6) agents have identical preferences and the latter are such that each agent finds it convenient to maintain a constant level of consumption throughout his life.
In the economy described above all agents receive the same level of income throughout their lives.
Given hypotheses 1 and 6, individual consumption is given by YN/L, so during their working period agents have a positive saving per unit of time equal to Y(1-N/L) and the consumption path over the life-cycle is described by CC’ in Fig.1, where OC=YN/L.
Hence, during his working years each agent has a positive saving equal to Y(1-N/L) and a propensity to save equal to (1-N/L), and during retirement agents have a negative saving equal to – YN/L.
Since by assumption each individual plans to consume all his resources during his life, total saving over the life-cycle, that is the sum of the positive savings made during the working years (represented by the area of the rectangle CDD’G, which is equal to Y(1- N/L)N, and the negative savings made during retirement, represented by the area of the rectangle NGC’L, which is equal (YN/L)(L-N), is zero.
As for individual wealth, it is clearly a function of agents’ age, T. More precisely, for T≤ N, this wealth is given by Y(1-N/L)T, while, for T>N, it is given by Y(1-N/L) N – (YN/L) (T-N) = YN (1 – T/L).
FIG. 1: Income, consumption, saving and wealth as functions of age Y,C,W A D D’ C C’ O N L T
The famous triangle of Modigliani Brumberg , showed by the kinked line OAL, describes the relationship between individual wealth and age. Population is constant so it is possible to derive the macroeconomic features of the stationary economy: if we represent on the abscissa the ages of the different cohorts, instead of the different ages of an individual, and we assume that there is only one individual per age cohort, the graph of Fig.1 gives us the level of income, consumption, saving and wealth for each age-cohort. So we can derive the aggregate level of income, consumption, saving and wealth for the whole economy. We can see in particular that aggregate saving is given by the difference between the area of the rectangle CDD’G (the aggregate positive saving of the active cohorts) and the area of the rectangle NGC’L (which represents the aggregate dissaving of the cohorts of retired workers). In the description of the behavior of the individual, we have established that the areas of the two rectangles are equal, so we can conclude that aggregate saving is zero; about the aggregate wealth in the figure 1is represented by the area of the triangle OAL, which is equal
to YN(L- N)/2, while the wealth /income ratio is given by (L-N)/2.
If we assume that in each age cohort there are X individuals, the levels of income, consumption, saving and wealth of each age-cohort are X times the level shown in Fig.1, but between the two situations there is only a difference of scale. Therefore aggregate saving (and the aggregate propensity to save) remains zero and also the wealth-income ratio does not change, since both the numerator and the denominator of the ratio increase by the same factor, X. The nature of this framework is shown by the value of the Gini Index associated with the distribution of consumption, i.e. all the agents have the same level of consumption throughout their lives, as a consequence the Index value is zero. To see the dimension of the Gini Index associated with income and wealth distribution, we make the following assumptions: individuals, after leaving their parents’ household at the age of 25, work for 40 years and retire for the rest of their life (10 years). Then, it emerges that the Gini Index for income is 0,2 and the one for wealth is 0,33 (Table 1).
TAB. 1.The model with a stationary economy, y=100, L=75, N=65.
S/Y W/Y GINI(w) GINI(c) GINI(y)
0 5 0,333 0 0 (0,2*)
*calculated on the whole population, considering pension benefits as decumulation of wealth (rather than income. Casarosa-Spataro working paper 64/0)
1.3 The temporal evolution of consumption, saving and wealth at the household level
Sinceit is convenient to realize a constant consumption level along the life of the agents, so it is not reasonable to assume that the same household finds it convenient to consume at a constant rate. So we can substitute assumption 6) with
the following:
6’) households have identical preferences and the latter are such that each household finds it convenient to maintain a constant level of per-adult-equivalent consumption through time.
With this, it is clear that the level and the dynamics of consumption, saving and wealth of a household depend on the dynamics of its composition. we assume always for simplicity that parents have the same age and live for the same time span, and that each household has two twin children; the latter leave their parents’ household and enter the labour force at age M. By extending the assumption of certainty as for the number of children each household is going to have, it emerges that each household finds it convenient to realize a per-adult- equivalent consumption equal to YN/(2L + M).
As a consequence, throughout the time interval in which children are at home, household consumption and saving are, respectively, 3YN/(2L+M) and Y-3YN/(2L+M), while both in the preceding and subsequent periods consumption is 2YN/(2L + M) and savings is Y- 2YN/(2L+M) for the households of active workers and –YN/(2L+M) for retired workers.
By maintaining the same numerical values of Y, L, N and M used in the previous section, we consider two households which have their twins, respectively, at age 26 and 36 and follow the dynamics of consumption, saving and wealth of these households by looking at Figs. 2a and 2b. From these figures it comes out that in both cases household consumption, described by the kinked line CC’, increases significantly at the time of births and decreases back to the initial value when children leave the household.
FIG. 2a: Longitudinal profile of income, consumption and wealth (F=26) A D D’ C C’ O F F+M N L T
FIG. 2b: Longitudinal profile of income, consumption and wealth (F=36)
A D D’ C C’ O F F+M N L T Symmetrically, household’s saving decreases dramatically by the time of children
births and reaches the starting value only when children exit the household. It follows that the time pattern of wealth of the two households is very different, since at the moment children are born the wealth already accumulated by the first household is very low and, thus, such a wealth remains relatively low for the whole period of children rearing, while the wealth accumulated by the second household is rather large and, thus, such a wealth remains relatively large for the whole period of children rearing. However, the temporal paths of wealth for the two houseolds coincide starting from the year F+M, when the children of the second household leave home.
FIG. 3: Longitudinal profile of income, consumption and wealth of two households: the first one with F=30 (solid lines) and the second one with F1=26 e F2=34 (dashed lines).
A
D D’
C C’
O F1 F F2 F1+M F+M F2+M N L T
Now we analyze the case of a household that has both children at age 30 and compare the dynamics of its consumption, savings and wealth with those of another household which has two children in different moments of its active life, at age 26 and 34 respectively (notice that the average timing of births is the same in both cases). The variables of both households are in Fig. 3, where dashed
lines are referred to the second household. It is obvious from the figure that consumption, savings and wealth of both households coincide for most of their lives. There are differences in the periods in which households differ as for the number of children they are currently feeding, especially the household that has children when at age 30 consumes less, and hence saves more than the other does, in the age intervals 26-29 e 56-59, while it consumes more and, hence, saves less, in the age intervals 30-33 e 51-54. As consequence the household whose timing of births is age 30 has higher wealth in the age interval 27-34 and lower wealth in the interval 52-59, while in the other years wealth levels coincide.
1.4 Aggregate wealth and wealth distribution in a stationary economy
Now, let use the same graphs to obtain the macroeconomic relations after having described the dynamics of the economic variables of households, in particular we will derive the relationships between the timing of birth, on the one hand, and aggregate wealth and wealth inequality on the other hand. Suppose that there is neither productivity nor population growth and that mortality rate is 1 at some age Land 0 before. The aggregate wealth-income ratio, W/Y, is given by the ratio of the sum of wealth held at each age to the area under the income path; as a consequence we have implications. First of all we understand that W/Y depends on a length of retirement M. so the relation between M and W/Y turns out to be simple, i.e: W/Y= M/2. As regards the aggregate propensity to save, there is nothing to explore; in fact with income and population stationary, aggregate wealth must remain constant in time and, therefore the change in wealth or rate of saving must be zero despite the large stock of wealth. The explanation is that in stationary state the dissaving of the retired from wealth accumulated earlier, just offset the accumulation of the active population in view of retirement. Let us consider first the graphs of Figs. 2a and 2b, now describing two stationary economies in which all households have two children at the same time, respectively, at age 26 and 34. By contrasting the two figures it clearly emerges: first, that the aggregate wealth of
Timing of births 26 30 34 35 36 37 40 26 and 34
S/Y 0 0 0 0 0 0 0 0
W/Y 2,7 3,5 4,3 4,5 4,7 4,9 5,5 3,5
Gini (W) 0,4508 0,2835 0,2250 0,2205 0,2191 0,2203 0,2372 0,3039 the first economy, represented
by the area of the polygon OAL in Fig. 2a, is much smaller than the aggregate wealth of the second economy, represented by the area of the polygon OAL of Fig. 2b and then, that inequality in the distribution of wealth is much higher in the first economy than in the second.
TAB. 2. Timing of births and macroeconomic variables (aggregate propensity of save, wealth- income ratio and Gini Index): case with two children
In the numerical results reported in the first and third column of Table 2 there are confirm the above observations. It is worth noting that, in particular, the Gini coefficient relating to the economy in which households have children at age 26 is more than twice the Gini coefficient relating to the economy in which
households have children at age 34.
FIG. 4: Cross section of three economies with different timing of births
A C’’ B’’ C’ B’ C B O F F F’’ N L T 12
the Gini coefficient progressively decreases, as the timing of births increases, reaches a minimum at age 36 and then rises.
The intuitive explanation of this result is that, when the timing of births increases, total wealth increases too; also for the fact that all the cohorts that before the increase in the timing had dependent children, now hold more wealth, since they have been saving more for a longer period.
We can see this in Fig. 4, where there are different cross-section profiles of aggregate wealth, depending on the timing of births. So, while the share of total wealth held by these cohorts increases when the age of parenthood increases, the opposite happens to all other cohorts.
Among the loosers there are some of the poorest cohorts, the youngest and the eldest ones, and all the richest cohorts, the eldest cohorts of active workers and the youngest cohorts of retired workers. Now, the loss of wealth share by the first group aggravates the distribution of wealth (“first effect”), while the loss experienced by the second group acts in the sense of improving it (“second effect”). Therefore, as the timing of births rises, the distribution of wealth can move in either direction, depending on the number of cohorts belonging to the two groups of loosers.
For example, if we start from a situation in which children are generated early in life, an increase of the timing of births causes a share loss to a very restricted number of cohorts of poor people and to a large number of cohorts of wealthy people.
As a result, a significant improvement of the distribution of wealth takes place. However, as the timing of births increases, the number of poor cohorts experiencing a loss in their wealth share increases, while the number of rich cohorts experiencing a loss of wealth share decreases. These effects can also be seen by looking at the Lorenz curves of wealth distribution associated with different timings of births and.
In Fig. 5a the Lorenz curves relating to two populations with timing of births at age 30 and 34 respectively, are depicted. First, the Figure shows that such
curves cross each other, which confirms that, when the timing of births rises, some cohorts gain and some others lose weight in the distribution of wealth. Secondly, as already mentioned, when the timing increases, both the poorest and wealthiest cohorts lose wealth in the wealth distribution.
In Fig. 5a the “first effect” is represented by the bottom-left area between the two curves, while the “second effect” is represented by the top-right area between the two curves).
When the age of parenthood is relatively low and the latter increases, the “first effect” is dominated by the “second effect”, so that inequality in the distribution of wealth is reduced.
On the contrary, when the timing of births is sufficiently high, as in Fig. 5b, where the timings of births are age 36 and 40, respectively, it happens that the “first effect” is bigger than the second and, as a consequence, the inequality in the distribution of wealth is increased.
c um u la ted s har e of w e a lt h
FIG. 5a: Lorenz curves of wealth distribution associated with different timings of births
1 0,9 0,8 0,7 0,6 0,5 Timing=34 0,4 Timing=30 0,3 0,2 0,1 0 0,02 0,18 0,34 0,5 0,66 0.82 0,98
cumulated share of population
FIG. 5b: Lorenz curves of wealth distribution associated with different timings of births
1 0,9 0,8 0,7 0,6 0,5 Timing=36 Timing=30 0,4 0,3 0,2 0,1 0 0,02 0,18 0,34 0,5 0,66 0,82 0,98
cumulated share of population C umulat e d shar e of w e alth
Finally, we interpret Fig. 3 as a cross section of two stationary economies, in the first of which all households have children at age 30, while in the second all households have the first child at 26 and the second one at age 34 (both economies the average timing of births is the same).
From the graphical analysis and the numerical results reported in the Table 2 it emerges that the aggregate wealth in both economies is the same, but the inequality coefficient is higher in the economic system with higher dispersion of births. So for the stationary economy we can state that: 1) the wealth-income ratio is an increasing function of the timing of births, but is independent of the degree of dispersion of births within the life cycle 2) the distribution of wealth among households depends on the timing of births; i.e. the degree of wealth inequality takes on a relatively high value when parents have children very early in life, decreases when the timing of births goes up and increases again beyond a certain age of parenthood and increases with the dispersion of births.
1.5 The egalitarian model with steadily growing population
In a closed economy, population grows if birth rates are higher than mortality rates. We assume in this model that population can growth if and only if households have, on average, more than two children, no matter the timing. If households have more than two children and, thus, population grows, its growth rate depends not only on the number of children per-household, but also on the timing of births. More precisely, the population growth rate is an increasing function of the number of children per-household and a decreasing function of the timing of births. We assume also, that agents choose consumption and saving independently of house composition, so the relationship between population growth and the timing of births is irrelevant for the relations between population growth rate, one hand, and aggregate propensity to save, wealth-income ratio and distribution of wealth, on the other hand.
1.5.1 The model with constant per-agent consumption
Here, population grows at a constant rate, but agent’s income remains constant through time and equal for all agents. We also assume constant per agent consumption at individual level but at the aggregate level we have innovations: the first is that if population increases, the aggregate propensity to save is positive and an increasing function of the growth rate population. The behavior of saving can be deduct from that of aggregate private wealth, W, through this relations, S=AW, implying: s=S/Y=(ΔW/W)(W/Y)=ρw , and ds/dp=w+ρ(dw/dp) where w is the
wealth-income ratio and p is the rate of growth of the economy which in steady state equals the rate of growth of wealth ΔW/W. This result derives from the fact that, when the growth rate of population raises, the weight of active workers, who have positive savings increases, while the relative weight of retirees who have negative savings, decreases.
The consequence is, when the population growth rate goes up, the aggregate propensity to save tends to the propensity to save of active workers. About the wealth-income ratio, it comes out that this ratio is a decreasing function of the rate of growth of population, since in steady state W/Y=s/g (where g is the income growth rate) and the saving rate increases less than proportionally than the rate of growth of population. Finally, since the higher the rate of growth of population, the higher the relative weight of younger cohorts, who hold little wealth, it comes out that the inequality coefficient of wealth distribution is an increasing function of the rate of growth of population. Remember that, when the source of growth is population, the mechanism behind positive saving may be called the Neisser effect, i.e.: younger households in their accumulation phase account for a larger share of population, and retired dissavers for a smaller share, than in the stationary society. By the way w falls with ρ because the younger people are also characterized by relatively lower levels of wealth holding. When the growth is due to productivity, the mechanism at work may be called the Bentzel effect: Productivity growth implies that younger cohorts have larger life time resources than older ones, and, therefore, their savings are larger than the
Rate of growth of
population n=1% S/Y (%) 4,5007 W/Y 4,5 GINI(w) 0,3547
n=2% 8,1029 4,0514 0,3763
n=3% 10,9495 3,6498 0,3978
dissaving of the poorer, retired cohorts.
TAB. 3. Rate of growth of population and macroeconomic variables (aggregate propensity to save, wealth-income ratio and Gini Index): the M.-B. model with constant per-agent consumption.
1.6 Theory-guided empirical analysis
The mixture of testable theory and theory-guided empirical analysis that Modigliani applied to each of his many research areas has found in the LCH his best example. The strength of his LCH model does not lie just in its ability to explain individual saving behavior, but even in providing a framework for a coherent interpretation of the most important macroeconomic variables, chiefly saving, growth, and social security. Many of the implications of the LCH have been shown to be robust with respect to new theoretical developments and new empirical evidence. Fifty years after the publication of the LCH, no single theory can explain the vast body of evidence on saving behavior, and no comparable theory has emerged. Some competing theories have emerged, and many empirical findings are difficult to reconcile with LCH. In fact still today the LCH is the benchmark model to think about individual saving decisions, the aggregate evidence and policy issues
1.7 The role of bequests and the bequests motive
The basic version of the LHC ignores the existence of bequests; by the way there are notable bequests in market economies. The basic LCH entails that with retirement, saving should become negative and so assets decline at a constant rate, reaching zero at death. But the empirical evidence seems to reveal a very different picture: dissaving in old age appears to be at best modest.
For example, according to Mirer, the wealth income ratio actually continues to rise in retirement. Most other recent analysts (Shorrocks) have found that the wealth of a given cohort tends to decline after reaching its peak in the 60-65 age range. In the 1970’ a number of simulation studies based on the life-cycle model found that the implied aggregate saving rate was substantially less than real-world levels. Davies and Shorrocks(1978) pointed out that very little can be deduced about the quantitative significance of the lifecycle component of saving until (at a minimum) one has first built a complete model able to replicating the main features of saving and wealth behavior observed in real world.
Davies, Hubbard and Hugget provide examples of models which suggested that the amounts of aggregate wealth can be generated from pure life-cycle behavior. A separate research performs wealth decomposition exercise which measure the impact of inheritance on current wealth by summing either past inheritance or past-life-cycle saving. We set the equation for the wealth of a family aged t:
Wt=∑𝑡𝑘=1(𝐸𝑘− 𝐶𝑘− 𝐼𝑘)∏𝑡𝑗=𝑘+1(1 + 𝑟𝑗) (1)
which can be rewritten as
W = ∑𝑡𝑘=1𝑆𝑘𝑅𝑘 + ∑𝑡𝑘=1𝐼𝑘𝑅𝑘 (2)
where Sk = Ek - Ck denotes savings from earned income at age k, and
Rk =∏𝑡𝑗=𝑘+1(1 + 𝑟𝑗) (3)
indicates the returns to investments over a number of years.
Equation (2) shows a decomposition of wealth into self-accumulated (or “lifecycle”) and inherited components. It is, however, somewhat arbitrary, since it
implicitly assumes that all the investment income from inherited wealth is saved, and that all consumption occurs out of earnings. It is equally valid to write (1) in the form:
Wt =∑𝑡𝑘=1(𝐸𝑘− 𝐶𝑘+ 𝑟𝑘𝑊𝑘−1) + ∑𝑡𝑘=1𝐼𝑘, (4)
and to identify the first term, which cumulates forward all saving out of income, with lifecycle saving, and the second component with inheritance. Assuming positive rates of return to investment, the difference between the two decompositions is seen to lie in the smaller contribution of inheritance in (3) compared to (2). Equation 3 might be thought to yield a lower bound to the contribution of inheritance, since it includes savings from returns on invested inheritances in the “lifecycle” component; but if one goes further and we assumes that some portion of inherited wealth is consumed directly, and that this consumption exceeds the saving from interest on inheritances (i.e. b > 0 in equation (2-4)), then the contribution of inheritance to current wealth would be smaller still. However, the latest study by Hurd (1986) using a very large sample and relying on panel data finds that, at least for retired people, marketable wealth systematically declines, especially so if one leaves out the very illiquid asset represented by owner occupied houses.
The finding that decumulation, though present, is slow, may partly reflect the fact that survey data give an upward biased picture of the true behavior of wealth during old age, and for two reasons.
First, as Shorrocks has argued (1975), one bias arises from the well-known positive association between longevity and (relative) income. This means that the average wealth of successively older age classes is the wealth of households with higher and higher life resources. But the most salient question is, how important is the bequests process in accounting for the existing stock of wealth? It was obtained a consistent picture suggesting that the proportion of existing wealth that has been inherited is around 20 percent, with a margin of something like 5 percentage
points. This conclusion has found support in the calculation of Ando and Kennickell (1985); started from estimates of national saving and allocating them by age, using the saving-age relation derived from a well-known budget study, they are able to estimate the aggregate amount of wealth accumulated through life saving by all the cohorts living in a given year. They then compare this with aggregate wealth to obtain an estimate of the shares of wealth that are, self accumulated and inherited. By the way their estimate of the share of inherited wealth turns out to be rather small.
These estimates are conspicuously at odds with that presented in the paper of Kotlikoff and Summers (1981) where they endeavor to estimate the share of bequests by two alternative methods: - from an estimated flow of bequests, as above, and - by an approach methodologically quite similar to that of Ando and Kennickell except that instead of allocating aggregate saving to households by age, they allocate labor income and consumption to individuals 18 and over by age. Through this procedure, they estimate the life cycle wealth, accumulated by every cohort present in a year. K. and S. K&S have suggested an alternative operational criterion of importance which should be independent of definitional differences, namely: by what percentage would aggregate wealth decline if the flow of bequests declined by 1 percent? The suggestion is sound but is very hard to implement from available observations, but a rough measure can be provided by
considering the response of the representative household confronted with a larger
bequest, but subject to the steady state conditions that he must, in turn, increase his bequest by even more. Another fundamental consideration is that, from the fact that bequeathed wealth is not much lower than the peak accumulation, one cannot conclude that most of the wealth ever accumulated is finally bequeathed. So the motive for bequest may be summarized as follows:
-the first is the precautionary motive, arising from uncertainty of the time of death. In view of the practical impossibility of having negative net worth, people tend to die with some wealth, unless they can manage to put all their retirement reserves into life annuities.
- pure altruism; parents care about their children’s future, and provide for their education (often very expensive where only private education is excellent) and for their well-being
- The conservation of ‘family’s silverware’: in many cases dynasties have
held for many generations houses, land, firms or other assets, and other kinds of wealth
- Joy of giving, or paternalistic bequest, also called
‘bequest-as-last-consumption’: in this case a direct utility is associated with the act of giving to one’s heirs
-Strategic bequest: the children take care of the old parents, providing all sorts of assistance until their death; the parents in return agree to bequeath all their wealth to them
It is clear that the presence of bequests in an economic system leads, all other things being equal, to the perpetuation of high levels of inequality in the distribution of wealth and so, though to a lesser extent, of total income.
We know that bequests play an important role in the determination of macro-economic aggregates (for example total savings, government receipts, etc.) as well as, in the determination of the level of wealth, but also on income from wealth and hence on all income inequalities.
References
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