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Wealth accumulation process by income class
JOURNAL
OF THE
JAPANESE
AND
INTERNATIONAL
ECONOMIES
5,
239-260 (1991)
Wealth Accumulation Process by Income Class* TOSHIAKI
TACHIBANAKI
Kyoto Institute of Economic Research, Kyoto University, Yoshida Honmachi, Sakyo-ku, Kyoto 606, Japan AND KEIKO
SHIMONO
Department of Economics, Nigata Sangyo University, Japan
Kashiwazaki,
Nigata
945-13,
Received March 22, 1988; revised May 31, 1990 Tachibanaki, Tosbiaki, and Shimono, Kelko-Wealth Income Class
Accumulation
Process by
The paper examines the empirical data on income and wealth in Japan carefully. The preliminary examination suggested the importance of intergenerational wealth transfers not only for high-income earners but also for some low-income earners. A simple model of savings behavior with a bequest motive was applied in order to estimate indirectly the amount of intergenerational wealth transfer by income class. This indirect method was reasonably successful in revealing the relative importance of intergenerational wealth transfers by income class in Japan, where no direct data on intergenerational wealth transfers are available. J. Japan. Int. Econ., September 1991,5(3), pp. 239-260. Kyoto Institute of Economic Research, Kyoto University, Yoshida Honmachi, Sakyo-ku, Kyoto 606, Japan; and Nigata Sangyo University, Department of Economics, Kashiwazaki, Nigata 945-13, Japan. 6 1991 Academic Ress, Inc. Journal of Economic Literature
I.
Classification Numbers 110, 840, 920. INTR~DuCTI~N
There have been few studies of wealth accumulation by class (income class or wealth class) in Japan. Studies of wealth accumulation which include both monetary wealth and physical wealth are quite rare because * The authors are most grateful to Tsuneo Ishikawa, who provided them with extremely constructive suggestions. Ken Ariga, Haruo Imai, and Takamitsu Sawa gave useful com239
0889-1583191 $3.00 Copyri.&t 0 1991 by Academic Press. Inc. Au rights of reproduction in any form reserved.
240
TACHIBANAKI AND SHIMONO
the data on physical wealth had been unavailable. Since we found a relevant source which contains useful data on both physical wealth and income (or wealth) class, we attempted to investigate the wealth accumulation process by income class. We believe that intergenerational wealth transfers such as gifts or bequests play an important role in determining the wealth accumulation process. Although the data which we use do not contain any information on gifts and bequests, we attempt to estimate them indirectly by examining the data source carefully. Thus, it is our intent to examine the influence of intergenerational transfers on the wealth accumulation process from the life-cycle point of view. Section II presents the data source. Section III examines the past studies related to this subject. Section IV investigates the raw data very carefully and draws several implications of intergenerational transfers of wealth on the basis of the wealth-income ratio. Section V presents the estimated amount of bequest derived from the life-cycle savings hypothesis with a bequest motive. Finally, conclusions and comments are provided. II.
DATA SOURCE
The principle data source is the Survey on Saving Behaviours and Consciousness conducted by the Department of Sociology, University of Tokyo, in 1981. The number of total observations used is 1708. The number of employees is 1134, and that of nonemployees is 574. The original survey included about 4300 observations. Since the survey contains a large number of unreported figures of wealth, the available number has been reduced considerably. Although this is quite usual and unavoidable when the survey asks about wealth figures, it is expected that future surveys will reduce the number of unreported figures. The survey asked a large number of questions on income and wealth (including the composition of wealth). Wealth consists of monetary wealth and physical wealth. Physical wealth is measured largely by residential house and land. Buildings for business use, agricultural land, and forest are eliminated, because their values are not reported. Since it is appropriate to utilize a homogenous group of people, single people and extremely rich families were excluded from the sample. i ments. Two unknown referees improved the quality of this paper substantially. The authors are responsible for possible errors. i Eliminating extremely rich people (in fact we have excluded households whose annual incomes are over 40 million yen) may be somewhat problematic. We did so because the behavior of these extremely rich people might be entirely different from that of ordinary people. In other words, it would be desirable to inquire about the wealth accumulation process separately for these extremely rich people. Nevertheless, the number of extremely rich people is very limited, only 1%. Thus, the bias due to such an elimination is very minor.
WEALTH ACCUMULATION PROCESSBY TABLE THE
DEGREE
OF INEQUALITY
241
INCOMECLASS
I
IN INCOME AND WEALTH GINI COEFFICIENT
DISTRIBUTIONS
BASED
ON THE
Income
Monetary wealth
Physical wealth
Total wealth
Net wealth
Gini coefficient Average (million yen) Standard deviation
0.258 4.45 2.13
Employees 0.546 3.72 4.06
0.623 12.60 15.02
0.549 16.32 16.78
0.581 14.15 16.01
Gini coefficient Average (million yen) Standard deviation
0.380 5.29 4.44
Nonemployees 0.550 6.36 7.18
0.575 21.98 25.02
0.518 28.34 28.46
0.545 25.64 27.49
Gini coefficient Average (millionyen) Standard deviation
0.308 4.73 3.18
Total households 0.563 4.61 5.64
0.616 15.75 20.18
0.553 20.36 22.93
0.584 18.01 22.02
Note. (1) The sample number is 1134 for employees, 574 for nonemployees, and 1708 for total samples. (2) Contributions to life insurance are not included in monetary wealth. (3) Physical wealth is the sum of the self-assessment of land and house. (4) Net wealth is the difference between total wealth and debt.
III.
EXAMINATIONS OF THE PAST STUDIES AND PRELIMINARY ANALYSIS
We cite several studies which investigated wealth distribution in Japan. These studies are reviewed very briefly as a rough introduction to the study of wealth accumulation in Japan. All the studies reveal that the inequality of wealth distribution is much higher than that of income distribution. Takayama (1980) found that the Gini coefficients for income distribution and for monetary wealth distribution for employees were 0.197 and 0.505, respectively, in the 1974 Survey on Household Consumption. Togashi (1979) reports that the Gini coefficients for income, monetary wealth, and total wealth (both monetary and physical wealth) for employees are 0.313, 0.661, and 0.614, respectively, in the 1977 Survey on Saving Behaviours and Consciousness. It is noted that this study uses the same data source as Togashi’s study, although the sample year is different. Table I shows the estimated Gini coefficients for various concepts of wealth based on the current data. See the Section IV for how the original data were arranged in order to prepare the figures of wealth, income, and others. Various categories, namely employees, nonemployees, and total
242
TACHIBANAKI
AND
SHIMONO
households, are considered. For employees, which can be compared with Togashi’s study, the estimated coefficients for income, monetary wealth, and total wealth are 0.258,0.546, and 0.549, respectively. It is worthwhile to note that both income and wealth inequalities have decreased. See Tachibanaki (1989) for a recent study which showed the opposite trend in wealth distribution. Two interesting observations are possible from Table I. First, inequality for physical wealth is considerably higher than that for both monetary wealth and total wealth (monetary plus physical wealth). At the same time, net wealth (total wealth minus total debt) gives an inequality higher than that of total wealth. Second, nonemployee households have an inequality in all dimensions of wealth lower than that of employees, except for monetary wealth, although income inequality for nonemployee households is higher than that for employees. One possible reason is that buildings for business use are excluded. It is very likely that nonemployees hold a considerable amount of land and buildings for their own businesses. If these buildings and land were included in the data, the inequality of wealth distribution would be higher for nonemployees than for employees, because the values of land and buildings are considerably high. It is possible to raise several factors to explain the higher inequality in wealth distribution. For example, Takayama (1980) raises the following: (1) age effect, (2) income differential, (3) the difference in the rate of return to wealth, (4) gifts and bequests, and (5) institutional factors such as the tax system. Other factors such as (6) inflation and (7) savings rates may be added. Under the strict life-cycle savings hypothesis the age effect is the most important for explaining wealth inequality. Only 40% is explained, however, by the age effect in determining the inequality of monetary wealth. The contribution of income differential to wealth inequality is only about 25%. These numbers were estimated by Takayama (1976). It is necessary to seek an alternative variable such as gifts and bequests, which can be an important component of wealth inequality. There are several studies which indicated the importance of intergenerational wealth transfers. Atkinson (1971) proposed that if the bequest was of luxury goods, wealth inequality would increase with the age of the person under the assumption that the growth rate of the population is lower than the rate of interest. Ishikawa (1975), however, raised the possibility that if education was of consumption goods, bequest would not necessarily enlarge the inequality of wealth distribution. Also, liquidity constraint (or imperfection of the capital market) may increase wealth inequality, as Ishikawa (1974), Tomes (1981), and Hayashi (1986) showed. The importance of intergenerational transfers in the field of wealth distribution and the savings hypothesis was proposed empirically by Atkin-
WEALTH ACCUMULATION PROCESSBYINCOMECLASS
243
son (1971), Oulton (1976), White (1978), Kotlikoff and Summers (1981), and others. We see a controversy between Kotlikoff (1988) and Modigliani (1988). For Japan, several studies such as those of Tachibanaki and Shimono (1986), Hayashi (1986), Ishikawa (1988), and Hayashi er al. (1988) proposed the inapplicability of the life-cycle savings hypothesis and suggested the importance of a bequest motive as a conceivable hypothesis. It is anticipated, however, that the influence of a bequest motive may differ significantly according to one’s income or wealth level. This is the subject of the present undertaking. Since there are no data on the amount of intergenerational wealth transfer by income class (equivalently, individual survey data on bequests), we adopt a methodology which enables us to estimate the amount indirectly.
IV.
WEALTH ACCUMULATION PROCESS
This section examines the raw data carefully and attempts to draw several implications of intergenerational transfer of wealth based on the observed wealth-income ratio.2 The empirical evidence found in this section forms a basis for deriving a theoretical model in Section V. We examine the sample of employees carefully. The result for nonemployees is not examined as closely because an adequate economic theory has not been established for nonemployees. Before the observed wealth-income ratio is discussed, several notes are presented with respect to preliminary data arrangements. First, the data on monetary wealth include cash, demand deposit, time deposit, equity, bond, and security. Contribution to life insurance programs is excluded simply because it is not reported. Shimono and Tachibanaki (1989) show that contribution to life insurance can be regarded as one form of savings. Very roughly, the share of life insurance in total monetary wealth is about 20%. However, it is controversial whether contribution to life insurance can be regarded as a form of savings. Some propose that life insurance is merely consumption. Since the data we used excluded it from 2 It is possible to consider the real value of the wealth-income ratio rather than the nominal value. What kind of deflator should be adopted to calculate the real value is controversial. Suppose we take the consumer price index Pi (i is the ith region) for both nominal income yi and nominal wealth Wi. Taking the real value of the wealth-income ratio, (W,lPJl(yilPJ = Wi/Yi)gives the same result. In other words, it does not matter whether we consider the nominal value or the real value, if we adopt the wealth-income ratio. This may be an advantage because the differences in consumer price indexes by region can be ignored by considering the wealth-income ratio. When the deflator for income and the deflator for wealth are different, the above result is not valid. We have to consider an alternative method in this case.
244
TACHIBANAKI
AND
SHIMONO
the list of savings, we simply followed this procedure. It is necessary to understand the difference, and the issue probably will have to be settled in the future. Second, the data on physical wealth are dependent upon the self-assessment of land and housing values. Obviously, they contain measurement errors. Since Togashi (1979) reported that the measurement error was within a range of lo%, we did not attempt to modify the value given by self-assessment. Also, it is an enormously difficult and even risky task to modify the appropriate value of physical assets based on self-assessment. The rates of landholding and of homeholding in this survey are 63 and 49%, respectively. The per capita average value of physical wealth is 16 million yen, and it is about four times higher than the value of monetary wealth, i.e., 4.3 million yen. Third, it is assumed that the degree of income mobility among the five income classes is zero over all ages. In other words, a representative person who was in the first quintile at his first life stage remains in the first quintile throughout his entire life. Persons in the other quintiles keep the same property. This is a somewhat drastic assumption adopted in order to make our analysis feasible. No panel data for income and wealth are available in Japan. The assumption is not, however, so unrealistic for the following three reasons. First, the Japanese wage determination system, i.e., seniority- and age-based wage payment, does not generate a wide range of wage and income mobility. In other words, one’s initial class in the payment structure determines one’s course of wage growth (or the class in the wage distribution) throughout one’s career to a great extent because the wage is largely determined by age and tenure. See Atoda and Tachibanaki (1991), who estimated a very low degree of wage mobility indirectly in Japan. A similar scenario would be supported for income distribution as well in view of the fact that wage is the most important component of total income, as shown by Atoda and Tachibanaki (1985). It is noted that we deal only with employees in the model analysis of this paper. Second, since there are only five income classes in this study, interclass income mobility is expected to be low although intraclass mobility is likely to be fairly high. In this paper we can safely ignore intraclass mobility because we are interested in representative persons. If the number of income classes were larger, interclass income mobility would be higher. See Tachibanaki and Atoda (1986) for a discussion of this. Third, our concern in this paper is a representative or hypothetical person rather than a real person. Thus, empirical plausibility is not our major goal. We recognize, however, that a modification taking interclass mobility into account is certainly required in the future. Only panel data enable us to perform such work. To return to data arrangements, fourth, we do not attempt to transform
WEALTH
ACCUMULATION
PROCESS BY INCOME
CLASS
245
our cross-sectionaldata into cohort data. In other words, the growth rate of GNP or productivity is assumedto be zero. This is againa simplified assumption.It is not, however,harmful, at least for our purpose,because thecross-sectionaldataaresufficientto showthe importanceof intergenerational transfersof wealth by income class.Also, it is true that we do not obtain a different result even if we take accountof the GNP growth rate. Our main tool for analyzing the wealth accumulation process is the wealth-income ratio. It is noted that wealth means net wealth, that is, total wealth minus debt. The wealth-income ratio has an important merit which enablesus to investigate the relative contribution of income and consumptionto wealth accumulation.In other words, the wealth-income ratio, which is standardizedby income level, is a more relevant variable than wealth itself becauseincome is a very rough indicator of the level of consumption.Also, a large number of studiessuch as those of Diamond (1977) and Diamond and Hausman (1984) adopt the concept of the wealth-income ratio. Under the pure life-cycle savingshypothesisDiamond (1977)was able to show that the required wealth-income ratio is about 4.0 at retirement age. Tachibanaki and Shimono (1986)presented the empirical result for Japan.This paperintendsto estimateit by income class. Figure 1 shows the wealth-income ratios for several income classes. Table II gives detailed wealth-income ratio numbers. A simple average of the wealth-income ratios for ages55-59is 5.18for employeesand 5.57 for the total sample (employeesand nonemployees).These values are considerablyhigher than the value estimatedby Diamond. It is important, however, to recall that these averagevaluesdo not describea very wide differencein the wealth-income ratios by income class. Severalobservations arepossiblefrom Fig. 1. First, the wealth-income ratio of the higher income classis higherthan the averageuntil the ageof 40,while it is lower than the averageafter that age.This is more obvious for employeesthan for all samples.Second,the wealth-income ratio of the lower incomeclass is higher than the averagefor all ageclasses.It is necessaryto determine the reasonsfor theseobservations.We beginwith the higherincomeclass. (a) Wealth-Income
Ratio of Higher Income Class
First, it is observedthat the rate of physical assetacquisitionby young peopleof the higher income class is considerablyhigh.3Figure 2 shows that the averagerate of householdingby young people(i.e., late 20s and 3 The following comment may be made: the liquidity constraint is weaker even for younger people whose income levels are higher. In other words, even younger people are able to borrow funds relatively easily to acquire physical assets if their incomes are higher. Thus, it is possible that easier accessibility of credit tinancing made the rate of physical asset holding higher for these people. However, our tool, namely the wealth-income ratio, is
246
TACHIBANAKI
2
AND SHIMONO
-.
1
FIG. 1. (Net) Wealth-Income
1t ratio by age class for the first and f&h quintiles.
early 30s) of the higher income class is about 70% and that of landholding is about 50-60%, while the average rate of householding by the same ageclass people of total households is about 30-40% and that of landholding is about 25-35%. The difference is large, and it is possible to conjecture that these high rates of physical wealthholding are due largely to intergenerational wealth transfers from parents. Second, income differentials become wider as the samples become older. While the index of income levels for people of higher income class are younger than 40 in comparison with the average income of the same age class (the index is specified as 100) is about 170-180, the index is higher than 200 for people of higher income class who are over 50. Simply speaking, the older the sample, the wider the income differential. In other words, since the denominator of the wealth-income ratio of this class increases more than the average as the sample becomes older, the estimated wealth-income ratio of the higher income class decreases disproportionately in comparison with the wealth-income ratio of other classes. defined by net wealth (total assets minus debt) rather than total assets. Thus, if the nonliquidity constraint hypothesis were prevalent, the (net) wealth-income ratio would be lower. In reality the (net) wealth-income ratio is higher for young people of the higher income class, as Fig. 1 indicates.
.5
330
wIO.0)
363
57
(100.0)
(15.7)
34
34
351
37
51 3s
39
36
51 44
343
;
Fourth
CLASS
(100.0)
(10.5)
(11.4)
(10.5)
(12.8)
(14.9)
.i,,l;l;)
quintile
BY INCOME
21
I2
12}49
25
37
43
60
52
321
‘;
allocations of the samples whose income figures are equal.
(100.0)
(10.5)
(9.7)
(9.7)
(13.1) (13.1)
ii(24.8)
II
RATIOS
TABLE Third quint&
Now. The unequal total numbers in the live quintiles are due to somewhat arbitrary
71
8.0-
TOtA
(21 .S)
(8.3)
(5.2)
91
30
I9
46 46
25
(4.2)
(7.3)
(8.3)
(16.3)
;
7.0-8.0
14
4.0-5.0
30
59
C;;(30,6)
6.0-7.0
24
3.0-4.0
(6.10
(10.6)
;-
Second quintile
I7
20
‘;;:;(28,5)
(10.0)
First quintile
WEALTH-INCOME
5.0-6.0
35
1.0-2.0
f}%
33
Number
2.0-3.0
ifB!i
-0.0
income ratios
Wealth-
(NET)
(100.0)
6.5)
~-;;},I,.,,
(11.5)
(13.4)
(18.7)
(16.2)
$16.2)
Fifth quintile
1708
221
;]2l6
243
I,-
;$C25.3)
(llw.0)
(12.9)
‘;]Cl2.6)
(14.2)
Total
248
TACHIBANAKI
AND
SHIMONO
a Hauar 100
Fifth
f
,,,J... XJ,’
______-----a’
,’
/‘--- .._. ._..__
quinti1e
-. Average
,,*’ .I’ T First
wintile
50 ..
/-?::-
50 .’
Fifth quintih2 A.-_ ,’ _,,_,-----..._ /,/’ .__--,/- Averege ,,,’ T quintile ,/’,/’ First fl
FIG. 2. The rate of house and landholding by income and age classes.
In summary, it is proposed that two factors, namely, (i) a high rate of physical asset acquisition by youth and (ii) a higher income level by older people, are responsible for explaining the movement of the wealth-income ratio of the hiiher income class by age. We emphasize that the intergenerational transfer is the most crucial factor. Even young people of higher income class did not acquire their physical wealth through credit financing but through gifts and/or bequests from their parents. (b) Wealth-Zncome Ratio of Lower Income Class It is necessary to determine why the wealth-income ratios are higher throughout all age classes for the lower income class than the average for all income classes. This is contrary to the result obtained by Diamond and
WEALTH
ACCUMULATION
PROCESS
BY
INCOME
CLASS
249
Hausman(1984),who found that thegreatmajority of lower incomeclasses have lower wealth-income ratios in the United States.Table II presentsa clueto the mystery. This table showsthedistribution of the wealth-income ratio for eachincome class(i.e., five quintiles). The distribution of householdsin eachincome classin Table II is obtainedthroughthe distribution of householdsbasedon the number of householdsin eachageclass(fiveyear intervals) in Fig. 1. The number of householdsbelongingto the first quintile in eachageclass in Fig. 1 forms the distribution of householdsin the first quintile in Table II. The distribution in the secondquintile is fabricatedthroughthe samemethodologyasthat in the first quintile. Thus, the age distribution in each income class is, roughly speaking,similar. Table II suggeststhat there are a large number of householdswhose wealth-income ratios are low amongthe low-income earners.For example, the shareof peoplewhosewealth-income ratios are lower than 1.Ois 38%for the first quintile. These numbersare 35%for the secondquintile, 30%for the third quintile, 28%for the fourth quintile, and 18%for the fifth quintile. Moreover, the lower the income level, the higherthe rate of low wealth-income ratio. This is easily observedwhen we look at the number of householdswhose wealth-income ratios are lower than zero. These findings lead to the conclusionthat the shareof very low wealth-income ratios is considerablyhigh among low-income earnersdespite a roughly equal agedistribution in eachincome class. When we look at the averagefigures, the wealth-income ratios are higher in the low income class than in the total income class. We must resolvethis apparentcontradictionagainstthe lower wealth-incomeratios of low-income earnerswhich wasdescribedabove.Table II againprovides us with a clue. It is noted that some low-income earnershave very high wealth-income ratios. For example,the shareof the wealth-income ratio higherthan 8.0 is 22%for the first quintile, while the sharesareabout 10% for the other quintiles. Another important result derived from Table II is the decreasingtendencyin the variancesof wealth-income ratios as the incomeclassbecomeshigher. For example,the shareof householdswhose wealth-income ratios are either extremely high or extremely low is quite low in higher income classes. Table III is presentedto show that the extremely high wealth-income ratio for low-income earners(i.e., the first quintile) is not causedby their low incomes(or wider income differentialswithin the first quintile). Table III shows that income differentials between low wealth-income ratios (Le., lower than 0.0 or 1.O)and high wealth-income ratios (i.e., higher than 5.0 or 8.0) are very marginal, while the differencein the amountsof both total wealth and net wealth betweenlower wealth-income ratios and higher wealth-income ratios are very large.The amount of total wealth is 0.741 million yen for a wealth-income ratio lower than 0.0 and 0.928 million yen for a ratio lower than 1.0, while it is 26.8 million yen for a
250
TACHIBANAKI
AND
TABLE
SHIMONO
III
(NET) WEALTH-INCOME RATIOS AND DETAILED FIGURES OF WEALTH FOR THE FIRST QUINTILE: THE DISTRIBUTIONS (MILLION YEN)
Wealth-income
‘C-1.0
>5.0
>8.0
110 4.37 22.44
71 5.00 28.49
0.93 8.21 0.11 2.04
26.81 1.21 25.60 1.94
33.49 1.33 32.15 1.84
Ages 30-39 60 0.81 0.15
21 2.94 20.45
Sample number Monetary wealth Physical wealth Zero wealth
All ages 127 0.72 0.21 115 (82s%) (91%)
Total wealth Debt Net wealth Income
0.74 2.56 -1.82 1.74
Sample number Monetary wealth Physical wealth Zero wealth
ratio
33 0.48 0.26
(2%) Total wealth Debt Net wealth Income
0.95 0.67 0.28 2.10
23.39 3.46 19.92 1.67
wealth-income ratio higher than 5.0 and 33.5 million yen for a ratio higher than 8.0. This large difference is to a great extent due to the large difference in the amount of physical wealth, as Table III shows. It is 0.257 million yen for a wealth-income ratio lower than 0.0 and 0.213 million yen for a ratio lower than 1 .O, while it is 22.4 million yen for a wealth-income ratio higher than 5.0 and 28.5 million yen for a ratio higher than 8.0. The difference in the amount of monetary wealth is also considerably large, although it is much smaller than the difference in physical wealth. The results for those aged 30-39 in Table III, who are relatively young and who would, possibly, be able to receive bequests, also support the above finding.4 In conclusion, it is clear that the higher wealth-income ratios for sOme low-income earners originated from their high amounts of wealth 4 It would be preferable, to make our conjecture more convincing, to show that there are fewer retirees in the low-income class. Since the data do not distinguish between retirees and nonretirees, this was not shown.
WEALTH
ACCUMULATION
PROCESS BY INCOME
CLASS
251
holding. Moreover, since their incomes are lower, it is possible to conjecture that the great majority of their wealth came from bequests and/or gifts from their parents or past generations.
V.
ESTIMATION OF INTERGENERATIONAL TRANSFERS CLASS BASED ON THE WEALTH MODEL
(a) Model Framework
and Preliminary
BY INCOME
Results
This section investigates whether a simple model of wealth accumulation by income class is appropriate for estimating the value of intergenerational wealth transfer. While the previous section estimated it by examining the raw data carefully, this section intends to estimate it through a model of savings behavior and to compare it with the actual data. We adopt a simple life-cycle hypothesis with a bequest motive a la Blinder (1973) as a basis of the savings behavior. The model is explained here briefly.5 An individual utility function is given by T WC,,
* . . ,
c’-Y
cT,A) = tz,e(l
+ p)‘-’
+ bF
:
/l
+ PFT,
(1)
where C, is consumption at time t. AT is bequest at death (t = 2’). -y is the elasticity of marginal utility with respect to consumption and bequest (y > 0 and y # 1). y is a measure of the relative risk aversion, and its inverse is equal to the inter-temporal substitution parameter. p is a discount rate. b is a parameter for bequest motive. An individual budget constraint is given by 2 C,(l + I)‘-’
+ A#
+ r)l-T = A,, + 5 W,(l + r)‘-‘, f=l
(2)
where W, is the wage income (or the pension payment) at time t. r is the real interest rate. A, is the receipt of intergenerational transfer from the past generation. 5 It is possible to consider the effect of the number of people in a household N, in this model framework. Shimono (1988) performed a sensitivity analysis by considering the number of family members. It turned out that the qualitative result was not very different from that of the current model, which ignores the intluence of family members. In any case not only the number of children but also the difference between sons and daughters is a future subject to be investigated very carefully for Japan.
252
TACHIBANAKI
AND
SHIMONO
We give a somewhat oversimplified assumption about the relationship between A, and A, in order to make the model workable: A, = A# + r)‘-r. This relationship implies that the higher the receipt of intergenerational wealth transfer, the higher the bequest left. In other words, intergenerational wealth transfers in this framework do not change the course of intergenerational wealth inequality, or they are neutral with respect to the wealth inequality of the next generation. This is probably the most stringent assumption made in this paper. It implies that parents plan to leave bequests whose present values are equal to that of the initial receipt from their parents. In other words, altruistic parents have altruistic children, while egoistic parents have egoistic children. It is not so unrealistic to conceive of this assumption because the empirical evidence given in Section IV supported it, especially for higher income class families. We do not say that it applies to all lower income class families. However, some lower income families can assume this property, as suggested in Section IV. Since the removal of this assumption does not change the qualitative result of this paper, we adopted this assumption. It is certainly a subject for future research, however. Under the assumption of A, = Ad1 f r)lPT, Eq. (1) is maximized subject to Eq. (2). The first-order conditions provide us with the equations
cf=cl
1+ r 0- IVY ( 1 l+p
(3)
where C, is given by
(4)
A,
= b”Y(l
+ r)(T-
‘)‘Y * C,.
(5)
The above equations suggest that when the value of b (or Ar) is assigned, AT (or b) is solved in the model. Since Eqs. (3), (4), and (5) are able to depict the entire course of consumption, savings and thus wealth during one’s lifetime can be determined when wage incomes during one’s lifetime are given. We have several robust estimations of age-earnings profiles in Japan which have a quadratic function of age, as shown, for example, by Tachibanaki and Shimono (1982,1986). Thus, the age-earnings profiles by income class, which were drawn from the Saving Survey, 1981, on the basis of
WEALTH
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CLASS
253
severalquadratic functions of age,are very realistic. The amount of pensions after retirement (age60) is equal to 60% of the wage earningsat retirement, which is believed to be close to the realistic value. The other valuesof r, p, and y are 0.03, 0.02, and 3.0, respectively.6 Table IV presentsthe estimatedvalues for some of the key variables for the averagewage and pension payments of the entire sample. This tableis presentedto showthe importanceof theinitial wealth (A,,) inherited from the past generationin determiningthe future courseof income and wealth accumulation. Specifically, two observationsare possible from Table IV. First, the higherthe initial wealth, the highertheinterestincome and thus the higher the total income level. Second,the previousobservation naturally generatesa higher wealth-income ratio and thus a higher bequestmotive (b). In sum, the influenceof the initial wealth (A,,) is quite important in determining the courseof income and the wealth accumulation process. (b) Zntergenerational
Transfers by Income
Class
This section intends to estimate the plausible amount of intergenerational transfersby income classbasedon the model presentedhere. This sectionis entirely different from Section Va. While that sectionassessed the importanceof intergenerationaltransfersin determiningthe courseof income and wealth accumulation on the basis of hypothetical values of intergenerationalwealth transfers, this section attempts to estimate the realistic amount of intergenerationaltransferon the basisof the observed wealth-income ratios. In other words, an attempt is made to infer the amount of intergenerationalwealth transfer, which is not availablein any data source, on the basis of other observablevariables such as wealthincome ratios. The estimated(or calculated)amount of intergenerational transfer by income class is influencedby the assignedcoefficientsin the model. See Shimono (1988).The qualitative feature, however, of intergenerationaltransfersor bequestmotives is not alteredby various coefficients. The estimation of intergenerationaltransfers(A, andAT) is fairly primitive. We iterate a large number of intergenerationalwealth transfersand find a value which minimizes the prediction error of the estimatedwealth income ratio in comparison with the observedwealth-income ratio for 6 These values are expected to be close to the plausible values in Japan. Since it is impossible to assign the absolutely relevant values in any society, a sensitivity test was added later. Shimono (1988) constructed an alternative model which takes into account the number of peopIe in a household, the change in the retirement age, and the recalculation of the pension payment. Also, a more- careful sensitivity test was attempted. Interested readers should refer to Shimono (1988).
Lifetime consumption
203.6 203.6 203.6 203.6 203.6 203.6 203.6
202.4 202.4 202.4 202.4 202.4 202.4 202.4
0 1 2 5 10 15 20
KEY
203.6 207.8 212.0 224.8 245.9 261.1 288.3
Lifetime income
OF SEVERAL
Lifetime wage
RESULTS
Initial wealth 640)
ESTIMATED
Annual income at age 5.43 5.51 5.60 5.74 6.27 6.70 7.12
IV
UNDER
TABLE VARIABLES
11.2 14.1 17.0 25.6 40.1 54.6 69.1
Wealth at age 60
DIFFERENT
WEALTHS
2.05 2.55 3.03 4.38 6.40 8.16 9.71
Wealth-income ratio at age 60
INITIAL
YEN)
0.0 5.2 10.5 26.2 52.3 78.5 104.7
Bequest at death
(MILLION
0.0 0.7 6.0 94.0 749.0 2528.0 5920.0
Parameter of a bequest motive
WEALTH
ACCUMULATION
PROCESS
BY
INCOME
CLASS
255
each income class. Specifically, we estimate an optimum A, which minimizes the sum of the three prediction errors at ages 40-44, 45-49, and 50-54 by considering the equation min {(WI,,
- w&2j2 + (WI,, - WI,,)2 + (WI,, - wI,2)2},
(6)
where WI, signifies the observed wealth income ratio at the ith age class, and WI, signifies the predicted or hypothetical wealth income ratio generated by various intergenerational transfers. Obviously, ages 40-44,45-49, and 50-54 are close to retirement age. Table V shows the estimated result of intergenerational transfers and several related statistics based on the method described above. Lifetime wage earnings, lifetime consumption, lifetime income, wealth-income ratios at ages 42 (representing ages 40-44), 47, and 52, and parameters of the bequest motive are provided in Table V for each income class. The numbers in row (A), where A,, = 0, are the estimated results in the case in which the initial intergenerational transfers are assumed to be zero. The numbers in row (B) are the estimated results which gave the minimum prediction errors, as described previously. In other words, the results based on A, = 0, i.e., row (A), are for the hypothetical world in which there are no intergenerational transfers, while the results of row (B) are the estimated values of intergenerational transfers and the related statistics based on the economic model considered here. The actual values of the wealth-income ratio at ages 42, 47, and 52 are also provided for comparison. Several observations are possible from Table V. First, the distinction between row (A) and row (B) is enormous. In other words, the case in which there are no intergenerational transfers generates extremely unrealistic values of the estimated wealth-income ratios at ages 42, 47, and 52, except possibly for the first quintile, suggesting that the life-cycle savings hypothesis without a bequest motive is a highly unrealistic theory. In other words, it is essential to take into account the contribution of intergenerational wealth transfer in investigating the wealth accumulation process. Second, row (B) generates increasing values of intergenerational transfers with income class. The estimated amounts of intergenerational transfer are 1.5 million yen for the first quintile, 5.2 million yen for the second quintile, 8.5 million yen for the third quintile, 12.1 million yen for the fourth quintile, and 19.4 million yen for the fifth quintile. In other words, the hypothesis “the higher the income class (or lifetime income and wealth), the higher the intergenerational transfer” is supported by the estimated amount of intergenerational wealth transfer. Equivalently, “the higher the income class, the higher the bequest motive” is supported. Third, the estimated wealth-income ratios after retirement give different
151.5 151.5
188.8 188.8
223.5 223.5
Actual value (A) A0 = 0 (B) A,, = 5.2
Actual value (A) A0 = 0 (B) A, = 8.5
Actual value (A) A, = 0 (B) A,, = 12.1
(A)A, = 0 (B) A,, = 19.4
309.6 309.6
102.2 102.2
Lifetime wage
Actual value (A) A0 = 0 (B) A0 = 1.5
Actual value
V
302.8 302.8
223.4 223.4
193.0 193.0
159.0 159.0
113.3 113.3
Lifetime consumption 2.75 1.74 2.65
2.87 - 1.12 2.48
Third quintile
3.66 0.17 2.74
302.8 385.0
223.4 274.7
3.57 -3.18 2.76
Fifth quintile
3.33 - 2.07 2.63
Fourth quintile
193.0 229.0
159.0 181.0
Second quintile
113.3 119.7
3.11 - 2.52 3.36
2.98 -1.33 3.40
2.96 -0.27 3.40
3.02 0.95 3.65
4.77 2.% 3.93
at 47
Wealth-income at 42
First quintile
Lifetime income
ratio
3.72 - 1.40 4.31
4.16 - 0.28 4.45
4.55 0.77 4.55
4.51 1.88 4.73
4.50 4.27 5.35
at 52
101.55
0.0
63.34
1663.0
0.0
0.0 10004.0
541 .o
44.49
0.0
0.0
221.0
0.0
27.22
0.0
2
E
G
az
*
6
8 i;;; % 0.0
I 0.0 15.0 7.85
Parameter of a bequest motive
E
0.0
Bequest
ESTIMATED VALUES OF INTERGENERATIONAL WEALTH TRANSFER (MILLION YEN)
TABLE
,
WEALTH
ACCUMULATION
PROCESS
BY
INCOME
CLASS
257
patterns by income class, as Fig. 1 shows; the lower income classes such as the first and second quintiles show a decreasing trend, while the other income classes show increasing trends. It is noted that the movement of the wealth-income ratio after retirement is similar to that of wealth because the amount of pension payment is fixed after retirement. Mirer (1979) showed that the wealth held by the aged did not decrease. The Japanese case shows a different outcome in the sense that the shape of wealth after retirement is different for different income classes. This is an interesting observation which has not been made previously. Finally, it is noted that a discontinuity (more precisely, a jump) of wealth-income ratios at the age of 60 arises entirely from the drop in income due to retirement. (c) Sensitivity
Test
It is necessary to explain why we adopted the above parameter values for the previous analysis and to provide some sensitivity test. As for wage figures, Shimono (1988) considered a model in which the retirement age is 65, and the wage rate at ages 60-64 is reduced considerably from that at ages 55-59. The result produced a lesser degree of drop in the income figures for ages 60-65. However, the overall result was not changed significantly. The difficult choice is the real interest rate r and the relative risk aversion parameter y. For y we adopted the value 3.0 in the previous part as a standard case because both Friend and Blume (1975) and Davies (1981) suggested a value higher than 2.0. We considered also 2.0 and 4.0 for the following sensitivity analysis. For r we considered also the value 0.02 in addition to the value 0.03. Since the real interest rate fluctuated considerably due largely to inflation despite the fairly fixed nominal interest rate in the past, it is almost impossible to assign an acceptable value of the real interest rate which will be relevant in the long run for Japan. Values around 0.02-0.03 are the most plausible. The sensitivity test is reviewed by considering the following equation for x: x = ((1 + r)l(l
+ p))?
(7)
As is given by Eq. (3), x indicates the growth path of consumption. Thus, the examination of x gives a sensitivity test for the simulation. Table VI gives the estimated values of x with various values of p and y and the given value of 0.02 for r. It is found that x becomes larger as the values of both y and p become smaller. In other words, the lower y and p, the higher the growth rate of consumption. It is possible to conclude on the basis of this sensitivity test that no qualitatively different result would
258
TACHIBANAKI
CHANGE CONSUMPTION
AND
SHIMONO
TABLE VI IN THE GROWTH PATH OF WITH DIFFERENT VALUES P AND Y
OF
Y P
2.0
3.0
4.0
0.02 0.01 0 -0.01 - 0.02 -0.05 -0.1
1.0 1.00494 1.00995 1.01504 1.0202 1.03619 1.06458
1St0329 1.00662 1.01 1.01342 1.02398 1.0426
1.0 1.00247 1.00496 1.00749 1.01005 1.01793 1.03179
1.0
Note. The numbers in this table are the growth path of consumptions given by x. x = ((1 + r)/( 1 + p))“y. r stands for the real interest rate. In this test we adopted 0.02 for r. p is the discount rate, and y is a measure of the relative risk aversion.
be obtained even if we used different parameter values. However, the quantitative difference would not be marginal, because the growth path of consumption is essential in determining the amount of intergenerational transfer.
VI.
CONCLUDING
REMARKS
This paper had two purposes. First, the empirical data on income and wealth were examined carefully. The examination suggested several interesting observations regarding the course of the wealth accumulation process by income class. In particular, the importance of intergenerational wealth transfers was suggested not only for high-income earners but also for some low-income earners. Second, a simple model of savings behavior with a bequest motive was applied to test whether it is useful to generate a plausible course of wealth accumulation. In particular, an attempt was made to estimate the amount of intergenerational wealth transfer by income class indirectly on the basis of the observed wealth-income ratios given the situation that no data on intergenerational wealth transfers are available in Japan. It is found that the higher the income class, the higher the amount of intergenerational transfer or the higher the bequest motive. Furthermore, the movement of wealth after retirement is different for different income classes. The aged of higher income classes do not de-
WEALTH
ACCUMULATION
PROCESSBY
INCOMECLASS
259
crease their wealth, while the aged of lower income classes decrease their wealth. The paper apparently suffers not only from stringent assumptions but also from simplistic theoretical development. It is true, however, that some of these problems can be solved only when panel data for individual entire life histories become available.
REFERENCES A. B. (1971). The distribution of wealth and the individual life-cycle, Oxford Econ. Pap, 23,239-254. ATODA, N., AND TACHIBANAKI, T. (1985). Decomposition of income inequality by income sources, Quart. Sot. Security Res. 20, 330-340, Spring. [In Japanese] ATODA, N., AND TACHIBANAKI, T. (1991). Earnings distribution and inequality over time: Education vs. relative position and cohort, Int. Econ. Rev., in press. BLINDER, A. S. (1973). A model of inherited wealth, Quart. J. Don. 87,608-626, Nov. DAVIES, J. (1981). Uncertain lifetime, consumption, and dissaving behavior, J. Polit. Econ. 89(3), 561-577. DIAMOND, P. A., AND HAUSMAN, J. (1984). Individual retirement and savings behavior, J. Public Econ. 23, 81-114, Feb./Mar. FRIEND, I., AND BLUME, M. E. (1975). The demand for risky assets, Amer. Econ. Rev. G(5), 900-922. HAYASHI, F. (1986). Why is Japan’s saving rate so apparently high? in “NBER Macroeconomics Annual, 1986” (S. Fischer, Ed.), MIT Press, Cambridge. HAYASHI, F., ITO, T., AND SLEMROD, J. (1988). Housing finance imperfection, taxation, and private saving: A comparative simulation analysis of the United States and Japan, J. Japan. ht. Econ. 2, 215-238. ISHIKAWA, T. (1974). Imperfection in the capital market and the institutional arrangement of inheritance, Rev. Econ. Stud. 41, 383-404, July. ISHIKAWA, T. (1975). Family structures and family values in the theory of income distribution, J. Polit. Econ. 83, 987-1008, Oct. ISHIKAWA, T. (1988). Saving and labor supply behavior of aged households in Japan, J. Japan. ht. Econ. 2, 417-449. KOTLIKOFF, L. J., AND SUMMERS, L. H. (1981). The role of intergenerational transfers in aggregate capital accumulation, J. Polit. Econ. 90, 706-732. KOTLIKOFF, L. J. (1988). International transfers and savings, J. Econ. Perspect. 2(2), 41-58. MIRER, T. W. (1979). The wealth-age relation among the aged, Amer. Econ. Rev. 69, 435-443. MODIGLIANI, F. (1988). The role of international transfers and life cycle saving in the accumulation of wealth, J. Econ. Perspect. 2(2), 15-40. OULTON, N. (1976). Inheritance and the distribution of wealth, Oxford Econ. Pap., 86-101, Mar. SHIMONO, K. (1988). Estimation of bequest motive by income class: A further result, mimeo. [In Japanese] ATKINSON,
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SHIMONO, K., AND TACHIBANAKI, T. (1989). Demand for insurance: A choice among safe assets, risky assets and insurance in Japan, mimeo. TACHIBANAKI, T., AND SHIMONO, K. (1982). Income redistribution effect of Kosei-nenkin system on the basis of internal rate of return. Monthly J. Japan. Inst. Labour, 2-14, Apr. [In Japanese] TACHIBANAKI, T., AND SHIMONO, K. (1986). Saving and life-cycle: A cohort analysis, J. Public Econ. 31(l), l-24, Oct. TACHIBANAKI, T., AND ATODA, N. (1986). Measurement of income mobility and modified Markov model, mimeo. TACHIBANAKI, T. (1989). Volatility in asset price and wealth distribution, JCER Econ. J. No. 18, 79-93 [In Japanese]; Japan’s new policy agenda: Coping with unequal asset distribution, J. Japan. Stud., Summer [In English]. TAKAYAMA, N. (1976). Inequality of income and wealth distribution and its causes, Keizai Kenkyu 27, 134-142, Apr. [In Japanese] TAKAYAMA, N. (1980). “Economic Analysis of Inequality,” Toyokeizai-shinposha, Tokyo. [In Japanese] TOGASHI, M. (1979). A study on wealth distribution of employees, Hitotsubashi Ronso 81, 114-125. [In Japanese] TOMES, N. (1981). The family, inheritance and the intergenerational transmission of inequality, J. Polit. Econ., 928-958, Dec. WHITE, B. B. (1978). Empirical tests of the life-cycle hypothesis, Amer. &on. Reu. 68, 547-560, Sept.
OF THE
JAPANESE
AND
INTERNATIONAL
ECONOMIES
5,
239-260 (1991)
Wealth Accumulation Process by Income Class* TOSHIAKI
TACHIBANAKI
Kyoto Institute of Economic Research, Kyoto University, Yoshida Honmachi, Sakyo-ku, Kyoto 606, Japan AND KEIKO
SHIMONO
Department of Economics, Nigata Sangyo University, Japan
Kashiwazaki,
Nigata
945-13,
Received March 22, 1988; revised May 31, 1990 Tachibanaki, Tosbiaki, and Shimono, Kelko-Wealth Income Class
Accumulation
Process by
The paper examines the empirical data on income and wealth in Japan carefully. The preliminary examination suggested the importance of intergenerational wealth transfers not only for high-income earners but also for some low-income earners. A simple model of savings behavior with a bequest motive was applied in order to estimate indirectly the amount of intergenerational wealth transfer by income class. This indirect method was reasonably successful in revealing the relative importance of intergenerational wealth transfers by income class in Japan, where no direct data on intergenerational wealth transfers are available. J. Japan. Int. Econ., September 1991,5(3), pp. 239-260. Kyoto Institute of Economic Research, Kyoto University, Yoshida Honmachi, Sakyo-ku, Kyoto 606, Japan; and Nigata Sangyo University, Department of Economics, Kashiwazaki, Nigata 945-13, Japan. 6 1991 Academic Ress, Inc. Journal of Economic Literature
I.
Classification Numbers 110, 840, 920. INTR~DuCTI~N
There have been few studies of wealth accumulation by class (income class or wealth class) in Japan. Studies of wealth accumulation which include both monetary wealth and physical wealth are quite rare because * The authors are most grateful to Tsuneo Ishikawa, who provided them with extremely constructive suggestions. Ken Ariga, Haruo Imai, and Takamitsu Sawa gave useful com239
0889-1583191 $3.00 Copyri.&t 0 1991 by Academic Press. Inc. Au rights of reproduction in any form reserved.
240
TACHIBANAKI AND SHIMONO
the data on physical wealth had been unavailable. Since we found a relevant source which contains useful data on both physical wealth and income (or wealth) class, we attempted to investigate the wealth accumulation process by income class. We believe that intergenerational wealth transfers such as gifts or bequests play an important role in determining the wealth accumulation process. Although the data which we use do not contain any information on gifts and bequests, we attempt to estimate them indirectly by examining the data source carefully. Thus, it is our intent to examine the influence of intergenerational transfers on the wealth accumulation process from the life-cycle point of view. Section II presents the data source. Section III examines the past studies related to this subject. Section IV investigates the raw data very carefully and draws several implications of intergenerational transfers of wealth on the basis of the wealth-income ratio. Section V presents the estimated amount of bequest derived from the life-cycle savings hypothesis with a bequest motive. Finally, conclusions and comments are provided. II.
DATA SOURCE
The principle data source is the Survey on Saving Behaviours and Consciousness conducted by the Department of Sociology, University of Tokyo, in 1981. The number of total observations used is 1708. The number of employees is 1134, and that of nonemployees is 574. The original survey included about 4300 observations. Since the survey contains a large number of unreported figures of wealth, the available number has been reduced considerably. Although this is quite usual and unavoidable when the survey asks about wealth figures, it is expected that future surveys will reduce the number of unreported figures. The survey asked a large number of questions on income and wealth (including the composition of wealth). Wealth consists of monetary wealth and physical wealth. Physical wealth is measured largely by residential house and land. Buildings for business use, agricultural land, and forest are eliminated, because their values are not reported. Since it is appropriate to utilize a homogenous group of people, single people and extremely rich families were excluded from the sample. i ments. Two unknown referees improved the quality of this paper substantially. The authors are responsible for possible errors. i Eliminating extremely rich people (in fact we have excluded households whose annual incomes are over 40 million yen) may be somewhat problematic. We did so because the behavior of these extremely rich people might be entirely different from that of ordinary people. In other words, it would be desirable to inquire about the wealth accumulation process separately for these extremely rich people. Nevertheless, the number of extremely rich people is very limited, only 1%. Thus, the bias due to such an elimination is very minor.
WEALTH ACCUMULATION PROCESSBY TABLE THE
DEGREE
OF INEQUALITY
241
INCOMECLASS
I
IN INCOME AND WEALTH GINI COEFFICIENT
DISTRIBUTIONS
BASED
ON THE
Income
Monetary wealth
Physical wealth
Total wealth
Net wealth
Gini coefficient Average (million yen) Standard deviation
0.258 4.45 2.13
Employees 0.546 3.72 4.06
0.623 12.60 15.02
0.549 16.32 16.78
0.581 14.15 16.01
Gini coefficient Average (million yen) Standard deviation
0.380 5.29 4.44
Nonemployees 0.550 6.36 7.18
0.575 21.98 25.02
0.518 28.34 28.46
0.545 25.64 27.49
Gini coefficient Average (millionyen) Standard deviation
0.308 4.73 3.18
Total households 0.563 4.61 5.64
0.616 15.75 20.18
0.553 20.36 22.93
0.584 18.01 22.02
Note. (1) The sample number is 1134 for employees, 574 for nonemployees, and 1708 for total samples. (2) Contributions to life insurance are not included in monetary wealth. (3) Physical wealth is the sum of the self-assessment of land and house. (4) Net wealth is the difference between total wealth and debt.
III.
EXAMINATIONS OF THE PAST STUDIES AND PRELIMINARY ANALYSIS
We cite several studies which investigated wealth distribution in Japan. These studies are reviewed very briefly as a rough introduction to the study of wealth accumulation in Japan. All the studies reveal that the inequality of wealth distribution is much higher than that of income distribution. Takayama (1980) found that the Gini coefficients for income distribution and for monetary wealth distribution for employees were 0.197 and 0.505, respectively, in the 1974 Survey on Household Consumption. Togashi (1979) reports that the Gini coefficients for income, monetary wealth, and total wealth (both monetary and physical wealth) for employees are 0.313, 0.661, and 0.614, respectively, in the 1977 Survey on Saving Behaviours and Consciousness. It is noted that this study uses the same data source as Togashi’s study, although the sample year is different. Table I shows the estimated Gini coefficients for various concepts of wealth based on the current data. See the Section IV for how the original data were arranged in order to prepare the figures of wealth, income, and others. Various categories, namely employees, nonemployees, and total
242
TACHIBANAKI
AND
SHIMONO
households, are considered. For employees, which can be compared with Togashi’s study, the estimated coefficients for income, monetary wealth, and total wealth are 0.258,0.546, and 0.549, respectively. It is worthwhile to note that both income and wealth inequalities have decreased. See Tachibanaki (1989) for a recent study which showed the opposite trend in wealth distribution. Two interesting observations are possible from Table I. First, inequality for physical wealth is considerably higher than that for both monetary wealth and total wealth (monetary plus physical wealth). At the same time, net wealth (total wealth minus total debt) gives an inequality higher than that of total wealth. Second, nonemployee households have an inequality in all dimensions of wealth lower than that of employees, except for monetary wealth, although income inequality for nonemployee households is higher than that for employees. One possible reason is that buildings for business use are excluded. It is very likely that nonemployees hold a considerable amount of land and buildings for their own businesses. If these buildings and land were included in the data, the inequality of wealth distribution would be higher for nonemployees than for employees, because the values of land and buildings are considerably high. It is possible to raise several factors to explain the higher inequality in wealth distribution. For example, Takayama (1980) raises the following: (1) age effect, (2) income differential, (3) the difference in the rate of return to wealth, (4) gifts and bequests, and (5) institutional factors such as the tax system. Other factors such as (6) inflation and (7) savings rates may be added. Under the strict life-cycle savings hypothesis the age effect is the most important for explaining wealth inequality. Only 40% is explained, however, by the age effect in determining the inequality of monetary wealth. The contribution of income differential to wealth inequality is only about 25%. These numbers were estimated by Takayama (1976). It is necessary to seek an alternative variable such as gifts and bequests, which can be an important component of wealth inequality. There are several studies which indicated the importance of intergenerational wealth transfers. Atkinson (1971) proposed that if the bequest was of luxury goods, wealth inequality would increase with the age of the person under the assumption that the growth rate of the population is lower than the rate of interest. Ishikawa (1975), however, raised the possibility that if education was of consumption goods, bequest would not necessarily enlarge the inequality of wealth distribution. Also, liquidity constraint (or imperfection of the capital market) may increase wealth inequality, as Ishikawa (1974), Tomes (1981), and Hayashi (1986) showed. The importance of intergenerational transfers in the field of wealth distribution and the savings hypothesis was proposed empirically by Atkin-
WEALTH ACCUMULATION PROCESSBYINCOMECLASS
243
son (1971), Oulton (1976), White (1978), Kotlikoff and Summers (1981), and others. We see a controversy between Kotlikoff (1988) and Modigliani (1988). For Japan, several studies such as those of Tachibanaki and Shimono (1986), Hayashi (1986), Ishikawa (1988), and Hayashi er al. (1988) proposed the inapplicability of the life-cycle savings hypothesis and suggested the importance of a bequest motive as a conceivable hypothesis. It is anticipated, however, that the influence of a bequest motive may differ significantly according to one’s income or wealth level. This is the subject of the present undertaking. Since there are no data on the amount of intergenerational wealth transfer by income class (equivalently, individual survey data on bequests), we adopt a methodology which enables us to estimate the amount indirectly.
IV.
WEALTH ACCUMULATION PROCESS
This section examines the raw data carefully and attempts to draw several implications of intergenerational transfer of wealth based on the observed wealth-income ratio.2 The empirical evidence found in this section forms a basis for deriving a theoretical model in Section V. We examine the sample of employees carefully. The result for nonemployees is not examined as closely because an adequate economic theory has not been established for nonemployees. Before the observed wealth-income ratio is discussed, several notes are presented with respect to preliminary data arrangements. First, the data on monetary wealth include cash, demand deposit, time deposit, equity, bond, and security. Contribution to life insurance programs is excluded simply because it is not reported. Shimono and Tachibanaki (1989) show that contribution to life insurance can be regarded as one form of savings. Very roughly, the share of life insurance in total monetary wealth is about 20%. However, it is controversial whether contribution to life insurance can be regarded as a form of savings. Some propose that life insurance is merely consumption. Since the data we used excluded it from 2 It is possible to consider the real value of the wealth-income ratio rather than the nominal value. What kind of deflator should be adopted to calculate the real value is controversial. Suppose we take the consumer price index Pi (i is the ith region) for both nominal income yi and nominal wealth Wi. Taking the real value of the wealth-income ratio, (W,lPJl(yilPJ = Wi/Yi)gives the same result. In other words, it does not matter whether we consider the nominal value or the real value, if we adopt the wealth-income ratio. This may be an advantage because the differences in consumer price indexes by region can be ignored by considering the wealth-income ratio. When the deflator for income and the deflator for wealth are different, the above result is not valid. We have to consider an alternative method in this case.
244
TACHIBANAKI
AND
SHIMONO
the list of savings, we simply followed this procedure. It is necessary to understand the difference, and the issue probably will have to be settled in the future. Second, the data on physical wealth are dependent upon the self-assessment of land and housing values. Obviously, they contain measurement errors. Since Togashi (1979) reported that the measurement error was within a range of lo%, we did not attempt to modify the value given by self-assessment. Also, it is an enormously difficult and even risky task to modify the appropriate value of physical assets based on self-assessment. The rates of landholding and of homeholding in this survey are 63 and 49%, respectively. The per capita average value of physical wealth is 16 million yen, and it is about four times higher than the value of monetary wealth, i.e., 4.3 million yen. Third, it is assumed that the degree of income mobility among the five income classes is zero over all ages. In other words, a representative person who was in the first quintile at his first life stage remains in the first quintile throughout his entire life. Persons in the other quintiles keep the same property. This is a somewhat drastic assumption adopted in order to make our analysis feasible. No panel data for income and wealth are available in Japan. The assumption is not, however, so unrealistic for the following three reasons. First, the Japanese wage determination system, i.e., seniority- and age-based wage payment, does not generate a wide range of wage and income mobility. In other words, one’s initial class in the payment structure determines one’s course of wage growth (or the class in the wage distribution) throughout one’s career to a great extent because the wage is largely determined by age and tenure. See Atoda and Tachibanaki (1991), who estimated a very low degree of wage mobility indirectly in Japan. A similar scenario would be supported for income distribution as well in view of the fact that wage is the most important component of total income, as shown by Atoda and Tachibanaki (1985). It is noted that we deal only with employees in the model analysis of this paper. Second, since there are only five income classes in this study, interclass income mobility is expected to be low although intraclass mobility is likely to be fairly high. In this paper we can safely ignore intraclass mobility because we are interested in representative persons. If the number of income classes were larger, interclass income mobility would be higher. See Tachibanaki and Atoda (1986) for a discussion of this. Third, our concern in this paper is a representative or hypothetical person rather than a real person. Thus, empirical plausibility is not our major goal. We recognize, however, that a modification taking interclass mobility into account is certainly required in the future. Only panel data enable us to perform such work. To return to data arrangements, fourth, we do not attempt to transform
WEALTH
ACCUMULATION
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CLASS
245
our cross-sectionaldata into cohort data. In other words, the growth rate of GNP or productivity is assumedto be zero. This is againa simplified assumption.It is not, however,harmful, at least for our purpose,because thecross-sectionaldataaresufficientto showthe importanceof intergenerational transfersof wealth by income class.Also, it is true that we do not obtain a different result even if we take accountof the GNP growth rate. Our main tool for analyzing the wealth accumulation process is the wealth-income ratio. It is noted that wealth means net wealth, that is, total wealth minus debt. The wealth-income ratio has an important merit which enablesus to investigate the relative contribution of income and consumptionto wealth accumulation.In other words, the wealth-income ratio, which is standardizedby income level, is a more relevant variable than wealth itself becauseincome is a very rough indicator of the level of consumption.Also, a large number of studiessuch as those of Diamond (1977) and Diamond and Hausman (1984) adopt the concept of the wealth-income ratio. Under the pure life-cycle savingshypothesisDiamond (1977)was able to show that the required wealth-income ratio is about 4.0 at retirement age. Tachibanaki and Shimono (1986)presented the empirical result for Japan.This paperintendsto estimateit by income class. Figure 1 shows the wealth-income ratios for several income classes. Table II gives detailed wealth-income ratio numbers. A simple average of the wealth-income ratios for ages55-59is 5.18for employeesand 5.57 for the total sample (employeesand nonemployees).These values are considerablyhigher than the value estimatedby Diamond. It is important, however, to recall that these averagevaluesdo not describea very wide differencein the wealth-income ratios by income class. Severalobservations arepossiblefrom Fig. 1. First, the wealth-income ratio of the higher income classis higherthan the averageuntil the ageof 40,while it is lower than the averageafter that age.This is more obvious for employeesthan for all samples.Second,the wealth-income ratio of the lower incomeclass is higher than the averagefor all ageclasses.It is necessaryto determine the reasonsfor theseobservations.We beginwith the higherincomeclass. (a) Wealth-Income
Ratio of Higher Income Class
First, it is observedthat the rate of physical assetacquisitionby young peopleof the higher income class is considerablyhigh.3Figure 2 shows that the averagerate of householdingby young people(i.e., late 20s and 3 The following comment may be made: the liquidity constraint is weaker even for younger people whose income levels are higher. In other words, even younger people are able to borrow funds relatively easily to acquire physical assets if their incomes are higher. Thus, it is possible that easier accessibility of credit tinancing made the rate of physical asset holding higher for these people. However, our tool, namely the wealth-income ratio, is
246
TACHIBANAKI
2
AND SHIMONO
-.
1
FIG. 1. (Net) Wealth-Income
1t ratio by age class for the first and f&h quintiles.
early 30s) of the higher income class is about 70% and that of landholding is about 50-60%, while the average rate of householding by the same ageclass people of total households is about 30-40% and that of landholding is about 25-35%. The difference is large, and it is possible to conjecture that these high rates of physical wealthholding are due largely to intergenerational wealth transfers from parents. Second, income differentials become wider as the samples become older. While the index of income levels for people of higher income class are younger than 40 in comparison with the average income of the same age class (the index is specified as 100) is about 170-180, the index is higher than 200 for people of higher income class who are over 50. Simply speaking, the older the sample, the wider the income differential. In other words, since the denominator of the wealth-income ratio of this class increases more than the average as the sample becomes older, the estimated wealth-income ratio of the higher income class decreases disproportionately in comparison with the wealth-income ratio of other classes. defined by net wealth (total assets minus debt) rather than total assets. Thus, if the nonliquidity constraint hypothesis were prevalent, the (net) wealth-income ratio would be lower. In reality the (net) wealth-income ratio is higher for young people of the higher income class, as Fig. 1 indicates.
.5
330
wIO.0)
363
57
(100.0)
(15.7)
34
34
351
37
51 3s
39
36
51 44
343
;
Fourth
CLASS
(100.0)
(10.5)
(11.4)
(10.5)
(12.8)
(14.9)
.i,,l;l;)
quintile
BY INCOME
21
I2
12}49
25
37
43
60
52
321
‘;
allocations of the samples whose income figures are equal.
(100.0)
(10.5)
(9.7)
(9.7)
(13.1) (13.1)
ii(24.8)
II
RATIOS
TABLE Third quint&
Now. The unequal total numbers in the live quintiles are due to somewhat arbitrary
71
8.0-
TOtA
(21 .S)
(8.3)
(5.2)
91
30
I9
46 46
25
(4.2)
(7.3)
(8.3)
(16.3)
;
7.0-8.0
14
4.0-5.0
30
59
C;;(30,6)
6.0-7.0
24
3.0-4.0
(6.10
(10.6)
;-
Second quintile
I7
20
‘;;:;(28,5)
(10.0)
First quintile
WEALTH-INCOME
5.0-6.0
35
1.0-2.0
f}%
33
Number
2.0-3.0
ifB!i
-0.0
income ratios
Wealth-
(NET)
(100.0)
6.5)
~-;;},I,.,,
(11.5)
(13.4)
(18.7)
(16.2)
$16.2)
Fifth quintile
1708
221
;]2l6
243
I,-
;$C25.3)
(llw.0)
(12.9)
‘;]Cl2.6)
(14.2)
Total
248
TACHIBANAKI
AND
SHIMONO
a Hauar 100
Fifth
f
,,,J... XJ,’
______-----a’
,’
/‘--- .._. ._..__
quinti1e
-. Average
,,*’ .I’ T First
wintile
50 ..
/-?::-
50 .’
Fifth quintih2 A.-_ ,’ _,,_,-----..._ /,/’ .__--,/- Averege ,,,’ T quintile ,/’,/’ First fl
FIG. 2. The rate of house and landholding by income and age classes.
In summary, it is proposed that two factors, namely, (i) a high rate of physical asset acquisition by youth and (ii) a higher income level by older people, are responsible for explaining the movement of the wealth-income ratio of the hiiher income class by age. We emphasize that the intergenerational transfer is the most crucial factor. Even young people of higher income class did not acquire their physical wealth through credit financing but through gifts and/or bequests from their parents. (b) Wealth-Zncome Ratio of Lower Income Class It is necessary to determine why the wealth-income ratios are higher throughout all age classes for the lower income class than the average for all income classes. This is contrary to the result obtained by Diamond and
WEALTH
ACCUMULATION
PROCESS
BY
INCOME
CLASS
249
Hausman(1984),who found that thegreatmajority of lower incomeclasses have lower wealth-income ratios in the United States.Table II presentsa clueto the mystery. This table showsthedistribution of the wealth-income ratio for eachincome class(i.e., five quintiles). The distribution of householdsin eachincome classin Table II is obtainedthroughthe distribution of householdsbasedon the number of householdsin eachageclass(fiveyear intervals) in Fig. 1. The number of householdsbelongingto the first quintile in eachageclass in Fig. 1 forms the distribution of householdsin the first quintile in Table II. The distribution in the secondquintile is fabricatedthroughthe samemethodologyasthat in the first quintile. Thus, the age distribution in each income class is, roughly speaking,similar. Table II suggeststhat there are a large number of householdswhose wealth-income ratios are low amongthe low-income earners.For example, the shareof peoplewhosewealth-income ratios are lower than 1.Ois 38%for the first quintile. These numbersare 35%for the secondquintile, 30%for the third quintile, 28%for the fourth quintile, and 18%for the fifth quintile. Moreover, the lower the income level, the higherthe rate of low wealth-income ratio. This is easily observedwhen we look at the number of householdswhose wealth-income ratios are lower than zero. These findings lead to the conclusionthat the shareof very low wealth-income ratios is considerablyhigh among low-income earnersdespite a roughly equal agedistribution in eachincome class. When we look at the averagefigures, the wealth-income ratios are higher in the low income class than in the total income class. We must resolvethis apparentcontradictionagainstthe lower wealth-incomeratios of low-income earnerswhich wasdescribedabove.Table II againprovides us with a clue. It is noted that some low-income earnershave very high wealth-income ratios. For example,the shareof the wealth-income ratio higherthan 8.0 is 22%for the first quintile, while the sharesareabout 10% for the other quintiles. Another important result derived from Table II is the decreasingtendencyin the variancesof wealth-income ratios as the incomeclassbecomeshigher. For example,the shareof householdswhose wealth-income ratios are either extremely high or extremely low is quite low in higher income classes. Table III is presentedto show that the extremely high wealth-income ratio for low-income earners(i.e., the first quintile) is not causedby their low incomes(or wider income differentialswithin the first quintile). Table III shows that income differentials between low wealth-income ratios (Le., lower than 0.0 or 1.O)and high wealth-income ratios (i.e., higher than 5.0 or 8.0) are very marginal, while the differencein the amountsof both total wealth and net wealth betweenlower wealth-income ratios and higher wealth-income ratios are very large.The amount of total wealth is 0.741 million yen for a wealth-income ratio lower than 0.0 and 0.928 million yen for a ratio lower than 1.0, while it is 26.8 million yen for a
250
TACHIBANAKI
AND
TABLE
SHIMONO
III
(NET) WEALTH-INCOME RATIOS AND DETAILED FIGURES OF WEALTH FOR THE FIRST QUINTILE: THE DISTRIBUTIONS (MILLION YEN)
Wealth-income
‘C-1.0
>5.0
>8.0
110 4.37 22.44
71 5.00 28.49
0.93 8.21 0.11 2.04
26.81 1.21 25.60 1.94
33.49 1.33 32.15 1.84
Ages 30-39 60 0.81 0.15
21 2.94 20.45
Sample number Monetary wealth Physical wealth Zero wealth
All ages 127 0.72 0.21 115 (82s%) (91%)
Total wealth Debt Net wealth Income
0.74 2.56 -1.82 1.74
Sample number Monetary wealth Physical wealth Zero wealth
ratio
33 0.48 0.26
(2%) Total wealth Debt Net wealth Income
0.95 0.67 0.28 2.10
23.39 3.46 19.92 1.67
wealth-income ratio higher than 5.0 and 33.5 million yen for a ratio higher than 8.0. This large difference is to a great extent due to the large difference in the amount of physical wealth, as Table III shows. It is 0.257 million yen for a wealth-income ratio lower than 0.0 and 0.213 million yen for a ratio lower than 1 .O, while it is 22.4 million yen for a wealth-income ratio higher than 5.0 and 28.5 million yen for a ratio higher than 8.0. The difference in the amount of monetary wealth is also considerably large, although it is much smaller than the difference in physical wealth. The results for those aged 30-39 in Table III, who are relatively young and who would, possibly, be able to receive bequests, also support the above finding.4 In conclusion, it is clear that the higher wealth-income ratios for sOme low-income earners originated from their high amounts of wealth 4 It would be preferable, to make our conjecture more convincing, to show that there are fewer retirees in the low-income class. Since the data do not distinguish between retirees and nonretirees, this was not shown.
WEALTH
ACCUMULATION
PROCESS BY INCOME
CLASS
251
holding. Moreover, since their incomes are lower, it is possible to conjecture that the great majority of their wealth came from bequests and/or gifts from their parents or past generations.
V.
ESTIMATION OF INTERGENERATIONAL TRANSFERS CLASS BASED ON THE WEALTH MODEL
(a) Model Framework
and Preliminary
BY INCOME
Results
This section investigates whether a simple model of wealth accumulation by income class is appropriate for estimating the value of intergenerational wealth transfer. While the previous section estimated it by examining the raw data carefully, this section intends to estimate it through a model of savings behavior and to compare it with the actual data. We adopt a simple life-cycle hypothesis with a bequest motive a la Blinder (1973) as a basis of the savings behavior. The model is explained here briefly.5 An individual utility function is given by T WC,,
* . . ,
c’-Y
cT,A) = tz,e(l
+ p)‘-’
+ bF
:
/l
+ PFT,
(1)
where C, is consumption at time t. AT is bequest at death (t = 2’). -y is the elasticity of marginal utility with respect to consumption and bequest (y > 0 and y # 1). y is a measure of the relative risk aversion, and its inverse is equal to the inter-temporal substitution parameter. p is a discount rate. b is a parameter for bequest motive. An individual budget constraint is given by 2 C,(l + I)‘-’
+ A#
+ r)l-T = A,, + 5 W,(l + r)‘-‘, f=l
(2)
where W, is the wage income (or the pension payment) at time t. r is the real interest rate. A, is the receipt of intergenerational transfer from the past generation. 5 It is possible to consider the effect of the number of people in a household N, in this model framework. Shimono (1988) performed a sensitivity analysis by considering the number of family members. It turned out that the qualitative result was not very different from that of the current model, which ignores the intluence of family members. In any case not only the number of children but also the difference between sons and daughters is a future subject to be investigated very carefully for Japan.
252
TACHIBANAKI
AND
SHIMONO
We give a somewhat oversimplified assumption about the relationship between A, and A, in order to make the model workable: A, = A# + r)‘-r. This relationship implies that the higher the receipt of intergenerational wealth transfer, the higher the bequest left. In other words, intergenerational wealth transfers in this framework do not change the course of intergenerational wealth inequality, or they are neutral with respect to the wealth inequality of the next generation. This is probably the most stringent assumption made in this paper. It implies that parents plan to leave bequests whose present values are equal to that of the initial receipt from their parents. In other words, altruistic parents have altruistic children, while egoistic parents have egoistic children. It is not so unrealistic to conceive of this assumption because the empirical evidence given in Section IV supported it, especially for higher income class families. We do not say that it applies to all lower income class families. However, some lower income families can assume this property, as suggested in Section IV. Since the removal of this assumption does not change the qualitative result of this paper, we adopted this assumption. It is certainly a subject for future research, however. Under the assumption of A, = Ad1 f r)lPT, Eq. (1) is maximized subject to Eq. (2). The first-order conditions provide us with the equations
cf=cl
1+ r 0- IVY ( 1 l+p
(3)
where C, is given by
(4)
A,
= b”Y(l
+ r)(T-
‘)‘Y * C,.
(5)
The above equations suggest that when the value of b (or Ar) is assigned, AT (or b) is solved in the model. Since Eqs. (3), (4), and (5) are able to depict the entire course of consumption, savings and thus wealth during one’s lifetime can be determined when wage incomes during one’s lifetime are given. We have several robust estimations of age-earnings profiles in Japan which have a quadratic function of age, as shown, for example, by Tachibanaki and Shimono (1982,1986). Thus, the age-earnings profiles by income class, which were drawn from the Saving Survey, 1981, on the basis of
WEALTH
ACCUMULATION
PROCESS BY INCOME
CLASS
253
severalquadratic functions of age,are very realistic. The amount of pensions after retirement (age60) is equal to 60% of the wage earningsat retirement, which is believed to be close to the realistic value. The other valuesof r, p, and y are 0.03, 0.02, and 3.0, respectively.6 Table IV presentsthe estimatedvalues for some of the key variables for the averagewage and pension payments of the entire sample. This tableis presentedto showthe importanceof theinitial wealth (A,,) inherited from the past generationin determiningthe future courseof income and wealth accumulation. Specifically, two observationsare possible from Table IV. First, the higherthe initial wealth, the highertheinterestincome and thus the higher the total income level. Second,the previousobservation naturally generatesa higher wealth-income ratio and thus a higher bequestmotive (b). In sum, the influenceof the initial wealth (A,,) is quite important in determining the courseof income and the wealth accumulation process. (b) Zntergenerational
Transfers by Income
Class
This section intends to estimate the plausible amount of intergenerational transfersby income classbasedon the model presentedhere. This sectionis entirely different from Section Va. While that sectionassessed the importanceof intergenerationaltransfersin determiningthe courseof income and wealth accumulation on the basis of hypothetical values of intergenerationalwealth transfers, this section attempts to estimate the realistic amount of intergenerationaltransferon the basisof the observed wealth-income ratios. In other words, an attempt is made to infer the amount of intergenerationalwealth transfer, which is not availablein any data source, on the basis of other observablevariables such as wealthincome ratios. The estimated(or calculated)amount of intergenerational transfer by income class is influencedby the assignedcoefficientsin the model. See Shimono (1988).The qualitative feature, however, of intergenerationaltransfersor bequestmotives is not alteredby various coefficients. The estimation of intergenerationaltransfers(A, andAT) is fairly primitive. We iterate a large number of intergenerationalwealth transfersand find a value which minimizes the prediction error of the estimatedwealth income ratio in comparison with the observedwealth-income ratio for 6 These values are expected to be close to the plausible values in Japan. Since it is impossible to assign the absolutely relevant values in any society, a sensitivity test was added later. Shimono (1988) constructed an alternative model which takes into account the number of peopIe in a household, the change in the retirement age, and the recalculation of the pension payment. Also, a more- careful sensitivity test was attempted. Interested readers should refer to Shimono (1988).
Lifetime consumption
203.6 203.6 203.6 203.6 203.6 203.6 203.6
202.4 202.4 202.4 202.4 202.4 202.4 202.4
0 1 2 5 10 15 20
KEY
203.6 207.8 212.0 224.8 245.9 261.1 288.3
Lifetime income
OF SEVERAL
Lifetime wage
RESULTS
Initial wealth 640)
ESTIMATED
Annual income at age 5.43 5.51 5.60 5.74 6.27 6.70 7.12
IV
UNDER
TABLE VARIABLES
11.2 14.1 17.0 25.6 40.1 54.6 69.1
Wealth at age 60
DIFFERENT
WEALTHS
2.05 2.55 3.03 4.38 6.40 8.16 9.71
Wealth-income ratio at age 60
INITIAL
YEN)
0.0 5.2 10.5 26.2 52.3 78.5 104.7
Bequest at death
(MILLION
0.0 0.7 6.0 94.0 749.0 2528.0 5920.0
Parameter of a bequest motive
WEALTH
ACCUMULATION
PROCESS
BY
INCOME
CLASS
255
each income class. Specifically, we estimate an optimum A, which minimizes the sum of the three prediction errors at ages 40-44, 45-49, and 50-54 by considering the equation min {(WI,,
- w&2j2 + (WI,, - WI,,)2 + (WI,, - wI,2)2},
(6)
where WI, signifies the observed wealth income ratio at the ith age class, and WI, signifies the predicted or hypothetical wealth income ratio generated by various intergenerational transfers. Obviously, ages 40-44,45-49, and 50-54 are close to retirement age. Table V shows the estimated result of intergenerational transfers and several related statistics based on the method described above. Lifetime wage earnings, lifetime consumption, lifetime income, wealth-income ratios at ages 42 (representing ages 40-44), 47, and 52, and parameters of the bequest motive are provided in Table V for each income class. The numbers in row (A), where A,, = 0, are the estimated results in the case in which the initial intergenerational transfers are assumed to be zero. The numbers in row (B) are the estimated results which gave the minimum prediction errors, as described previously. In other words, the results based on A, = 0, i.e., row (A), are for the hypothetical world in which there are no intergenerational transfers, while the results of row (B) are the estimated values of intergenerational transfers and the related statistics based on the economic model considered here. The actual values of the wealth-income ratio at ages 42, 47, and 52 are also provided for comparison. Several observations are possible from Table V. First, the distinction between row (A) and row (B) is enormous. In other words, the case in which there are no intergenerational transfers generates extremely unrealistic values of the estimated wealth-income ratios at ages 42, 47, and 52, except possibly for the first quintile, suggesting that the life-cycle savings hypothesis without a bequest motive is a highly unrealistic theory. In other words, it is essential to take into account the contribution of intergenerational wealth transfer in investigating the wealth accumulation process. Second, row (B) generates increasing values of intergenerational transfers with income class. The estimated amounts of intergenerational transfer are 1.5 million yen for the first quintile, 5.2 million yen for the second quintile, 8.5 million yen for the third quintile, 12.1 million yen for the fourth quintile, and 19.4 million yen for the fifth quintile. In other words, the hypothesis “the higher the income class (or lifetime income and wealth), the higher the intergenerational transfer” is supported by the estimated amount of intergenerational wealth transfer. Equivalently, “the higher the income class, the higher the bequest motive” is supported. Third, the estimated wealth-income ratios after retirement give different
151.5 151.5
188.8 188.8
223.5 223.5
Actual value (A) A0 = 0 (B) A,, = 5.2
Actual value (A) A0 = 0 (B) A, = 8.5
Actual value (A) A, = 0 (B) A,, = 12.1
(A)A, = 0 (B) A,, = 19.4
309.6 309.6
102.2 102.2
Lifetime wage
Actual value (A) A0 = 0 (B) A0 = 1.5
Actual value
V
302.8 302.8
223.4 223.4
193.0 193.0
159.0 159.0
113.3 113.3
Lifetime consumption 2.75 1.74 2.65
2.87 - 1.12 2.48
Third quintile
3.66 0.17 2.74
302.8 385.0
223.4 274.7
3.57 -3.18 2.76
Fifth quintile
3.33 - 2.07 2.63
Fourth quintile
193.0 229.0
159.0 181.0
Second quintile
113.3 119.7
3.11 - 2.52 3.36
2.98 -1.33 3.40
2.96 -0.27 3.40
3.02 0.95 3.65
4.77 2.% 3.93
at 47
Wealth-income at 42
First quintile
Lifetime income
ratio
3.72 - 1.40 4.31
4.16 - 0.28 4.45
4.55 0.77 4.55
4.51 1.88 4.73
4.50 4.27 5.35
at 52
101.55
0.0
63.34
1663.0
0.0
0.0 10004.0
541 .o
44.49
0.0
0.0
221.0
0.0
27.22
0.0
2
E
G
az
*
6
8 i;;; % 0.0
I 0.0 15.0 7.85
Parameter of a bequest motive
E
0.0
Bequest
ESTIMATED VALUES OF INTERGENERATIONAL WEALTH TRANSFER (MILLION YEN)
TABLE
,
WEALTH
ACCUMULATION
PROCESS
BY
INCOME
CLASS
257
patterns by income class, as Fig. 1 shows; the lower income classes such as the first and second quintiles show a decreasing trend, while the other income classes show increasing trends. It is noted that the movement of the wealth-income ratio after retirement is similar to that of wealth because the amount of pension payment is fixed after retirement. Mirer (1979) showed that the wealth held by the aged did not decrease. The Japanese case shows a different outcome in the sense that the shape of wealth after retirement is different for different income classes. This is an interesting observation which has not been made previously. Finally, it is noted that a discontinuity (more precisely, a jump) of wealth-income ratios at the age of 60 arises entirely from the drop in income due to retirement. (c) Sensitivity
Test
It is necessary to explain why we adopted the above parameter values for the previous analysis and to provide some sensitivity test. As for wage figures, Shimono (1988) considered a model in which the retirement age is 65, and the wage rate at ages 60-64 is reduced considerably from that at ages 55-59. The result produced a lesser degree of drop in the income figures for ages 60-65. However, the overall result was not changed significantly. The difficult choice is the real interest rate r and the relative risk aversion parameter y. For y we adopted the value 3.0 in the previous part as a standard case because both Friend and Blume (1975) and Davies (1981) suggested a value higher than 2.0. We considered also 2.0 and 4.0 for the following sensitivity analysis. For r we considered also the value 0.02 in addition to the value 0.03. Since the real interest rate fluctuated considerably due largely to inflation despite the fairly fixed nominal interest rate in the past, it is almost impossible to assign an acceptable value of the real interest rate which will be relevant in the long run for Japan. Values around 0.02-0.03 are the most plausible. The sensitivity test is reviewed by considering the following equation for x: x = ((1 + r)l(l
+ p))?
(7)
As is given by Eq. (3), x indicates the growth path of consumption. Thus, the examination of x gives a sensitivity test for the simulation. Table VI gives the estimated values of x with various values of p and y and the given value of 0.02 for r. It is found that x becomes larger as the values of both y and p become smaller. In other words, the lower y and p, the higher the growth rate of consumption. It is possible to conclude on the basis of this sensitivity test that no qualitatively different result would
258
TACHIBANAKI
CHANGE CONSUMPTION
AND
SHIMONO
TABLE VI IN THE GROWTH PATH OF WITH DIFFERENT VALUES P AND Y
OF
Y P
2.0
3.0
4.0
0.02 0.01 0 -0.01 - 0.02 -0.05 -0.1
1.0 1.00494 1.00995 1.01504 1.0202 1.03619 1.06458
1St0329 1.00662 1.01 1.01342 1.02398 1.0426
1.0 1.00247 1.00496 1.00749 1.01005 1.01793 1.03179
1.0
Note. The numbers in this table are the growth path of consumptions given by x. x = ((1 + r)/( 1 + p))“y. r stands for the real interest rate. In this test we adopted 0.02 for r. p is the discount rate, and y is a measure of the relative risk aversion.
be obtained even if we used different parameter values. However, the quantitative difference would not be marginal, because the growth path of consumption is essential in determining the amount of intergenerational transfer.
VI.
CONCLUDING
REMARKS
This paper had two purposes. First, the empirical data on income and wealth were examined carefully. The examination suggested several interesting observations regarding the course of the wealth accumulation process by income class. In particular, the importance of intergenerational wealth transfers was suggested not only for high-income earners but also for some low-income earners. Second, a simple model of savings behavior with a bequest motive was applied to test whether it is useful to generate a plausible course of wealth accumulation. In particular, an attempt was made to estimate the amount of intergenerational wealth transfer by income class indirectly on the basis of the observed wealth-income ratios given the situation that no data on intergenerational wealth transfers are available in Japan. It is found that the higher the income class, the higher the amount of intergenerational transfer or the higher the bequest motive. Furthermore, the movement of wealth after retirement is different for different income classes. The aged of higher income classes do not de-
WEALTH
ACCUMULATION
PROCESSBY
INCOMECLASS
259
crease their wealth, while the aged of lower income classes decrease their wealth. The paper apparently suffers not only from stringent assumptions but also from simplistic theoretical development. It is true, however, that some of these problems can be solved only when panel data for individual entire life histories become available.
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