Bequest Behavior and the Effect of Heirs' Earnings: Testing the Altruistic Model of Bequests
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Bequest Behavior and the Effect of Heirs' Earnings:
Testing the Altruistic Model of Bequests
By MARK O . WILHELM*
That parents transfer resources to children because of altruistic concern is a
reasonable a priori assumption. However, economic theories of altruistic trans-
fers have produced many counterintuitive conclusions, and, consequently, much
debate. When applied to bequests, these theories predict that inheritances will
compensate for eamings differences between siblings as well as between parents
and children. This paper tests these implications. Using a new data set centered
on federal estate tax retums, little support can be found for an altruistic theory
of bequests. This finding has implications for macroeconomic policy, govemment
transfer programs, and inequality. {JEL D19)
Hundreds of billions of dollars per year are theories of such intergenerational trjmsfers, the
bequeathed by people in the United States,' most prominent is that bequest behavior is mo-
and about two thirds of this passes from par- tivated by altruism. As defined by Robert J.
ents to children.^ Among several economic Barro (1974) or Gary S. Becker (1974), this
means that parents bequeath because they gain
utility from the utility or lifetime resources,
respectively, of their children. It follows that
* Department of Economics, 608 Kern, Pennsylvania bequests are compensatory. Parents will be-
State University, University Park, PA 16802. This work
is drawn from the author's dissertation research, and was queath unequal amounts to their offspring,
accomplished during an internship at the Office of Tax compensating children who have low eam-
Analysis (OTA), U.S. Treasury Department. Appreciation ings. In addition, bequests compensate inter-
is expressed to OTA for access to the data and the provi- generational differences, with lower average
sion of facilities which were necessary to complete the
work. Special thanks go to David Joulfaian for very kind eamings of children eliciting larger bequests
logistical support during the revision. I am grateful to from parents.
Joseph Altonji, Charles De Bartolome, Chris Flinn, Roger Although altmistic bequest models have
Gordon, David Joulfaian, Myoung-Jae Lee, Dave Ribar, raised much controversy in the theoretical lit-
Mark Roberts, David Shapiro, Charles Wilson, the partic-
ipants at the 1991 Institute for Research on Poverty Sum- erature, they have been subject to few empir-
mer Workshop, and anonymous referees for their valuable ical investigations. Using a new data set of
suggestions. I am responsible for any remaining errors. parents' estate tax retums linked to the par-
The views in this paper are those of the author, and do not ents' and children's income tax retums this
necessarily reflect those of the Treasury Department.
paper finds evidence which is generally incon-
' The exact figure is unknown. Based on estate tax data
discussed in Marvin Schwartz (1988) and Mary F. Bentz sistent with the compensatory bequest impli-
(1984), a rough calculation is that in 1982 about $200 cations of altruistic models. This lack of
billion was transferred at death. This is in line with Harry support for an altmistic bequest theory has im-
L. Gutman's (1979) also rough estimate of $131 billion plications for the relevance of Ricardian
transferred at death in 1977.
^ Again, the exact amount inherited by children is un-
equivalence propositions, the degree to which
known. The marital deduction is approximately one third private transf^ers may undo govemment redis-
of aggregate gross estates (see Bentz, 1984). From the tributional efforts, the relationship between in-
smaller sample used in this paper, children's inheritances heritance and inequality, and for the use of
are twice the level of bequests to spouses. Combining altmistic bequests to legitimize models with
these two figures leads to the rough estimate of two thirds.
Robert B. Avery and Michael S. Rendall (1994) estimate infinitely-lived agents.
that children inherited $39.4 billion in 1990, but note this The paper is organized as follows. The next
is likely an underestimate. section reviews the previous empirical work
874VOL 86 NO. 4 WILHELM: BEQUEST BEHAVIOR AND EARNINGS 875
on intergenerational transfers. The data are in- threat, and, consistent with this argument, the
troduced in Section II. Section III discusses the positive link between visits and bequeathable
altmistic models that are estimated. The results wealth was not found in one-child families.
in Section IV are followed by concluding In contrast to this evidence supporting an
comments. exchange model, and using the only previ-
ously available bequest data which have in-
I. Previous Work cluded information on heirs' incomes. Tomes
(1981, 1988) found evidence that bequests
Data on heirs' incomes are not necessary for were compensatory both across families and
preliminary investigations of bequest prac- within families, respectively. In addition, he
tices. Therefore, several authors have studied found that visits by children were not related
the incidence of unequal division of estates to to the inheritances they later received.
glean some indirect evidence of bequest be- Clearly bequests are not the only financial
havior. From Connecticut probate records, transfer between parents and children; in the
Paul L. Menchik (1980) found that most par- aggregate, inter-vivos gifts are of the same or-
ents bequeath equal amounts to their children. der of magnitude.^ Examination of inter-vivos
However, the predominance of equal division gifts by Cox (1987) and Cox and Mark Rank
has been challenged by Nigel Tomes (1988) (1992) have found that, conditional on the
who used survey data from Cleveland to show event of a positive transfer having occurred,
that most parents divided their estates un- inter-vivos transfers increased as the income
equally. Menchik (1988) cast doubt on this of the recipient increased. Such a finding is
result by replicating Tomes' sample using pro- consistent with a theory of transfers based on
bate records and finding that most parents exchange between parents and children, but
were equal dividers. Denis Kessler and Andre not with altmism.
Masson (1988a) consider this empirical de- Joseph G. Altonji et al. (1992) have tested
bate unresolved, noting the importance as- consumption and income data for the implicit
cribed to unequal estate division in the U.S. presence of compensatory inter-vivos trans-
legal literature, and, elsewhere (1988b), call- fers among extended family members. If trans-
ing for additional empirical evidence. In ad- fers are altmistically motivated, within-family
dition to the potential survey response error in consumption differences should be independent
Tomes' data, the divergence in estate division of the within-family distribution of income,
results may be caused by the small sample but the evidence is to the contrary. In addi-
sizes being considered. tion, more general tests of the within-family
The data requirements for bequest analysis income-consumption covariance restrictions
beyond the division of estates are stringent, but implied by altmism have failed to support
nevertheless several researchers have made the model, although the rejection is slightly
use of some data sets which contain informa- weaker for the subset of adult children who
tion, albeit incomplete, on parents and chil- are expecting a bequest (Fumio Hayashi et al.,
dren. B. Douglas Bemheim et al. (1985) found 1991).
evidence in the Longitudinal Retirement His- Thus, the available empirical research offers
tory Survey that children visited and called an inconsistent picture of the behavior behind
their parents more frequently when their par- bequests and inter-vivos gifts. Within the
ents had larger amounts of bequeathable
wealth. They interpret this finding as evidence
of an exchange theory of transfers in which
' Aggregate estimates vary by data source. Data from
bequests are made to children in exchange for the Survey of Consumer Finances (William G. Gale and
their earlier attention and care. Parents are able John Karl Scholz, 1994) show bequests and inter-vivos
to elicit attention because they can threaten gifts to be of approximately the same magnitude, but data
any child not providing attention with the from the President's Commission on Pension Policy
(Donald Cox and Fredric Raines, 1985) indicate that the
credible promise to disinherit him in favor of latter are twice as large as the former. Tax data imply that
his siblings. However, parents with only one aggregate bequests are larger than either study suggests
child would be unable to credibly make this (see footnote 1).876 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 1996
bequest literature there are conflicting results, The average gross estate among the decedents
even regarding the seemingly straightforward is $2.56 million and their net wealth is of sim-
issue of the frequency with which children in- ilar magnitude. Not surprisingly, their average
herit equal amounts. Note that if equal division annual income ($169,400) was high.' Income
is the rule, then exchange and altruistic expla- tax returns from either 1980 or 1981 were
nations of bequest behavior are somewhat dis- found for 96.5 percent of the decedents.
credited because they both imply that bequests Slightly more than half of the decedents were
should vary according to the characteristics of survived by spouses, and they bequeathed to
children. 2.26 children, on average. The average child
inheritance is $238,200, and the average ab-
II. The Estate-Income Tax Match Data solute value of the deviations of children's
inheritances from within-family averages is
A. The Data $14,600. Note that this reflects many children
who receive bequests equal to those of their
The Estate-Income Tax Match (EITM) data siblings. Forty-five percent of these decedents
set was constructed by the Statistics of Income had children who are of different sexes. The
Division of the Internal Revenue Service. The decedents' average age was 75 years and only
federal estate tax returns of 1982 decedents 39.5 percent were female. One quarter used
were merged with their own and their benefi- trusts to transfer part of their estate. Twenty-
ciaries' (1980-1982) income tax returns. The five percent made inter-vivos gifts during the
initial subsample is a 1-percent random sam- three years prior to death; these amounts are
ple of decedents with gross estates over $0.3 included in the gross estate.
million but under $1 million (453 decedents) It was more difficult to match income tax
and a 100-percent sample of gross estates ex- returns to the child beneficiaries. At least one
ceeding $1 million (8056 decedents). David return from 1980-1982 could be found for
Joulfaian (1992) has described the data in 73.2 percent of the children named as heirs on
more detail. These data have several advan- the estate tax returns.* Descriptive statistics for
tages over those previously available for be- these matched children are presented in col-
quest analyses. Most significantly, they are the umn 2, as are statistics for their parents, like-
first bequest data which contain reliable in- wise conditional on being matched. The
come information for both parents and child average age of the children is 42.7 years.
heirs. In contrast. Tomes (1981) had no pa- Forty-nine percent are female and 66 percent
rental income data. The data set contains com- are married. On average, the children report
plete families (rather than only a single child 1.092 dependents, likely an underestimate of
per parent), indisputably matched together via
social security numbers (a weak link in some
intergenerational data sets). Finally, the data
permit separation of labor earnings from re- shows positive, but insignificant, relationships to both the
turns to capital, do not suffer from survey re- size of the gross estate and the age of the decedent.
sponse bias, are national in coverage, and ' Decedent income is defined to be wages and salaries,
earnings from self-employment and partnerships, and re-
contain substantially more observations than turns from capital. The positive income concept (negative
earlier studies. income components are set equal to zero) is used to reduce
Summary statistics for the 4188 decedents the noise caused by tax-shelter behavior (see Susan
who bequeathed directly (as opposed to indi- Nelson, 1985). When returns from both 1980 and 1981
were found, income is the two-year average.
rectly via trusts) to natural bom or adopted chil- '' If children's income tax returns were not found be-
dren are presented in column 1 of Table 1.'' cause they had low income, and if they received larger
inheritances, then excluding these unmatched children
would stack the data against the altruistic model. Together
these hypotheses imply that the larger a child's inheri-
•* Evidence (available from the author upon request in tance, the less likely would the child's tax retum be found.
Appendix A) implies that these decedents were neither In contrast. Appendix A (available from the author) indi-
disproportionally less wealthy nor younger. A probit cates that the probability of matching a child's tax return
model of the probability of bequeathing directly to a child increases with his inheritance.VOL 86 NO. 4 WILHELM: BEQUEST BEHAVIOR AND EARNINGS 877
TABLE 1—DESCRIPTIVE STATISTICS
Decendents
with one or Decedents/children Completely matched
more children Matched children matched; restricted multichild families
(Sample 1) (Sample 2) (Sample 3) (Sample 4)
Parents (decedents):
Gross estate 25,635 26,350 25,498 27,661
(77,179) (88,588) (97,803) (132,110)
Net wealth 23,946 24,676 24,108 26,391
(73,630) (84,386) (92,758) (125,210)
Parent income 1,694" 1,723 1,671 1,710
(2,789) (2,926) (2,584) (3,118)
Parent age 75,347 75,627 76,982 77,724
(12,104) (11,484) (9,782) (8,831)
Parent sex 0,395 0,390 0,409 0,425
(0,489) (0,487) (0,491) (0,494)
Surviving spouse 0,519 0,524 0,496 0,489
(0,499) (0,499) (0,500) (0,500)
Number of children 2,259 2,281 2,171 2,476
(1,276) (1,273) (1,142) (0,756)
Children are of 0,451 0,453 0,440 0,599
different sexes (0,497) (0,497) (0,496) (0,490)
Trust 0,256 0,251 0.264 0,239
(0,436) (0,433) (0,441) (0,426)
Lifetime gifts 0,253 0,252 0,257 0,264
(0,435) (0,434) (0,437) (0,441)
Families (number of 4188 3010 2020 948
decedents)
Children;
Inheritance 2,382 2,468 2,690 2,561
(2,989) (2,983) (2,898) (2,397)
Earnings — 0,461 0,530 0,552
(0,915) (0,771) (0,753)
Age — 42,685" 44,752 45,564
(12,432) (10,016) (9,402)
Sex 0,507 0,494 0,488 0,488
(0,499) (0,500) (0,499) (0,499)
Spouse — 0,661 0,743 0,768
(0,473) (0,436) (0,421)
Grandchild (children's — 1,092 1,223 1,297
children) (1,289) (1,300) (1,320)
Average inheritance of 0,146 0.137 0,142 0,155
children'' (0,592) (0,557) (0,593) (0,646)
Average earnings of — — — 0,272
children" (0,415)
Number of children: 9464 6928 4153 2348
Used in tables: 2 — 3,5 4,5
Notes: Dollar amounts are in $100,000's (1982 dollars). Entries are omitted when their interpretation is ambiguous: that
is, children's infonnation when the sample contains unmatched children; and intersibling differences when the sample
contains unmatched siblings,
" Income averaged over the 4042 matched decedents,
^ Averaged over the 6212 children who had nonmissing age data,
° Absolute value of deviation from within-family average.878 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 1996
the decedents' grandchildren because many suiting sample contains 4153 children; their
grandchildren may have already formed in- summary statistics are listed in column 3. As
dependent households. expected from the restrictions, these children are
The average inheritance of matched chil- somewhat older, more likely to be married, and
dren is $246,800, over five times their average have higher eamings than those in column 2.
labor eamings of $46,100. Note that, on the Some of the models considered below in-
basis of their labor eamings alone, the average clude the decedent's decision to divide her es-
child beneficiary is well above the lower tate among several children. The data used to
bound ($39,704) of the top quintile of the estimate these models contain additional ex-
family income distribution. Because labor clusions. First, single-child families are ex-
eamings are intended to proxy children's hu- cluded because there is no decision conceming
man capital, they are defined to be the sum of the division of the estate among children. Sec-
wages and salaries and eamings from self- ond, families are dropped from the sample un-
employment. Partnership income is added less income tax retums could be found for each
only if it dominates each of these two com- child named in the estate tax retum. This is
ponents. Otherwise, it is likely that the part- done to avoid error in the measurement of sib-
nership is being used as a tax shelter, a ling averages and within-family differences.
common practice among high income indi- Third, families are excluded if they contain any
viduals (Nelson, 1985). In addition, a lower children less than twenty-five or greater than
bound of zero is assumed for each income sixty-five years old. These exclusions reduce
component. If the children are married, the the sample of children to 2348 observations
combined eamings of spouses are used, and (column 4 ) , primarily because of the require-
bequests to such children are combined with ment that families be completely matched.'
bequests given to their spouses. Finally, In addition to the children's individual data,
each child's eamings are averaged over as column 4 shows the average absolute value of
many years between 1980-1982 as could be the differences between children's eamings
matched. This reduces the influence of the and the within-family means to be $27,200.
annual transitory component of eamings.^ Several limitations of these data should be
In addition to the requirements that children noted. First, observations of children's inher-
be matched to an income tax retum and that itances are those amounts received directly
their parents be similarly matched, two sample and do not include assets transferred in trust.
restrictions are used when estimating the be- Unfortunately, the life tenants (recipients of
quest models to be formulated below. First, income flows from such assets) and remain-
children are excluded if they are less than dermen (eventual recipients of such assets) of
twenty-five or greater than sixty-five years old bequests via tmst are unidentified in the data.
(or if their age data are missing). This retains Hence, the amounts inherited directly by the
a focus on adult offspring and avoids compli- children of the 25 percent of decedents who
cations surrounding transitions into and out of created trusts may simply be a lower bound to
the labor force. Second, children from farm their total inheritance. Though the results pre-
families are omitted due to the difficulties in sented below refer to bequests made directly
using tax data to deduce the economic income to children, as part of a sensitivity analysis the
from farms. Each of these restrictions removes findings will be reexamined with the decedents
nearly 1300 children from the sample.* The re- forming trusts removed from the sample. Also
note that although some trusts are certainly es-
tablished for children with health problems
' Eighty-one percent of all matched children were which cause low eamings, Menchik's (1980)
matched in each of the three years. Thirteen percent were
matched in two years and 6 percent in only one year.
* Nearly 200 children are dropped because their parents
were not matched to an income tax retum. Eleven children ' Sample 4 includes one family (two children) in which
are dropped because either their parent reported zero in- the decedent reported zero income. This observation is
come in the two years prior to death or made a zero direct included in the within-family analysis, but is dropped from
bequest to them. the between-family analysis.VOL 86 NO. 4 WILHELM: BEQUEST BEHAVIOR AND EARNINGS 879
evidence implies that most provide equal re- lems lead to the existence of many children
mainder interests. who are not observed in the data, then the ob-
Second, if compensatory inter-vivos trans- served family size distribution should be
fers are frequently made and of substantial skewed toward smaller families. Appendix B
magnitude, it is possible that altruistic parents (available from the author upon request) pre-
do not need to make compensatory bequests. sents a comparison of the family-size distri-
Because the EITM data do not inform us of butions in the EITM data with those from other
the inter-vivos transfers made from a parent to data sets, and shows that EITM family sizes
her children, except for those made during the are in fact smaller. To the extent that this re-
last three years of her life, this possibility can- flects the omission of disinherited children,
not be definitively ruled out. However, there and if this disinheritance is motivated by altru-
are several indications that extensive compen- istic parents choosing bequests at comer so-
satory inter-vivos gifts are unlikely. Recall, lutions, then the analysis will be biased against
that previously discussed inter-vivos gifts re- compensatory bequests. However, other data
search generally produced results inconsistent sets have found that disinheritance occurs in-
with altruism. Also, the EITM data suggest frequently (Marvin B. Sussman et al., 1970;
that inter-vivos gifts were not frequently made Menchik, 1980) and usually for reasons con-
by the parents; only 25 percent made such gifts sistent with an exchange motivation (Sussman
in the three years prior to death. A more con- et al.). Moreover, the EITM data are drawn
servative interpretation of this result is that it from the extreme upper tail of the wealth dis-
reflects a hesitancy to make inter-vivos trans- tribution, and there is a inverse relationship
fers on a regular basis, not an unwillingness to between socioeconomic status and fertility
make gifts when children experience times of (Judith Blake, 1989). Hence, although there
reasonable need. Note that because the aver- is undoubtedly some unobserved disinheri-
age EITM child was in his forties when his tance, the many small families in the data do
parent died, the major occasions of such need not necessarily indicate extensive disinheri-
(for instance, help with a down payment on a tance. All of these arguments are more fully
first house and assistance at the birth of chil- developed in Appendix B. Despite these in-
dren) would have occurred well in advance of dications that disinheritance is not widespread,
the parent's death. Consequently, gifts in re- its incidence in the EITM data cannot be di-
sponse to such need would not be observed rectly ascertained, and this paper's results
in the data. Even so, EITM children received should be interpreted with this in mind.
an average inheritance of nearly $250,000; Einally, note that these data describe only
achieving a transfer of similar magnitude with the wealthiest of decedents, and therefore are
inter-vivos gifts would have required a sus- not representative of the U.S. adult population.
tained level of large gifts in addition to the Studying approximately the same sample from
transfers made at the times of need. Parents which the EITM data were drawn, Schwartz
are likely aware of the deleterious effects such (1988) estimated that 1982 decedents who
large inter-vivos gifts may have on their chil- filed estate tax retums represented the richest
dren's behavior (see Neil Bruce and Michael 2.8 percent of adults who in tum owned about
Waldman, 1990). 30 percent of U.S. personal wealth.'" Although
The third data issue is whether the number this percentage is not precisely accurate," it is
of children in a family can be accurately de-
termined from the EITM data because only
children receiving direct inheritances are re- '"The EITM decedents were subject to a slightly lower
gross estate filing threshold (Schwartz used $325,000) and
quired to be recorded on estate tax retums. were necessarily matched to their income tax retums. As in-
Living children would not be observed in the dicated above, this match did not impose much selection.
data if their entire inheritance was received as '' The estimate is biased because it was based on mor-
a trust transfer or if they had been disinherited. tality rates which were not adjusted for education, occu-
pation, and other individual characteristics which affect
Similarly, and unfortunately, stepchildren were mortality. For instance, Martin H. David and Menchik
coded into a residual relationship category, (1988) found that estate multiplier estimates of wealth are
and hence cannot be identified. If these prob- too low if not corrected for occupation.880 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 1996
TABLE 2—INCIDENCE OF EQUAL DIVISION AND INHERITANCE INEQUALITY AMONG CHILDREN
Number of children
Two or Two Three Four Five
more children children children children Six or more
Estate division:
Exactly equal 0.686 0.697 0.700 0.651 0.672 0.555
Within ± 2 percent 0.766 0.776 0.782 0.718 0.793 0.616
Inheritance inequality:
Coefficient of variation
(squared) 1.3308 0.9940 1.4123 1.2649 1.1147 1.0834
Within-family component 0.1007 0.0927 0.0569 0.1541 0.1763 0.1347
Families: 2913 1531 797 370 116 99
Note: The sample is all decedents in Sample 1 of Table 1 who bequeathed to more than one child.
a qualitative indication that the EITM data are tates "approximately equally," '^ compared to
representative of a substantial share of indi- 50.4 percent in Tomes (1988).
viduals' wealth, despite their representation of The incidence of equal division of estates is
only a small percentage of individuals. extremely high. The frequency of exactly
equal estate division was reported to be 21.1
B. Equal and Unequal Division percent by Tomes (1988), 62.5 percent by
Among Children Menchik (1980), and 84.3 percent in Menchik
(1988). The table shows no systematic rela-
Table 2 reports the incidence of equal estate tionship between division choices and family
division in the EITM multichild families size, except that very large families experience
(Sample 1 with single-child families ex- more unequal division. Finally, the squared
cluded). Over two thirds (68.6 percent) of the coefficient of variation of inheritances re-
decedents divided their estates exactly equally ceived by children indicates substantial inher-
among their children. Over three quarters itance inequality. However, the within-family
(76.6 percent) divided their estates so that component of this inequality measure shows that
each child received within ±2 percent of the very little inequality results from unequal inher-
average inheritance among children in the itances to children within the same family.
family.'^ Eighty-eight percent divided their es-
m . The Altruistic Bequest Model
In this section the standard altruistic model
" Unequal bequests that occur via trusts cannot be ob- is generalized to be consistent with the exten-
served in the data. Indeed, decedents creating trusts are
less likely to bequeath equal amounts (63.2 percent) com-
sive amount of equal division which appears
pared to decedents not creating trusts (70.2 percent). Of in the data. To begin, consider the standard
course, unequal bequests may be made via trusts, despite model in which the utility of the 7 th parent,
equal direct bequests, or unequal direct bequests may be U{coj, y^j, y2j, ... , yNjj), is defined over her
rendered inconsequential by very large and equal bequests own lifetime consumption (cq,) and her chil-
via trusts. A referee points out that while children gener-
ally receive equal shares of remaining interests (excepting dren's lifetime resources (yy). The subscript
larger amounts for children with atypical disadvantages), " 0 " indicates a parent variable, and / = 1,...,
creating generation-skipping trusts of equal amounts in A', indexes her natural bom and adopted
which children receive a life interest are essentially un-
equal bequests because the children have different lengths
of life. Making the very conservative assumption that
every trust creator bequeathed unequally, then the true in- '"' Tomes (1988) defined "approximately equal" estate
cidence of equal division among all the EITM decedents division to be when the difference between the maximum
would be 54.3 percent. Note that Menchik's (1980) equal and minimum sibling inheritances is no more than one
division results do include amounts transferred via trust. quarter of the mean inheritance per child.VOL. 86 NO. 4 WILHELM: BEQUEST BEHAVIOR AND EARNINGS 881
children, the number (Nj) of which is as- where Dp, is a vector of parent-specific de-
sumed exogenous. As is regularly assumed, mographic characteristics, Dy is a vector of
the parent has symmetric concem over her child-specific demographic characteristics, Sp
children; the yy enter the utility function sym- and S^ are the respective parameter vectors, r]j
metrically. The lifetime resources of children is a parent-specific heterogeneity term, and e^
are defined to be is a child-specific heterogeneity term (for ex-
ample, it would include unobserved child
(1) yy^hy-^by needs). Each error term is independent and
identically distributed. Note that although (4b)
where bjj is the bequest from the parent and hjj allows bequests to be affected by observable
is the exogenous lifetime eamings (human cap- and unobservable characteristics of children,
ital) of the child. The parent then chooses Cq, and assuming these characteristics infiuence be-
the bjj to maximize utiUty subject to a budget quests independent of the identities of the chil-
constraint determined by her lifetime resources dren possessing them implies that utility
(yoj) and the intergenerational discount factor p. remains symmetric in the (yij — y^). With (4a)
It is assumed that parents take p as fixed. It is and (4b) optimal bequests are
convenient to reformulate the choice problem in
terms of yy instead of bij (Becker, 1981), yield- (5)
ing the budget constraint:
where Yj is family income redefined to include
yoj and within-family sums of the -y,y. Family
(2) Coy + = yaj + income thus redefined remains a family-level
variable; all of its stochastic components are
family-specific unobservables. Symmetric con-
where the right-hand side is "family income," cem again implies that the scalar/( Yj,p) is com-
a family-level variable henceforth denoted Yj. mon to all children within each family. Hence,
The first-order conditions produce a solu- /(Yj, p) can be modeled as a family fixed effect
tion,/( Yj, p), for children's lifetime resources in the estimation of (5); controlling for the fixed
which is a function of family income and the effects, the estimated coefficient on heirs' eam-
discount factor, and which with (1) yields a ings enables a test of the altruistic model's pre-
prediction conceming bequests in standard al- diction that this coefficient is - 1 . Moreover,
truistic models: note that imperfect observation of parental re-
sources does not bias the test because family
(3) fixed effects control for yq,.
However, there is a complication in apply-
The assumption of symmetric concem implies ing this test to the data at hand. To see this, it
that the scalar/(y,, p) does not vary across is helpful to rewrite (5) in terms of deviations
children in the same family. Hence, when con- from within-family means:
trol-ling for this family-specific scalar, altru-
istic bequests are a negative linear function of (6) - b*j =
eamings.
A stochastic specification which is similar
to (3) can be developed if utility is modified
to be a function of Cq, — joj and y^ - y^, where where the overbar denotes within-family av-
jdj and jij are minimum demand levels for erages and Ph is the degree to which parents
consumption and children's lifetime resources, use bequests to compensate intersibling dif-
respectively. Assume the minimum demand ferences in eamings (in the altmistic model
levels can be written 0h= — 1). It^s clear from (6) that equal di-
vision (b* = b*j) should occur only in the un-
(4a) joj = Di,.5^ + r,j likely event that siblings have equivalent
lifetime eamings and other characteristics. Be-
(4b) y,j = D^Se + e^ cause this contradicts the prevalence of equal882 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 1996
division documented above, a generalization The intuition of the division rule is straightfor-
of the standard model is required. I generalize ward. The likelihood of an unequal division is
the model by assuming that the parent suffers higher if siblings differ greatly in their earnings
a psychic cost KJ, resulting from intersibling and other characteristics, including the unob-
jealousy and family conflict, if she chooses to servable Ey's, and if parental psychic cost is low.
divide her estate unequally among her chil- The generalized model recognizes that
dren. This seems entirely plausible, although parents select themselves into the set of un-
other explanations of equal division exist.'* equal dividers with a decision rule based on
The decision process in this model can be the same observable and unobservable child
thought of as having three steps. First, the par- characteristics which determine the within-
ent determines the optimal unequal bequests family bequest differences. Hence, it suggests
as in (5). Next, she calculates the optimal a potential selectivity bias in estimates of
equal bequests {b*j*) which maximize utility within-family bequest models like (5) or (6)
subject to (2) and the additional constraint that based on the subsample of families with un-
bij = bkj for all children i and k in her family. equal bequests. To illustrate this bias, consider
Finally, she selects unequal division only if it using data from families with tinequal divi-
gives her higher utility after the psychic cost sions to run a regression of (fty - b.j) on (/i,y -
of unequal division is deducted, that is if Uf — h.j); also assume that altruism is the true
Kj> Uf*. model (PI, = —1). Then, equation (7) implies
This expression is an estate division rule. that in the sample of families for which un-
Using a second-order Taylor series expansion equal divisions are observed, it must be that
of Uf * around the optimal unequal bequests siblings with greater_[lower] than average
b*, and assuming that parental utility is sep- earnings (/i,^ > [ < ] h.j) tend to have lower
arable in the y^ - y.y, leads to the following [greater] than average unobserved compo-
approximation of U* - Uf* > KJ-.'^ nents of minimal demand (ey < [ > ] e.y). If
not (for example, /ly > h.j and e,^ > e y) then
(7) b, = b* the terms -(/j,y - hj) and (e.y - e.j) would
offset each other in (7) and unequal division
would _be less likely. The implication is that
if (hij — hj) and (£„ - e.^) are negatively cor-
related within the subsample of unequal divid-
ers. Consequently, regressing (bij — fo.j) on
(hij - h.j) without controlling for this negative
correlation would produce estimates of /S/, that
are biased away from zero—that is, less than
- 1 . In a multiple regression model, estimates
otherwise (for all / in familyy). of Sc are potentially biased as well; of course,
in this case the covariance of earnings with the
implies that the second-order cross-partial derivatives of
''' Menchik (1988) considers the psychic cost explana- utility are zero, and this leads to a Taylor expansion with-
tion more reasonable than a purely financial cost (of mak- out interactions between the characteristics of different
ing a will) rationale, or explanations based on uncertainty siblings. The derivation also requires that bf,*VOL 86 NO. 4 WILHELM: BEQUEST BEHAVIOR AND EARNINGS 883
Dy prevents an a priori determination of the on estimating (5) with fixed effects is never-
direction of any of the biases. theless of interest. First, if parental psychic
Unbiased estimates of P^ and 5^ can be ob- costs dominate intersibling differences as de-
tained by estimating (6) along with (7) as a terminants of unequal division, the bias will
generalized tobit model.'^ To implement this be small because the division decision is only
model, I will assume a linear specification of weakly correlated with differences in chil-
parental psychic costs: dren's characteristics." Second, the bias may
tum out to be weaker in families with more
(8) K, = Z'a-I- UJj than two children. This is because when a par-
ent chooses unequal division in a large family,
where Zj is a vector of parental characteristics it may be that just a few of her children have
( a is the corresponding parameter vector), characteristics sufficiently far from the within-
and ujj is an i.i.d. N{O,ai) unobservable com- family averages to cause the left-hand side of
ponent. Note that both the unobserved com- (J) to exceed ttie psychic costs. The (/i,y -
ponent and the total psychic costs may be h.j) and (Dy — D.^) are not correlated with the
negative. Therefore, the sensitivity of the re- (s,y — s.j) for the children who were not in-
sults will be examined by considering a log- fluential in their parent's division decision.
normal heterogeneity component and psychic Conversely, there is only one intersibling dif-
costs which are the square of the right-hand ference in two-child families and it necessarily
side of (8). influences the division decision (hence, the
Computing the contribution to the general- bias is likely to be largest in two-child fami-
ized tobit likelihood function from a family of lies). Third, equation (5) is estimable with all
Nj children requires either numerical integra- matched children (Sample 3) without mea-
tion of {Nj — 1 )-variate densities over regions surement error bias caused by the unobserved
of the error space defined by the nonlinear re- data of unmatched siblings. In contrast, the
lationship among error terms which results left-hand side of (7) cannot be accurately mea-
from (7) and (8), or using simulated maxi- sured for families with one or more unmatched
mum likelihood (SML). I estimate the model children. Hence, the generalized tobit model
using SML with a kernel-smoothed frequency of (6) and (7) is estimated using the data from
simulator (see, for example, John Geweke et Sample 4.
al., 1994). The probabilities of equal and un- Regardless of these differences, there are
equal division based on (7) and (8) are esti- several advantages to using either the fixed-
mated by taking 50 draws for each of the (e,y - effects estimation of (5) or the generalized to-
e .j) and Uj fi'om their respective distributions; bit estimation of (6) and (7) to test for an
the (Cy - s.j) are assumed to be A^(0, cri). A inverse relationship between bequests and
disadvantage of simulated maximum likeli- eamings. Essentially, equations (5) and (6)
hood estimation is that the simulated likeli- result from a bequest model in which parents
hood is a biased estimate of the true likelihood are the only decision makers (rather than being
for a finite number of draws. Therefore, I have engaged in strategic exchange), children's
verified the performance accuracy of this pro- lifetime resources less the minimum demand
cedure in a series of Monte Carlo experiments; levels are the appropriate arguments in par-
these results are available upon request. ents' utility functions (rather than the bequest
Finally, note that despite the potential selec- amounts themselves), and parental utility is a
tivity bias, a test of the altruistic model based
" The bias is also small in the reverse case where in-
"• A two-stage procedure (following James Heckman, tersibling differences dominate psychic costs in the estate
1976) cannot be used. Although an estimate of the mag- division decision. In this event there is little selectivity
nitude of £[(e,y - s.,)\U* - Uf* > KJ] can be formed bias because there is essentially no selection. That is,
from a discrete choice model based on (7), its sign is in- among parents whose children's characteristics differ, al-
determinate because (e,^ - e .j) enters (7) in quadratic form most all bequeath unequal amounts. As described in
only. Section II, the EITM data do not reflect this pattem.884 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 1996
TABLE 3—INHERITANCE MODELS WITH FAMILY FIXED EFFECTS
(UNEQUALLY DIVIDED ESTATES)
Dependent variable: Inheritance
Variables (1) (2) (3)
-0.12682" -0.15135" -0.17225"
Eamings (0.07550) (0.07896) (0.09774)
-0.02456" -0.03081"
Age — (0.01429) (0.01838)
-0.01559 -0.01513
Sex — (0.1211) (0.1584)
0.29003" 0.35685"
Spouse — (0.1589) (0.2089)
-0.02347 -0.02380
Grandchild — (0.05457) (0.06946)
Children: 1089 1089 821
Families: 527 527 396
Adjusted R^\ 0.625 0.626 0.497
E statistic: 2.821 1.815 1.653
(Probability value) (0.089) (0.107) (0.145)
Notes: Observations are the children in Sample 3 who received unequal bequests.
Family fixed effects are included in each regression. Earnings and inheritances are in
$100,000's. Standard errors are in parentheses. The E statistic tests the hypothesis that
all the independent variables, except the fixed effects, have zero coefficients. Likeli-
hood ratio tests in column (1) indicate significance at 2 percent and in columns (2)
and (3) at 1 percent. Columns (1) and (2) employ a strict definition of unequal division.
Column (3) considers unequal division exceeding ± 2 percent of the average bequest
to children.
" Significant at 10 percent.
symmetric function of these arguments (a the 10-percent level), the 99-percent confi-
standard assumption). Consequently, other dence interval ( - 0 . 3 2 , -1-0.07) implies re-
than symmetry, tests based on (5) and (6) do jection of the altruistic null hypothesis that
not depend on functional form assumptions the coefficient is —1 at the highest levels
concerning preferences, that is, / ( , ), which of significance. Also note that (5) is an
may be parent specific. intergenerational model based on lifetime
eamings, but it is being estimated with (a
rv. Results three-year average of) annual eamings. Ad-
justing the point estimate to account for the
A. Fixed-Effects Estimates conversion of annual eamings into a lifetime
stock variable implies substantially less com-
Table 3 presents fixed-effects estimates of pensation regardless of assumptions concem-
equation (5) using the children in Sample 3 ing interest rates and time horizons. For
whose parents chose unequal division. Assum- instance, an annual interest rate of 5 percent
ing that eamings are the only child character- over an infinite horizon implies compensation
istics which affect bequests, the estimate in of 0.63 cents on the dollar.
column (1) indicates that when a child's eam- The estimated compensation is similar when
ings are $1 below the within-family average the available demographic controls are added
child eamings, he receives almost $0.13 more in column (2). These results also show that
than the average inheritance of that family's younger and married children receive more
children. This compensation is small and, al- than their siblings. In column (3) the defini-
though significantly different from zero (at tion of unequal division is relaxed by definingVOL 86 NO. 4 WILHELM: BEQUEST BEHAVIOR AND EARNINGS 885 it to have occurred if any child inherits more (coefficient = -1.308, standard error = or less than 2 percent of the average bequest 0.353). The first of these results suggests that to children. The estimated effect of own eam- for two parents to come to an agreement on an ings is slightly stronger. unequal treatment of their children, the chil- Additional sensitivity analyses produce dren must have different needs.^' qualitatively similar results, the most interest- ing of which are now briefly described.'* B. Generalized Tobit Estimates There is evidence that those who leave trusts simultaneously use direct bequests to children Generalized tobit estimates of (6) and (7) to compensate for eamings differences (coef- are presented in Table 4. The variables used ficient = -0.734, standard error = 0.165). Of in this model require data on all of the children course, if the present value of bequests via in each family; thus. Sample 4 is used rather tmsts could be assigned to the appropriate than Sample 3. Ordinary least-squares (OLS) children, there may be evidence of a stronger estimates of (6) using Sample 4 are presented altmistic effect, but the effect is not likely to for purposes of comparison. One observation be large.'' There is weak evidence that those per family is dropped to adjust for the loss of not leaving tmsts reinforce eamings differ- degrees of freedom by taking within-family ences. In addition, excluding decedents who differences. The estimates of the psychic cost made gifts during the years before death does parameters are relative to
886 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 1996
TABLE 4—GENERALIZED TOBIT MODELS OF WITHIN-FAMILY INHERITANCE
Variables Exactly equal division Division within 2 percent
OLS Generalized tobit OLS Generalized tobit
(1) (2) (3) (4)
Children's characteristics:''
Eamings -0,16300 -0,12594" -0,19160 -0,14326
(0,10356) (0,06797) (0,13152) (0,12291)
Age -0,03535' -0,01744° -0,04428' -0,01698
(0,01864) (0,00942) (0,02407) (0,01123)
Sex -0,05238 -0,03936 -0,06350 -0,02916
(0,14462) (0,07401) (0.19105) (0,08773)
Spouse 0,27877 0,16492' 0.36753 0,16772
(0,18355) (0,09572) (0,24590) (0,11209)
Grandchild -0,00317 0,00768 0.00002 0,00436
(0,06442) (0,03224) (0,08417) (0,04015)
1,156 0,816 1,345 0,862
Parent's psychic cost:
Parent income -0,01208 -0,02096*
(0,01131) (0.00903)
Surviving spouse — -0,04897 — 0,23538'
(0,10491) (0,12821)
Number of children — -0,07099 -0,13144'
(0,05360) (0,07050)
Parent age — 0,00159 — 0,00205
(0,00488) (0,00575)
Parent sex — -0,11062 — 0,22247'
(0,10743) (0,12504)
Constant — 1,15569** 1,35920**
(0,42989) (0,52519)
Families: 259 948 187 948
tjnequal divisions: 259 259 187 187
Observations: 397 1400 293 1400
Average log-likelihood: -1,558 -0,967 -1,707 -0,825
0,010 13,656 0,012 18,896
Notes: The sample is all multichiid families for which income tax retums were found for all children (Sample 4), In
columns (1) and (2) the exact definition of equal division is used. In columns (3) and (4), equal division is defined to
have occurred if all siblings inherit within ± two percent of average, Eamings and parental income are in $100,000's.
Asymptotic standard errors are in parentheses. The OLS results include R^; the x^ statistics for a model with zero-slope
coefficients are reported for the generalized tobits. The generalized tobit estimates are generated using simulated maximum
likelihood with kemel frequency smoothing. The smoothing parameter is 0,10, and 50 random draws are taken for each
random variable. Both (e,j - e.j) and uij are normal; at is normalized to 1,0,
' Significant at 10 percent,
'' Children's characteristics are deviations from within-family averages,
* Significant at 5 percent,
** Significant at 1 percent.
that the slope coefficients are zero cannot be whether a spouse survives, the number of chil-
rejected at conventional significance levels. dren, and the parent's sex are significant de-
Applying the model with the relaxed defi- terminants of psychic costs and consequently
nition of unequal division in column (4) pro- the decision to divide an estate unequally. To
vides a better fit; the chi-squared statistic is examine the marginal effects, consider a sim-
significant at 5 percent. As before, the gener- ulation of the probability of unequal division
alized tobit estimate of the effect of children's using 500 draws for each of the gy and uij. The
eamings is smaller than found with OLS (in simulated probability of unequal division for
column (3)). In addition, parental income. a male decedent who is survived by a spouseVOL. 86 NO. 4 WILHELM: BEQUEST BEHAVIOR AND EARNINGS 887
is 0.307 (the other parental variables are eval- that in approximately half of the 259 families
uated at their means, and the intersibling where unequal division occurs eaming differ-
differences are evaluated at the means of their ences between siblings are reinforced by larger
absolute values). The probability falls by bequests to children with higher eamings.
0.034 for a female decedent and rises by 0.048
if the male decedent is not survived by a C. Additional Results
spouse. A one standard-deviation (just under
$40,000) increase in the mean absolute value Altruistic models also predict intergener-
of children's eamings differences increases the ational compensation, that is, a negative
unequal division probability by 0.015. Al- relationship between the average bequest to
though the estimates indicate that the proba- children and children's average eamings.
bility of unequal division rises by 0.004 with Between-family models—equation (5) aver-
a $100,000 increase in parental income, this aged across the Nj children in each family—
result is not robust to using the parent's gross are necessary to estimate the magnitude of this
estate as the measure of resources (a $1 mil- effect, which unlike its direction is theoreti-
lion increase in the gross estate lowers the cally indeterminate.^^ Estimates of these mod-
unequal division probability by 0.002). Al- els are not necessarily subject to selectivity
though the direction of the effect of parental bias as long as sy and UJJ are uncorrelated.^"*
resources on estate division depends upon the Columns (1) and (2) in Table 5 present es-
resource measure used, it does appear that the timates of between-family models for families
magnitude of the resource effect is very small. with unequal and equal division, respective-
Moreover, there is essentially no change in the ly. Several functional forms were estimated
estimate of intersibling compensation under (linear, cubic, semi-log, double-log, and a
different measures of parental resources.
The generalized tobit estimate of intersib-
ling compensation also is robust to several
parent utility function with asymmetric weighting of chil-
other sensitivity checks. Specifically, there is dren is only slightly higher (-0.375, standard error =
little change in the estimate when u}j is drawn 0.205) than was estimated in the fixed-effects model for
from a lognormal distribution, when the psy- two-child families. Furthermore, modeling within-family
chic costs in (8) are squared, and when the inheritance differences with nonlinear functional forms
does not substantially affect the estimated compensation,
model is estimated with 200 draws for each By as it may under more complicated asymmetric utility. Fi-
and ujj. Furthermore, as expected, the bias nally, dthough some parent characteristics do affect
in the OLS estimate is more severe when within-family bequest differences (as they would be
two-child families are analyzed in isolation; expected to do under asymmetric concem), their inclusion
does not alter the effect of children's eamings. Statistically
the fixed-effects estimate of intersibling com- significant parent effects are a surviving spouse and the
pensation reported in the previous section is number of children, both of which reduce within-family
more than twice the magnitude of the gener- bequest differences. Bequest differences are larger if the
alized tobit estimate (coefficient = -0.144, decedent had a closely held business. _ _
standard error = 0.021). Relaxing the as- ^•' The negative compensatory effect ofhj on b*j is off-
set by its positive income effect through Yj. The magnitude
sumption of symmetric concern by permitting of the latter depends upon functional form and is unknown
a correlation between s^j and Uj produces an a priori. However, the net effect of h.j is negative if pa-
inconsequential change in the effect of chil- rental consumption is a normal good.
dren's eamings in two-child families. Simi- ^'' If e.j and Uj are uncorrelated then no selection bias
can arise from a correlation between E .J (an error term in
larly, investigating several other possible the between-family bequest function) and the (EJ, - E .;)
implications of more complicated forms of terms in (7) because £[E.y(e,j — e .J)] = 0. There may be
asymmetric concem does not substantially af- correlation between the unobserved minimum demand
fect the estimated amount of intersibling com- component of parental own consumption (77^) and Uj, but
pensation.^^ Finally, it is interesting to note this would imply a difference in average bequests to chil-
dren between families experiencing equal and unequal
division. However, as previously noted, b** » ^* on av-
erage in the EITM data. Finally, controlling for selection
^^ The OLS estimate of intersibling compensation in a bias in the between-family models produces virtually no
regression derived from a two-child quasi-homothetic change in the results.THE AMERICAN ECONOMIC REVIEW SEPTEMBER 1996
TABLE 5—ADDITIONAL INHERITANCE MODELS
Families with unequal division Families with equal division All matched children
Average inheritance of children Average inheritance of children Inheritance
Dependent variable (1) (2) (3)
Earnings" -1.30674 -0.19616 -0.51273
(1.03119) (0.16129) (0.33295)
Eamings" squared 1.67793*
(0.65780)
Eamings" cubed -0.29374**
(0.10486)
Age" -0.00089 0.02605**
(0.01707) (0.01003)
Sex" -0.23341 -0.46983*
(0.48539) (0.23413)
Spouse' -0.84774 -0.26351
(0.52856) (0.30390)
Grandchild" 0.08601 0.07070 0.08524
(0.15191) (0.09588) (0.04951)
Parent income 0.14620** 0.15752** 0.21538**
(0.04579) (0.02708) (0.05719)
Surviving spouse -1.09362** -1.55441** -1.56870**
(0.28302) (0.16667) (0.12665)
Number of children -0.67397** -0.47628** -0.63237**
(0.14494) (0.08723) (0.04818)
Constant 5.26712 3.62506 3.49620
(1.01316) (0.58840) (0.50765)
Adjusted Rh 0.191 0.208 0.159
F statistic: 7.099 23.627 113.734
Sample: 4 4 3
Children: — 4153
Families: 259 688 2020
Notes: Dollar amounts in $100,0(K)'s. Standard errors are in parentheses (corrected for the correlation in error terms
among siblings in column (3). Column (1) gives the average bequest to children in each family with unequal division.
Child variables are the within-family averages. Estimates are weighted least squares using the number of children per
family as weights. Column (2) is the same as column (1) except the bequests are from families with equal division.
Column (3) gives inheritances of children. Estimates are two-stage least squares with eamings identified by an age
quadratic, sex, and marital status. The regression also includes parent's sex and age (age is significant).
" Children's within-family average in columns (1) and (2).
* Significant at 5 percent.
** Significant at 1 percent.
specification mimicking that of Tomes' (1981 that experience bequest reductions as their
Table 4), and the ones in Table 5 were chosen eamings increase.^^ The decedents who made
because they yield the strongest evidence of equal bequests to their children reduced these
intergenerational compensation. In principle, bequests by $0,196 if children's average eam-
the use of different functional forms for un- ings were $1 higher, but this estimate is not
equal and equal divisions is not inconsistent
with the generalized model because it permits
different bequest functions for b *• andfc* * de-
^' The estimates imply a $0.60 lower average bequest
spite their being derived from the same utihty per each additional dollar of children's average eamings
function. if eamings are below $45,(XX), but a $1.01 higher bequest
The cubic specification estimated for the av- if eamings are between $45,000 and $145,000.1 am grate-
ful to a referee who points out that this pattem is consistent
erage bequest when estate division was un- with a model containing both altruistic and exchange com-
equal suggests that to the extent altruism exists ponents, and with the latter dominating as children's eam-
in the data, it is children with lower eamings ings increase.VOL 86 NO. 4 WILHELM: BEQUEST BEHAVIOR AND EARNINGS 889
significantly different from zero. Also, recall measures of parent resources also were con-
that the amount of intergenerational compen- sidered. Replacing parent income with im-
sation is considerably smaller than these point puted lifetime income (based on a regression
estimates indicate because the models are be- using the Panel Study of Income Dynamics)
ing estimated in units of annual, not lifetime, or parent net wealth, both arguably better mea-
eamings. sures of the parent's lifetime resources, makes
An altemative interpretation of the lack of little difference in the effect of child eamings
strong altmistic evidence in both the within- in columns (1), (2), and (3), and in the gen-
and between-family models is that compen- eralized tohit models of Table 4.^^
sating behavior is undetectable with the EITM Reconsidering the models in columns (1),
data because of measurement error in parent (2), and (3) of Table 5, there is some evidence
income and child eamings. However, Monte of more intergenerational compensation among
Carlo experiments suggest that while mea- decedents who either are survived by a spouse,
surement error can create a large bias toward have gross estates over $5 million, or who do
zero in the estimate of the effect of eamings not create tmsts.^* This last finding is in con-
in within-family models (even with three trast to the weak evidence that those not leav-
years of observed eamings), it is unlikely to ing tmsts reinforce intersibling differences.
have led to the present results unless the tran- Finally, estimating the specification used in
sitory component of children's eamings is column (3) for one-child families alone pro-
considerably larger than has been measured in vides the largest point estimate of the degree
other data. The simulation is described in of intergenerational compensation ( — 1.136,
Appendix D (available from the author upon standard error = 1.436) obtained in the paper.
request).
While the transitory component of chil-
dren's eamings is less of a problem in the
between-family analyses because eamings are of parent's age: omitting it reduces the estimate of inter-
generational compensation to —0.067 (standard error =
averaged over several siblings as well as up to 0.320). In contrast, the compensation estimated in col-
three years, measurement error in parent in- umns (1) and (2) is insensitive to the inclusion of parent
come would generate a positive bias in the co- age.
efficient on average child eamings because of " However, the coefficients on imputed lifetime in-
the positive correlation between the latter and come are 41.4 to 173 percent larger than those on parent
income presented in columns (1), (2), and (3), of Table 5.
unobserved parent income. However, simula- The imputation is based on 22 years of income data for
tion exercises again indicate that it is likely nonfarm parents over age 40 in the PSID's Survey Re-
this measurement error would not generate the search Center cross section (n = 747). Their lifetime in-
results obtained from the EITM data. More- come (discounted present value of annual income divided
by 22) is regressed on variables which have a correspond-
over, the bias can be mitigated by the use of ing measure in the EITM data, most importantly their av-
instrumental variables as in column (3); note erage income over the last two years, their 1989 net
that this specification combines children re- wealth, and the eamings of their children (averaged over
ceiving equal and unequal divisions. Using all children remaining in the PSID and over the last three
years). The coefficients on these variables are 0.347 (stan-
sex, marital status, and an age quadratic to dard error = 0.016), 0.008 (0.002), and 0.227 (0.042), re-
identify children's eamings yields a negative spectively. The regression also includes a quartic age
point estimate on child eamings which is sig- profile, sex, whether married, the numher of children, and
nificant at 12 percent, but has httle effect on whether ever self-employed. The adjusted /?^ is 0.673.
the parent-income coefficient.^* Altemative ^' The evidence of greater compensation of child eam-
ings occurs when a parent survives [-0.392 (standard
error = 0.187) and -0.763 (0.436) in Table 5, columns
(2) and (3), respectively] and when no trusts are created
[-0.292 (0.201) and -0.850 (0.441) in columns (2) and
^"The OLS estimate is +0.156 (standard error = (3), respectively]. Excluding gross estates greater than
0.155). Issue may he taken with the instruments selected $5 million reduces the estimated effect to -0.090 (0.139)
to identify child eamings hecause the excluded variahles and -0.254 (0.279) in columns (2) and (3), respectively.
may directly affect the parent's bequest decision. Unfor- Excluding decedents who made gifts prior to death does
tunately, these are the most reasonable instruments avail- not produce stronger evidence of intergenerational
able in the data. These results are sensitive to the exclusion compensation.You can also read
