Applied Economics, 2008, 40, 413–436
Parent–child bargaining, parental
transfers, and the post-secondary
education decision
Charlene Kalenkoski
Department of Economics, Ohio University, Athens, Ohio, USA
E-mail: kalenkos@ohio.edu
Schooling decisions are often modelled within a unitary preference
framework. In this article, an alternative to the unitary preference model
is proposed in which parents and child have conflicting preferences over
parental transfers and the level of post-secondary schooling and participate
in cooperative bargaining as a means of resolving this conflict.
Comparisons of the implications of the bargaining and unitary preference
models motivate tests of parental altruism and income pooling. To test
these hypotheses, reduced form transfer and schooling equations are
estimated using data from the High School and Beyond Surveys.
The evidence suggests that the unitary preference model be rejected.
I. Introduction
The standard models used throughout the human
capital literature to examine the educational and
earnings outcomes achieved by children are unitary
preference models, with either parents making all of
the schooling decisions for their children or an
individual child making all of the schooling decisions
for himself, given some level of parental resources.
The importance of these human capital decisions lies
in the fact that they are major determinants of
a child’s future earnings, and hence, his consumption.
These models, however, ignore or assume away the
process by which parents and children resolve any
disagreements.
Disagreements between parents and child may arise
over whether or not the child should attend college,
how much effort the child should expend if college
is chosen, and how the financial cost of such an
undertaking would be split between them. Parents
may disregard their child’s effort disutility, parents
and child may have different rates of time preference,
or the child may lack concern over his parents’
consumption.
Sometimes, ignoring such disagreement may be
appropriate. When a child is very young, he must rely
completely on his parents for financial support.
Hence, even if he disagrees with his parents, his
parents are likely to have all of the bargaining power,
and a model in which his parents make all decisions is
appropriate. On the other hand, when a child
is grown up and financially independent from his
parents, he has all of the bargaining power. In this
case, a model in which the adult child makes all of the
decisions is appropriate. However, for a college-age
child, the disposition of bargaining power is less clear.
On the one hand, a college student has access
to nonparental funds for post-secondary schooling,
including his own earnings and financial aid. On the
other hand, he may find it difficult to completely
finance the level of schooling he desires with such
resources. Time constraints limit the amount of time
a student can work to pay for school. In addition,
need-based financial aid for undergraduate students
Applied Economics ISSN 0003–6846 print/ISSN 1466–4283 online ß 2008 Taylor & Francis 413
http://www.tandf.co.uk/journals
DOI: 10.1080/00036840600690264
(including both grants and loans) is awarded
assuming that parents make an Expected
Parental Contribution (EPC) towards their child’s
post-secondary education. If parents do not pay, a
student may be unable to cover the difference.1
Federally-guaranteed student loans are also subject to
loan maximums. Finally, private loans are often
unattainable by students without parents willing to
co-sign them. For students constrained by any of
these factors, parental transfers matter, and it thus
becomes important how disagreements with their
parents are resolved.
This article addresses parent–child disagreement
over the level and parental financing of
post-secondary education by introducing conflicting
preferences and parent–child bargaining into the
modelling of the post-secondary education decision.
A cooperative bargaining model is proposed in which
parents’ consumption, their child’s consumption,
and the child’s level of post-secondary schooling
are explicit choice variables and the level of
parent-to-child transfers is an implicit choice
variable. The implications of this bargaining
model for the level of post-secondary schooling and
the dollar value of parental transfers are then
compared to those of the corresponding unitary
preference model.
These comparisons lead to several testable hypotheses.
First, the unitary preference model implies that
only pooled income enters the demand function for
schooling (the income pooling hypothesis), while the
bargaining model allows parents’ and child’s incomes
to enter separately. Thus, empirical evidence showing
that parents’ and child’s incomes have different
effects on the level of schooling would reject the
unitary preference model but be consistent with the
bargaining model. Second, while the unitary preference
model allows only positive income effects and
negative price effects on schooling, the bargaining
model also allows negative income effects and
positive price effects. Thus, empirical evidence of
negative income effects or positive price effects would
reject the unitary preference model but would be
consistent with the bargaining model. Finally, while it
is an implication of the unitary preference model that
a 1 dollar increase in child’s income along with
a simultaneous 1 dollar reduction in parents’ income
reduces the level of parent-to-child transfers by
1 dollar (the parental altruism hypothesis), the
bargaining model allows for both a reduction in
transfers of less than or more than 1 dollar as well as
an increase in transfers. Therefore, empirical evidence
showing something other than a dollar reduction
in transfers would be a rejection of the unitary
preference model but would be consistent with the
bargaining model.
In order to test these hypotheses, reduced form
equations for transfers and schooling are estimated.
In these estimations there are two important
econometric issues that are addressed. First,
these hypotheses must be tested for children in
cooperating families, those families in which
parents make a transfer. However, whether or
not transfers are made is only observed if the child
enrols in a post-secondary programme. Therefore,
the reduced form equations for transfers and
schooling are estimated on the subsample of
respondents who both enrol in post-secondary
school and receive parental transfers. This sample
selection is addressed using a two-stage selectivity
correction procedure. Second, because three of the
right-hand-side variables in the transfer and
schooling equations are potentially endogenous,
the price of schooling, the dollar value of scholarships
and grants received, and the child’s income,
predicted variables replace the actual variables in
these equations.
The data used to test these hypotheses are
restricted-use student-level data from the High
School and Beyond Surveys conducted for the
National Center for Education Statistics (NCES),
US Department of Education, by the National
Opinion Research Council (NORC). Respondents
to this survey were high school sophomores in 1980
and were reinterviewed in 1982, 1984, 1986 and 1992.
In addition to results for the full sample, results are
provided for subsamples defined according to
whether parents want more, parents want less, or
there is no disagreement over the level of schooling.
This is done in order to determine whether negative
income effects and/or positive price effects for those
groups most predisposed to them are revealed by
the data.
This article proceeds as follows. Section II overviews
the related schooling, intergenerational
transfer, and family bargaining literatures. Section
III presents both the unitary preference and bargaining
models and compares and contrasts their
implications. Section IV introduces the data and
discusses the construction and relevance of key
variables. Section V presents the econometric model
and the hypotheses to be tested. Section VI describes
and interprets the main empirical results as well as
results from several sensitivity analyses. Section VII
concludes with an overall interpretation of the results
and directions for future research.
1
Kalenkoski (2005) provides evidence that a substantial percentage of parents contribute less than their EPC.
414 C. Kalenkoski
II. Literature Review
Models used throughout the human capital literature
to examine the educational and earnings outcomes
achieved by children can be categorized into one of
two types. Models of the first type assume that
parents have total control over decisions regarding
their child’s human capital. In these models a child’s
earnings are determined entirely by his initial
endowment, his parents’ investments in his human
capital, and his ‘market luck’. Examples of
such models include those of Becker and
Tomes (1976, 1979, 1986) and Becker (1981, 1993).
A major characteristic of these models is that they
abstract from any sort of schooling decisions a child
will eventually make for himself, relying on the
assumption of parental altruism and Becker’s Rotten
Kid Theorem (Becker, 1974) to assume away any
parent–child conflict.
The parental altruism assumed by the Rotten Kid
Theorem is parents’ complete acceptance of their
child’s preferences (i.e. goods that affect the child’s
utility enter into the parents’ utility function only
through the child’s utility function). With regard
to the post-secondary decision, however, this is
probably not the case. A more realistic assumption
is that parents may have paternalistic preferences
(Pollak, 1988). With paternalistic preferences,
a child’s utility may enter his parents’ utility function,
but his parents may also have direct and conflicting
preferences over goods, such as schooling, over which
the child also has direct preferences. For example,
parents may want their child to attend their college
alma mater even though their child would rather
attend a different school that all of his friends are
attending. Or, parents may feel their child is too
myopic when it comes to his education decisions.
Alternatively, a child may want to go to college even
though his parents would prefer him to work in the
family business.
In contrast to this parent-as-decision maker type of
model, the second type of human capital model
focuses on a young adult’s own schooling decisions
(e.g. whether or not to attend college), given some
pre-existing endowment determined both by inherent
ability and previous investments by parents. Such a
sequential parent-then-child approach has led to
numerous regressions of schooling variables on
standardized test scores, family background, and
neighbourhood and peer characteristics. Recent
examples include Tobias (2003) who investigates the
effects of cognitive ability and high school quality on
college entry decisions, Lemke and Rischall (2003)
who use parental education as an instrument for
schooling in a wage equation, Ioannides (2003) who
analyzes the effects of parents’ education and
education level of census tract on an individual’s
education, and Rainey and Murova (2004) who
examine the relationships between ACT scores and
characteristics of school districts in Arkansas,
Louisiana, Oklahoma, and Texas. An excellent
survey of much of the earlier literature can be
found in Haveman and Wolfe (1994, 1995).
Neither the parent-as-decision maker nor the
child-as-decision maker models allow for disagreement
between a parent and child to affect education
decisions.2
The intergenerational transfer literature,
however, has not ignored such parent–child conflict.
In this literature, parents are often assumed to be less
than perfectly altruistic and children’s concerns often
directly conflict with their parents’. In these models,
transfers are used as a strategic device by parents to
regulate their children’s behaviour. For example, in
Bernheim et al. (1985), parents provide strategic
bequests to their adult children to induce them to visit
more often than they otherwise would. In Pollak
(1988), parents provide strategic transfers to their
children to increase their consumption of particular
merit goods. More recently, Hao et al. (2000)
formulate a bargaining model in which parents
provide strategic transfers to their children to deter
them from taking an action, in this case having a teen
birth, that they deem undesirable.
Many empirical analyses in the transfer literature
have attempted to determine whether the data are
more consistent with the ‘altruistic parents’ models or
with those in which parents are not so altruistic
(Menchik, 1980; Wilhelm, 1996; Bernheim et al.,
1985; Cox and Rank, 1992; Altonji et al., 1997;
McGarry and Schoeni, 1995; McGarry, 2000). Their
results cannot be generalized, however, because the
studies differ widely across choice variables, age
groups, whether or not in-kind transfers are
considered, and whether the transfers considered
are bequests or inter-vivos transfers. Looking at
bequests made by parents to multiple children,
Menchik (1980) finds that equal sharing among
children is the rule, rather than the exception,
a result which does not support the altruism
model put forth by Becker and Tomes (1976).
Wilhelm (1996) tests a more general model of
parental altruism that is consistent with the extensive
amount of equal division in the data, yet still rejects
parental altruism. Bernheim et al. (1985), who also
2
There are several studies that allow disagreement between parents to affect their children’s human capital. For example,
see Thomas (1994).
Parent–child bargaining, parental transfers, and post-secondary education 415
look at bequests, find that bequests are often used as
compensation for services provided by beneficiaries,
evidence inconsistent with the altruism model. Cox
and Rank (1992) and Altonji et al. (1997) focus on
inter-vivos transfers rather than bequests and test the
implication of the altruism model that an increase
in child’s income by 1 dollar, along with a decrease in
parents’ income by 1 dollar, results in a reduction in
parental transfers of 1 dollar, a result that does not
hold in exchange models (models in which parents
expect to obtain something for their transfers). They
obtain results that are more consistent with exchange
models than with altruistic models. However,
analyzes of inter-vivos transfers by McGarry and
Schoeni (1995) and McGarry (2000) do not reject the
altruism model.
Another literature that focuses on conflict between
household members is the family bargaining literature.
The driving force behind this literature is the
idea that the unitary preference model of household
decision making is inappropriate in cases where
household members (usually husbands and wives)
have conflicting preferences, and a cooperative
bargaining model in which the Nash bargaining
solution is the method of resolving conflict is often
proposed as an alternative. An important testable
implication of this Nash model is that income is not
pooled (Manser and Brown, 1980, McElroy and
Horney, 1981). This means that household members’
incomes enter separately into the Nash-bargained
demand functions, unlike the unitary preference
demand functions which depend only on total
household income. It is important to note, however,
that a rejection of income pooling is also an
implication of other cooperative and noncooperative
bargaining models, such as the collective model
of Browning and Chiappori (1998) and the noncooperative
models of Lundberg and Pollak (1994),
so a rejection of income pooling does not support
the Nash model over any particular alternative to the
unitary preference model. It does, however, reject the
unitary preference model and is consistent with
bargaining.
While the primary focus of these family
bargaining models has been intrahousehold
allocations between husbands and wives, two studies
focus on intra-household allocations between parents
and children. McElroy (1985) uses a cooperative
bargaining model to investigate the labour supply
and household membership decisions of young adult
males, while Pezzin and Schone (1998) investigate the
intergenerational household formation, female labour
supply, and informal caregiving decisions that arise in
the context of adult children’s care for elderly
parents. The model presented in this article extends
this research on parent–child bargaining.
This article makes both theoretical and empirical
contributions to these three different literatures.
First, this article contributes to the human capital
literature by incorporating parent–child disagreement
and cooperative bargaining as a method of resolving
this disagreement into a model of post-secondary
schooling. It also contributes to the intergenerational
transfer literature by investigating inter-vivos transfers
from parents to child and testing the parental
altruism hypothesis within the new context of the
post-secondary education decision. Finally, this
article contributes to the family bargaining literature
by applying the standard cooperative bargaining
model to decisions regarding a child’s post-secondary
education and by testing the income pooling hypothesis
within this new context.
III. Theoretical Models
Unitary preference model
The basic unitary preference model assumes a single
decision maker household with utility function given
by W(cp
, cc
, s), where cp
, cc
, and s are, respectively, the
parents’ consumption, the child’s consumption, and
the child’s level of schooling, and W(Á) is the parents’
utility function.3,4,5
Assume this utility function is
twice continuously differentiable, nondecreasing, and
quasiconcave. The household’s budget constraint is
given by
cp
Á pp þ cc
Á pc þ s Á ps ¼ Mp þ Mc ð1Þ
3
Post-secondary schooling has aspects of both an investment good and a consumption good as both gains in future earnings
and current social or psychic benefits may be derived from it. This model assumes that utility is a direct function of s in order
to abstract from the particular mechanisms by which schooling affects utility. See Collins and Snell (2000) for a discussion of
school attributes of interest to parents choosing secondary schools for their children in the UK.
4
This utility function nests a more restricted specification, W(cp
, Uc
(cc
, s)), which would explicitly allow the child’s preferences
to enter the parents’ utility function.
5
A child-as-decision maker unitary preference model in which the child is independent and selfish would ignore parents’
consumption, cp
, and treat parental transfers as an exogenous source of income. The parent-as-decision maker unitary
preference model is discussed here because it treats transfers as endogenous, facilitating comparisons between the unitary
preference and the bargaining framework.
416 C. Kalenkoski
where pp, pc, and ps are the respective prices of
parents’ consumption, child’s consumption, and
schooling, Mp is the parents’ exogenous income,
and Mc is the child’s exogenous income. Note that by
assuming that the price of schooling and child’s
income are exogenous, the model abstracts from
school quality and labour-leisure–schooling choices,
although the potential endogeneity of these variables
is addressed in the empirical analysis. Maximizing the
household utility function, W, subject to (1) and
assuming an interior solution yields the following
demand functions:
cpÃ
u ¼ cp
uðpp, pc, ps, Mp þ McÞ ð2aÞ
ccÃ
u ¼ cc
uðpp, pc, ps, Mp þ McÞ ð2bÞ
sÃ
u ¼ suðpp, pc, ps, Mp þ McÞ ð2cÞ
where * indicates solution values and the u
subscript refers to the unitary preference model
(to distinguish these demand functions from
the bargained demand functions to be described
next). Note that only pooled income, Mp þ Mc, enters
these demand functions, indicating that only total
income, not the source of income, affects the level
of schooling demanded. This is the unitary
preference model’s pooled income hypothesis, and
can also be written in terms of the following
comparative statics:
@cpÃ
u
@Mp
¼
@cpÃ
u
@Mc
ð3aÞ
@ccÃ
u
@Mp
¼
@ccÃ
u
@Mc
ð3bÞ
@sÃ
u
@Mp
¼
@sÃ
u
@Mc
: ð3cÞ
Another interesting implication of the unitary
preference model relates to transfers. Let tÃ
u be
the amount of transfers parents make to
their child, where tÃ
u ¼ Mp À cpÃ
u Á pp. Taking
partial derivatives with respect to Mp and
Mc, we have @tÃ
u=@Mp ¼ 1 À ppð@cpÃ
u =@MpÞ and
@tÃ
u=@Mc ¼ Àppð@cpÃ
u =@McÞ. Subtracting @tÃ
u=@Mp
from @tÃ
u=@Mc and substituting from (3a), the
implication of the unitary preference model with
respect to transfers is:
@tÃ
u
@Mc
À
@tÃ
u
@Mp
¼ À1 þ pp
@cpÃ
u
@Mp
À
@cpÃ
u
@Mc
 
¼ À1 ð4Þ
indicating that a 1 dollar increase in child’s income
accompanied by a simultaneous 1-dollar decrease in
parents’ income results in a reduction in parental
transfers of 1 dollar. Other studies have referred
to this income derivative restriction as the
parental altruism hypothesis (Cox and Rank, 1992;
McGarry and Schoeni, 1995; Altonji et al., 1997;
McGarry 2000) because the unitary preference model
is often justified by the assumption of an altruistic
head of household (Becker, 1974).6
Bargaining model
The simple bargaining model of household decision
making that is presented here adapts McElroy and
Horney’s (1981) husband–wife bargaining model and
McElroy’s (1985) parent–child bargaining model to
a situation in which parents and child bargain over
consumption and post-secondary schooling decisions.
The model requires several assumptions:
Assumption 1: A household consists of two decision
makers. Parents present a united front and thus act as
one decision maker. Their child acts as the other.
Assumption 2: Parents and child have two decisionmaking
options. They may choose either to make their
decisions independently and without regard for each
other (sever their relationship) or to participate in
cooperative bargaining with each other, thus making
joint decisions.
Assumption 3: If the parent–child relationship is
severed, parents and child each maximize their own
twice continuously differentiable, nondecreasing,
quasiconcave utility function subject to their own
budget constraint.
At the severed relationship threat point, parents
choose cp
to maximize Up
(cp
) subject to cp
Á pp ¼ Mp
with the resulting indirect utility function given by
Vp
(pp, Mp), the maximum utility the parents can
attain in the absence of cooperation. Simultaneously,
yet independently, the child chooses cc
and s to
maximize Uc
(cc
, s), subject to his or her budget
constraint, cc
Á pc þ s Á ps ¼ Mc. The indirect utility
resulting from this maximization is given by
Vc
(pc, ps, Mc), and is the maximum utility the
child can attain in the absence of cooperation.
Note that because the relationship between parent
and child is severed, no transfers are made from
parents to child or vice versa.
6
The unitary preference model has also been justified by assuming the household head has dictatorial control over all
household decisions.
Parent–child bargaining, parental transfers, and post-secondary education 417
Assumption 4: If the parent–child relationship is not
severed, the utility of the parent depends on the child’s
consumption and schooling. However, the child is
selfish and cares only about his or her own consumption
and schooling.7
If the parent–child relationship is not severed, the
parents’ utility function is given by Up
(cp
, cc
, s) and
the child’s utility function is given by Uc
(cc
, s). Note
that the selfish child assumption implies that any
transfers will flow in the direction from parents to
children. It also ensures that cooperating families will
be those in which parents make a positive transfer.
While this assumption affects the sample used to
conduct the empirical analysis, it is relaxed in a
sensitivity analysis discussed in Section VI and does
not qualitatively affect the results.
Assumption 5: The Nash bargaining solution is
obtained as the result of bargaining between the
parents and their child.
To obtain the Nash bargaining solution, the
cooperative state utility functions and the parents’
and child’s threat points described above are
combined into the following cooperative state
‘family’ utility function:
N ¼ ½Up
ðcp
, cc
, sÞ À Vp
ð pp, Mpފ½Uc
ðcc
, sÞ
À Vc
ð pc, ps, Mcފ ð5Þ
where N denotes the Nash product function. This
Nash product function has been called the utility-gain
product function (McElroy and Horney, 1981)
because the first term, [Up
À Vp], is the parents’ gain
from cooperation (the difference in the parents’ utility
between the cooperative and noncooperative states),
and the second term, [Uc
À Vc
], is the child’s gain
from cooperation.
The cooperative Nash bargaining solution is used
because it is ‘intended to treat situations involving
two individuals whose interests are neither completely
opposed nor completely coincident. The two individuals
are supposed to be able to discuss this situation
and agree on a rational joint plan of action, whereas
in a noncooperative model it is impossible for the
players to communicate or collaborate in any way
(Nash, 1953).’ Thus the cooperative approach
seems to be more appropriate for family decision
making.8,9
Maximizing (5) subject to the household budget
constraint given in (1) yields the following bargained
demand functions for consumption and schooling:
cpÃ
b ¼ cp
bðpp, pc, ps, Mp, McÞ ð6aÞ
ccÃ
b ¼ cbðpp, pc, ps, Mp, McÞ ð6bÞ
sÃ
b ¼ sbðpp, pc, ps, Mp, McÞ ð6cÞ
where the subscript b refers to the bargaining model.
Note that in this model Mp and Mc enter separately
into the above demand functions. This is a rejection
of the income pooling hypothesis of the unitary
preference model, and can be written in terms of the
following comparative statics:
@cpÃ
b
@Mp
>
<
@cpÃ
b
@Mc
ð7aÞ
@ccÃ
b
@Mp
>
<
@ccÃ
b
@Mc
ð7bÞ
@sÃ
b
@Mp
>
<
@sÃ
b
@Mc
: ð7cÞ
This means that, unlike in the unitary preference
model, the source of income matters. For example, an
increase in parents’ income brings with it an increase
in bargaining power that is used to adjust the chosen
levels of individual consumption and schooling to
better suit the parents’ own preferences. Similarly, an
increase in child’s income brings the child an increase
in bargaining power that the child uses to better suit
his preferences.
Another feature of the bargaining model is that it
allows for negative income and positive price effects
on the level of post-secondary schooling, while the
unitary preference model does not. If parents want
less schooling for their child than their child wants for
himself, parents may exert their bargaining power so
that less schooling is obtained than the child wants,
resulting in an overall negative effect of parents’
income on the child’s post-secondary schooling.
On the other hand, if the child wants less schooling
than his parents want for him, the child may exert his
bargaining power so that less schooling is obtained
than the parents want. In this case, the child’s income
effect may be negative. Note that the price of
schooling enters the child’s threat point and that
@Vc
=@ps < 0. A positive price effect could occur then
7
This is a commonly-made assumption that motivates Becker’s (1974) Rotten Kid Theorem.
8
Again, however, noncooperative models of family behaviour have been proposed (see Lundberg and Pollak, 1994).
9
Seaton (2001) investigates conditions under which a type of model similar to Cournot oligopoly would be more appropriate
than a bargaining model in describing family behaviour.
418 C. Kalenkoski
as a result of an increase in price decreasing the
child’s threat point relative to his parents’, allowing
parents that prefer more schooling to use their
increase in relative bargaining power to increase the
level of schooling. For example, parents may point
out that schooling is too expensive for the student to
go it alone, causing the child to submit to parental
demands.
Another interesting implication of this bargaining
model relates to transfers. Note that tÃ
b ¼ Mp À cpÃ
b Á pp
and that, taking partial derivatives with respect to
Mp and Mc, we have @tÃ
b=@Mp ¼ 1 À ppð@cpÃ
b =@MpÞ
and @tÃ
b=@Mc ¼ Àppð@cpÃ
b =@McÞ. Subtracting @tÃ
b=@Mp
from @tÃ
b=@Mc and substituting from (7a), the
implication of the bargaining model with respect to
transfers is:
@tÃ
b
@Mc
À
@tÃ
b
@Mp
¼ À1 þ pp
@cpÃ
c
@Mp
À
@cpÃ
b
@Mc
 
>
<
À 1: ð8Þ
In words, this means that a 1-dollar increase in child’s
income and a simultaneous 1-dollar decrease in
parents’ income do not necessarily result in a
reduction of transfers of one dollar. Thus the altruism
assumption of the unitary preference model is
rejected. In fact, if ð@cpÃ
b =@Mp À @cpÃ
b =@McÞ > 0 (parents’
income has a greater effect on parents’
consumption than their child’s income does), then
@tÃ
b=@Mc À @tÃ
b=@Mp > À1. That is, there is a reduction
in transfers by less than one dollar or possibly even an
increase in transfers. Again, this means that a change
in the distribution of income in the family affects
individual consumption and the level of schooling
even if total income does not change.
IV. Econometric Model
To test the hypotheses presented in Section III,
the following reduced form equations might be
estimated:
t ¼ X1 þ 1e1 ð9Þ
s ¼ X2 þ 2e2 ð10Þ
where t is the level of parental transfers, s is the level
of post-secondary schooling, X is a vector of
explanatory variables that includes the price and
income variables implied by (6a)–(6c) as well as
demographic characteristics to control for preferences,
1 and 2 are vectors of coefficients, 1 and 2
are unknown scale parameters, and ei $ N(0, 1),
i ¼ 1, 2. As both t and s are chosen simultaneously,
e1 and e2 are likely correlated. However, Equations 9
and 10 are estimated separately here using singleequation
estimation techniques due to several
complicating factors.
Assuming e1 is uncorrelated with X, Equation 9
could be estimated using ordinary least squares
(OLS), with the estimated coefficients on parents’
and child’s incomes used to test the unitary preference
model’s altruism hypothesis given by (4). When a
continuous years of schooling variable is used to
measure the level of schooling, Equation 10 could
likewise be estimated using OLS to test the income
pooling hypothesis given by (3c). However, when
a dichotomous initial programme choice variable is
used (e.g. one enrols in either a 4-year or a 2-year
programme) and a linear probability model is
estimated, the SEs must be corrected for
heteroscedasticity.
OLS estimates of 1 and 2 are likely to be biased,
however, if the error terms in (9) and (10) are
correlated with X. One reason for concern is that,
although the theoretical model treats the price of
schooling and child’s income as exogenous, these
variables are in reality potentially endogenous. The
price of schooling and the amount of scholarships
and grants received may vary with the type, quality
or the level of schooling chosen. In addition, although
the theoretical model abstracts from the child’s
labour-leisure-schooling decision, if market work or
leisure compete with schooling for the child’s time,
the child’s income may also be endogenous. To
address all of these endogeneity issues, predicted
variables replace these potentially endogenous
right-hand-side variables.
A second reason OLS coefficient estimates may be
biased is that Equations 9 and 10 are estimated using
a selected sample. This selection comes from two
sources. First, the demand functions in (6a)–(6c) are
valid only for those families in which the parents
make a positive transfer. This is because, from
Equation 5, parents and child cooperate if and only
if (Up
À Vp
)(Uc
À Vc
) > 0 and, because the child is
selfish (parents’ consumption does not enter into the
term representing the child’s gain from cooperation),
cooperation is equivalent to parents making a
positive transfer. Let t* be a latent variable measuring
the benefits from making a transfer. Because t*
depends on Up
, Vp
, Uc
, and Vc
, all of which depend
on X, a transfer receipt selection equation can be
written:
tÃ
¼ X1 þ v1 ð11Þ
where 1 is a vector of coefficients and v1 $ N(0, 1).
Note that t* is unobserved. However, if the
Parent–child bargaining, parental transfers, and post-secondary education 419
benefits of making a transfer are positive (t* > 0),
then a transfer is made. Let T be an indicator variable
equal to 1 if t* > 0 and equal to 0 otherwise.
Unfortunately, T is observed only for children
enroled in post-secondary school. This is the second
source of selection. Let s* be a latent variable
measuring the benefits from attending post-secondary
school. Because the level of post-secondary schooling
is a choice variable in the model, s* depends on the
same variables X that enter the right-hand-side of the
schooling Equation 10. However, one exclusion
restriction is necessary to identify the conditional
bivariate probit that is estimated. Therefore, a postsecondary
enrolment selection equation is written:
sÃ
¼ Z2 þ v2 ð12Þ
where Z is a vector of explanatory variables that
includes X plus one additional variable, where this
additional variable provides the exclusion restriction
necessary for identification (to be discussed in the
next section), 2 is a vector of coefficients, v2 $ N(0, 1)
and corr(v1, v2) ¼ . Although s* is unobserved, if
s* > 0 then the child enrols. Let S be an indicator
variable equal to 1 if s* > 0 and equal to 0 otherwise.
S is observed for all children.
An observation is thus a member of the select
sample if T ¼ 1 and S ¼ 1. The regression function for
the transfer Equation 9 for this subsample may be
written as
EðtjX, Þ ¼ X1 þ 1Eðe1jX, Þ ð13Þ
where denotes the joint outcome of the two
selection rules given by (11) and (12). A similar
regression function can be written for Equation 10.
Following Tunali (1986), (13) can be rewritten
EðtjX, Þ ¼ X1 þ 11 þ 22 þ 1w1 ð14Þ
where 1 and 2 are regression coefficients,
w1 ¼ e1 À 11 À 22 with Eðw1jtÃ
> 0, sÃ
> 0Þ ¼ 0,
and 1 and 2 are highly nonlinear functions of 1,
, and 2. As Tunali notes, 1 and 2 are the doubleselection
analogues of the inverse Mill’s ratio that
arises in the context of single-selection. The parallel
regression function for Equation 10 is given by
EðsjX, Þ ¼ X2 þ 11 þ 22 þ 2w2 ð15Þ
where 1 and 2 are regression coefficients and
w2 ¼ e2 À 11 À 22 with E(w2|t* > 0, s* > 0) ¼ 0.
In order to estimate (14) and (15), the potentially
endogenous variables in X need to be replaced by
predicted variables and estimates of 1 and 2 must be
constructed. Because there are three endogenous
variables, three predicting equations must be estimated,
and at least three instruments are needed. The
predicting equations are discussed in detail in the
empirical analysis. For now, let ^X denote the vector
that includes the predicted variables. Then, to
construct ^1 and ^2, a two stage procedure is
followed. First, a conditional bivariate probit model
in which T and S are the dependent variables and ^X
and ^Z are the respective vectors of explanatory
variables is estimated.10
The resulting estimates ^, ^1,
and ^2 are then substituted into the formulas for
1 and 2 to obtain ^1 and ^2. Finally, the following
equations are then estimated
Eðtj ^X, Þ ¼ ^X1 þ 1
^1 þ 2
^2 þ 1w1 ð140
Þ
Eðsj ^X, Þ ¼ ^X2 þ 1
^1 þ 2
^2 þ 2w2: ð150
Þ
^1 and ^2 are identified in Equations 140
and 150
by
nonlinearities in the formulas used to construct them.
Note that the errors are heteroscedastic because of
their inclusion. In addition, corrections to the SEs
should be made because of the substitution of the
predicted variables for the potentially endogenous
variables. To correct these SEs, a bootstrapping
technique is used.11
V. Data
The High School and Beyond Surveys (HS&B),
administered by the US Department of Education’s
National Center for Education Statistics, provide the
data for the analysis. The base year survey was
conducted in 1980 for both high school sophomores
and seniors, with follow-up surveys for both the
sophomore and senior cohorts conducted in 1982,
1984 and 1986, and an additional follow-up for the
sophomore cohort in 1992. Although follow-ups did
not occur every year, retrospective questions were
asked in each of the follow-up years to fill in
information relevant to nonsurvey years. To supplement
the survey data, post-secondary education
transcripts for the sophomore cohort were merged
with their survey data. In order to take advantage of
this transcript information, the analysis will focus
only on the sophomore cohort.
The HS&B sophomore database contains 14 825
students, although only 5015 student observations are
actually used in the analysis. First, respondents who
did not participate in all of the first three surveys are
dropped, leaving 12 423 respondents. This is done
10
Recall that Z includes X and that is why Z is given the ‘hat’ designation.
11
Estimated SEs are based on 200 replications.
420 C. Kalenkoski
because variables used in the analysis are taken from
responses to the first three surveys.12
An additional
6785 respondents are dropped because they are
missing information on at least one key variable.
Finally, an additional 623 respondents are dropped
because they are either the only respondent from a
particular high school with nonmissing information
or, if there is more than one student from that high
school with nonmissing information, there is no
variation among these students in terms of their
post-secondary enrolment status. Such within-school
variation is necessary in order to use high school
dummy variables as instruments in the predicting
equations. In order to investigate whether this
reduced sample is representative, the means of the
demographic variables that can be measured for all
students in the database are compared for the full
sample and the analysis sample. Appendix Table A1
shows some differences. The analysis sample includes
a larger proportion of females and a smaller
proportion of minorities than does the full HS&B
sample. It also includes a larger proportion of rural
residents. There are also some differences in the
proportions living in different regions of the country.
While these differences are not enormous, caution
should be used in generalizing the empirical results.
The dependent variable used in the transfer
regression is the dollar value of parental transfers
made during the 1982–83 academic year. This
variable includes not only cash transfers made
directly to the student but also tuition and fees,
room and board, and other schooling-related
expenses paid by the parent on the child’s behalf.
Unfortunately, parental transfers are observed only
for those students who reported attending postsecondary
school during the year, even though it is
likely that some children who did not attend postsecondary
school in that year did indeed receive
transfers from their parents. This potential source of
sample selection bias is addressed in the empirical
analysis in Section VI.
The dependent variable used in the schooling
regression is years of post-secondary schooling.
To construct this variable, information on enrolment
status that is provided in the HS&B database for
every month during the 10-year period from June
1982 through June 1992 is used. Part-time enrolment
is treated as ½ month. The number of months is
then divided by 12 to obtain the number of years of
post-secondary schooling. The strength of this variable
is that it reports actual post-secondary education
attained by the student, rather than just the initial
programme attended by the child. Thus, if the child
started out at a 2-year community college but had
every intention of transferring to a 4-year programme,
this would be captured by the years of
post-secondary schooling variable. However, because
the theoretical model on which the hypothesis tests
are based considers only an initial single-period
decision, to use this variable one must assume that
all post-secondary education is decided at one point
in time.
An alternative schooling variable used in a
sensitivity analysis is the initial choice of postsecondary
programme. This initial programme
choice variable is a dichotomous variable that takes
a value of 1 if the child was enroled in a 4-year postsecondary
programme in October of 1982 (the fall
semester following the typical cohort member’s high
school graduation) and a value of 0 if the child was
enroled in a 2-year programme.13
The strength of this
variable lies in the fact that it is a single period
measure and therefore more consistent with the single
period decision assumed in the theoretical model than
the years of post-secondary schooling variable.
A weakness of this variable, however, is that it
does not address intentional progression from a
2-year to a 4-year programme.
A key explanatory variable is parents’ income.
However, because only categorical family income
rather than parents’ income is reported in the HS&B
database and a continuous measure is needed to
conduct the hypothesis tests, a continuous parents’
income variable needs to be constructed. Data from
the internal version of the 1983 March Supplement to
the Current Population Survey (CPS), which contains
nontopcoded income information, are used to do this.
First, a subsample is selected from the CPS to match
the characteristics of the HS&B sample. This
subsample includes persons aged 17–19 who are
children of an interviewed head of household. For
these children, parents’ income and several variables
expected to be correlated with parents’ income are
then constructed to match variables available in the
HS&B data. These include family income category
dummies, parents’ highest education dummies, state
dummies, an urban dummy, a dummy indicating
whether the family was a traditional family during
12
While data from three survey years are used, the analysis is a static one. A longitudinal analysis cannot be performed due
to a lack of key data.
13
Students choosing other programmes, e.g. a 1-year vocational programme, are excluded. An alternative way to define this
programme choice variable allows it to take on a value of 1 if the child attends a 4-year programme and a value of 0 if the
child attends any other post-secondary programme. Defining the initial programme choice variable in this way does not
materially affect the results.
Parent–child bargaining, parental transfers, and post-secondary education 421
the child’s senior year (the child lived with both his
mother and father), the number of siblings, and the
child’s gender. Parents’ income is then regressed on
these variables using OLS. The regression results are
reported in Appendix Table A2. Parents’ income is
then predicted by applying these CPS regression
coefficients to the matching variables in the HS&B
data and adding a random term created by generating
a random variable with mean zero and variance one
and multiplying it by the root mean squared error
from the CPS regression. The major strength of this
parents’ income variable is that more information
than just the student-reported family income category
is used in its prediction. However, it is a predicted
rather than an observed variable.
An alternative, and much cruder, parents’ income
variable is constructed in order to test the sensitivity
of the results. This variable is constructed by
subtracting the child’s reported income from the
midpoint of the reported family income range for all
income categories except the top income category,
‘$50 000 and over’. As no midpoint is available for
this category, child’s reported income is instead
subtracted from an estimate of average family
income calculated using the internal, nontopcoded
version of the 1983 March CPS data.
Child’s income is another key explanatory variable.
It is constructed from the child’s survey responses to
questions about the income he or she received from
various sources in 1982, and includes all own and
spousal earnings and nonlabour income except
parental transfers, transfers from other relatives,
and scholarships and grants. Parental transfers are
excluded as they are a dependent variable in the
analysis and do not enter into the child’s threat point
when bargaining with parents. Gifts from other
relatives are excluded due to insufficient data.
Scholarships and grants are also not included in the
child’s income as they are instead treated as a
(negative) price variable in the analysis. The strength
of this variable is that it includes all nontransfer
income potentially available to the child (including a
spouse’s income, if one is present) and thus gives a
very good picture of the child’s bargaining position.
To test the sensitivity of the results, an alternative
child’s income variable is constructed by taking the
simple average of the child’s reported 1982 and 1983
incomes. This is done because, while the decision
about post-secondary education was probably made
in 1982 before the child graduated from high school,
the academic period over which many of the other
variables are measured is the 1982–83 academic year.
Other economic explanatory variables that enter
into the schooling and transfer equations include the
price of schooling and the dollar value of scholarships
and grants received. The price of schooling is
measured by the tuition and fees charged to the
student by his post-secondary institution for the
1982–83 academic year, regardless of the source of
payment. The scholarships and grants variable
measures the total amount of scholarships and
grants the student received for the 1982/83 academic
year. An advantage of these individual-level variables
over state-level averages is that they better represent
the opportunity set faced by an individual student
which may vary based on the student’s ability, high
school grades, and other personal and family
characteristics. A disadvantage of the price of schooling
and scholarship and grant variables, however, is
that they are potentially endogenous. Another
disadvantage of these variables is that they are
reported only for those students attending postsecondary
school. However, these issues are dealt
with in the empirical analysis.
Key personal background variables include the
child’s standardized test score and high school GPA,
gender and race dummies, the overall number of
siblings and the number of older siblings (each
topcoded at six siblings), a traditional family
dummy, the number of rooms in the family home
(topcoded at 10 rooms), and dummies for the parents’
highest level of education.
Additional variables that do not enter the main
regressions but enter as the dependent variables in the
conditional bivariate probit used to correct for the
two sources of sample selection include a transfer
receipt dummy and an enrolment dummy. The receipt
dummy takes on a value of 1 if the child received
a transfer from his parents during the 1982/83
academic year and a value of 0 if he did not. The
enrolment dummy takes on a value of 1 if the child
enroled in post-secondary school during that year
and a value of 0 if he did not enrol. A conditional
bivariate probit is estimated because the receipt
dummy is only observed if the child enroled during
the 1982–83 academic year. An additional variable,
the percent of the child’s high school’s 1978–79 class
that is in college in 1980, is used to identify the
conditional bivariate probit model. It is intended to
proxy for the ‘supply’ of post-secondary education,
i.e. the likelihood of being accepted into a postsecondary
institution.
In Section VI, the key regression results are
disaggregated according to whether parents want
more, parents want less, or parents want the same
level of post-secondary schooling for their children as
their children expect for themselves. This is done in
order to provide insight into how income coefficients
differ according to the type of parent–child conflict,
and to investigate whether negative income and
422 C. Kalenkoski
positive price effects on schooling exist for those
individuals most predisposed to them. Variables used
to subset the sample by disagreement status include
the level of schooling the child expects to attain and
the level of schooling he believes his parents want him
to attain. Any difference between what parents want
and what the child expects places a student into one
of the disagreement groups. One caveat, however, is
that the child is reporting an expectation, not
necessarily a desire or preference. Therefore, if the
child expects to attain more or less than he would
wish given that he or she expects to compromise, then
partitioning the sample based on these survey
responses may be biased against including a student
in one of the disagreement subsamples.
Sample statistics for all of the key analysis
variables, including predicted variables to be discussed
in Section VI, are given in appendix Table A3.
VI. Empirical Results
Predicted variables and selectivity correction
Before the transfer and schooling Equations 140
and 150
, can be estimated, the potentially endogenous
variables in X need to be replaced by predicted
variables and the selectivity correction terms need to
be constructed. Table 1 shows the predicting equations
for the price of schooling (tuition and fees), the
dollar value of scholarships and grants received, and
the child’s income.14
Parents’ income, parents’
education, and student and family characteristics
enter as explanatory variables in these predicting
equations because they enter the main transfer and
schooling equations (with the exception of parents’
income, all as demographic controls to account for
heterogenous preferences). In addition, for identification
purposes, because there are three endogenous
variables to be predicted, at least three variables must
be included in the predicting equations that are
excluded from the second stage transfer and schooling
equations. Because of the unique nature of the
HS&B data set, there are multiple students surveyed
per school. Thus, 654 high school dummies are able
to be used as instruments. In the price of schooling
equation, these school dummies are intended to
capture the average price of post-secondary schooling
faced by students from a given high school or
geographic area. In the scholarships and grants
equation, they are intended to capture the average
financial aid award faced by students from a given
high school or geographic area. Finally, in the child’s
income equation, they are intended to control for
local labour market conditions. In all three of these
equations the high school dummies are jointly
significant at the 1% level. Thus, they are correlated
with the variables they are used to predict.
There is a potential overidentification problem,
however. While only three instruments are needed,
654 are used and the results may be sensitive to the
choice of instruments. Thus, a Hausman overidentification
test is performed for each second-stage
equation (the transfer and schooling equations) to
determine the validity of the school dummy instruments
used. Each test involves regressing second stage
residuals on all of the predetermined variables in the
system, including the high school dummies. The test
results are reported with the second stage results in
Tables 2 and 5. For the transfer equation, a Hausman
Chi-squared statistic is calculated and determined to
be below the critical value with a p-value of 0.7884,
indicating that the transfer results are not sensitive to
the choice of instruments. For the schooling equation,
the calculated Hausman statistic also falls below
the critical value with a p-value of 0.1600. Therefore,
the schooling results are also not sensitive to the
choice of instruments.
A disadvantage of the school dummy variables as
instruments is that a child’s high school may not be
truly exogenous. Parental preferences that determine
parental transfers and the child’s level of postsecondary
schooling may also determine the high
school the child attends. To the extent that demographic
controls do not adequately account for
parental preferences, these instruments may not be
valid. However, given the inclusion of so many
parental demographic variables and the fact that
the high school dummies are allowed to indirectly
affect parental transfers and years of schooling via
the price of schooling, the scholarship and grant
award, and the child’s income, this potential problem
is likely minimized.
Other instrumenting strategies have been
attempted, however. In one attempt, state dummies
were used instead of high school dummies as these
broader geographic variables are less likely to be
14
It is important to note that there are alternative interpretations of the predicted ‘price’ variable. If school quality is thought
to be constant, or adequately captured by the observable demographic characteristics included in the predicting equation,
then this predicted price can be treated as a true price variable. If it is believed that higher tuition and fees are associated with
higher quality schooling, and that the demographic characteristics included in the price regression do not adequately control
for quality, then this variable is better thought of as a predicted expenditure. While the word ‘price’ is used in this discussion,
it should be kept in mind that this may actually represent schooling expenditure.
Parent–child bargaining, parental transfers, and post-secondary education 423
Table1.Predictingequations
Price(tuitionandfees)ScholarshipsandgrantsChild’sincome(in$10000s)
ExplanatoryvariablesCoefficientt-StatCoefficientt-StatCoefficientt-Stat
InterceptÀ1291.96À0.93À3580.42***À3.900.42**2.12
Parents’income(in$10000s)13.810.47À84.05***À4.360.01*1.85
Standardizedtestscore11.44***3.5912.58***5.980.00***À4.40
StandardizedhighschoolGPA1323.69***9.091010.97***10.54À0.03*À1.89
Genderdummy(1¼male,0¼female)76.680.71188.93***2.650.06***3.17
Hispanicdummy164.950.98379.81***3.41À0.03À1.06
NativeAmericandummy661.571.30594.98*1.78À0.01À0.10
Asian/PacificIslanderdummyÀ61.36À0.2062.590.31À0.11**À2.06
AfricanAmericandummy568.24**2.54714.12***4.84À0.20***À5.84
NumberofsiblingsÀ213.68***À4.59À24.85À0.810.03***4.03
Numberofoldersiblings74.86*1.7515.530.55À0.02**À2.50
Traditionalfamilydummy85.090.71À198.63**À2.50À0.06***À3.41
Roomsinhome127.57***4.380.500.030.000.92
Parents’highesteducationdummies
HighschoolgraduateÀ181.89À0.75À83.10À0.520.030.74
Lessthan2yearsvocationalschool578.31***3.05633.50***5.070.020.77
2þyearsvocationalschool283.961.51322.87***2.60À0.05*À1.72
Lessthan2yearscollege368.05**2.00270.77**2.23À0.05*À1.82
2ormoreyearscollege614.93***3.58236.07**2.08À0.04*À1.73
4or5yearcollegedegree740.88***3.77567.19***4.38À0.09***À3.03
Master’sdegree
(654schooldummiesnotreported)
951.48***4.51331.75**2.39À0.08**À2.28
1571.12***4.521243.20***5.42
R-squared0.350.320.20
Numberofobservations328732875015
Testsofjointsignificanceofinstruments
F-stat[654,2612]p-ValueF-stat[654,2612]p-ValueF-stat[654,4341]p-Value
1.750.00001.240.00021.350.0000
Source:HighSchoolandBeyondSurveydata,NationalCenterforEducationStatistics,USDepartmentofEducation.
***indicatessignificanceat1%level.
**indicatessignificanceat5%level.
*indicatessignificanceat10%level.
424 C. Kalenkoski
correlated with parental preferences regarding their
child’s education. While these state dummies were
jointly significant in the price and scholarship and
grant equations, they were not significant predictors
of the child’s income. Therefore, they could not be
used as instruments. In another attempt, all available
state and county level variables that could possibly
affect the price of schooling, the scholarship and
grant award, and/or the child’s income were included.
These variables included a county’s overall unemployment
rate, a county’s per capita income, a state’s
average manufacturing wage, a state’s youth
unemployment rate, average in-state tuition charged
by 4-year public colleges and universities in a state,
Table 2. Transfers: regression results and hypothesis tests
Double selection correction only
Predicted values and double
selection correction
Explanatory variables Coefficient t-Stat Coefficient t-Stat
Intercept 1770.77 1.06 À14705.12*** À2.82
Price 0.52*** 10.77 – –
Predicted price – – 1.06*** 5.26
Scholarships and grants À0.54*** À11.37 – –
Predicted scholarships and grants – – À0.94*** À3.30
Child’s income (in $10 000s) À845.75*** À4.33 – –
Predicted child’s income (in $10 000s) – – À1654.86 À1.44
Parents’ income (in $10 000s) 165.41*** 3.31 574.35*** 3.81
Standardized test score 1.75 0.36 38.13** 2.51
Standardized high school GPA 136.78 0.93 810.31 1.55
Gender dummy (1 ¼ male, 0 ¼ female) 174.34 0.86 À1508.17** À2.51
Hispanic dummy À163.09 À0.86 1035.51* 1.77
Native American dummy 521.36 0.84 À1282.83 À0.49
Asian/Pacific Islander dummy 336.66 1.38 1195.18 1.26
African American dummy À43.35 À0.21 417.71 0.52
Number of siblings À36.27 À0.35 À889.97*** À2.88
Number of older siblings 34.37 0.59 322.79* 1.68
Traditional family dummy À172.22 193.92 1074.48* 1.92
Number of rooms in home 83.75** 2.25 268.20** 2.26
Parents’ highest education dummies
High school graduate 38.57 0.15 538.40 0.57
Less than 2 years vocational school À126.31 À0.62 À699.66 À0.88
2þ years vocational school À162.50 À0.89 142.29 0.18
Less than 2 years college À134.11 À0.67 À381.51 À0.51
2 or more years college 235.10 1.08 1327.81* 1.74
4 or 5 year college degree À168.18 À0.72 1045.43 1.24
Master’s degree À125.38 À0.40 1852.05** 2.20
1 À1636.48 À1.17 13294.87*** 2.92
2 À165.45 À0.36 À865.10 À0.61
No. observations 1886 1886
R-squared 0.39 0.25
Test of altruism hypothesis
F-Stat [1, 1861] p-Value t-Stat [1861] p-Value
1895.83 0.0000 6.35 0.0000
Specification tests
Exogeneity test X2
[19] p-Value Overidentification test X2
[583] p-Value
25.10 0.1571 555.43 0.7884
Source: High School and Beyond Survey data, National Center for Education Statistics, US Department of Education.
***indicates significance at 1% level.
**indicates significance at 5% level.
*indicates significance at 10% level.
Parent–child bargaining, parental transfers, and post-secondary education 425
average tuition charged by 4-year private colleges and
universities in the state, the percent of a state’s
college-age population enroled in an undergraduate
programme, a state’s average post-secondary faculty
salary, the number of post-secondary institutions in
a state, the percent of a state’s population over 25
that has at least a bachelor’s degree, and average
government expenditure on higher education in a
state. Most of these variables were individually
significant in the predicting equations and were
jointly significant in all three equations. However,
the R-squares for these predicting equations were
much lower than for the regressions with the high
school dummy instruments, with the lowest
R-squared of 0.05 for the child’s income predicting
equation. Therefore, while these instruments were
also rejected in favour of the high school dummies,
the second stage equations were estimated using these
instruments as a sensitivity analysis, and the results
compared to those presented here. While some of the
coefficient estimates were affected in magnitude and
statistical significance, probably due to the poor
predictive ability of these instruments, the key results
regarding parental altruism and income pooling were
not affected.
Because the price of schooling and the dollar value
of scholarships and grants received are observed only
for those respondents enroled in post-secondary
school, a single selectivity correction term  has
been included in their predicting equations and
is identified on the basis of functional form. Note
that the coefficient on the lambda term is large
and significant in both equations. The results
from the first-stage enrolment probit used to
create this lambda term are reported in appendix
Table A4.
The bivariate probit coefficients used to construct
the two sample selection terms ^1 and ^2 used in the
transfer and years of schooling equations are shown
in Table A5.15
Recall that while these terms are
identified in the transfer and years of schooling
equations by the nonlinearities in their construction
(see Tunali, 1986 for the exact formulas), identification
of the bivariate probit requires one exclusion
restriction. That is, one variable must be included in
one of the probit equations and excluded from the
other. Therefore, the percent of the child’s high
school’s 1978–79 senior class that was in college
in 1980, a proxy for the local college acceptance rate,
is included in the enrolment equation but is excluded
from the receipt equation.16
Transfers
The parental transfer equation is estimated on the
sample of post-secondary students who receive a
transfer from their parents. Table 2 presents the
results from two different specifications of this
regression. Column (1) reports least squares results
correct for two sources of sample selection and
column (2) reports the results of a least squares
specification that uses predicted variables in addition
to correcting for selection. Robust SEs are used in
calculating the t-statistics presented in the first
specification and bootstrapped SEs are used in the
second specification. Note that one of the selectivity
correction terms is significant at the 1% level in the
second specification. In the first specification, neither
of the selectivity correction terms is significant,
although one has a t-statistic over one. In order to
determine whether use of predicted variables is
appropriate, a Hausman exogeneity test is performed.
The resulting Chi-squared statistic is below the
critical value with a p-value of 0.1571, indicating the
hypothesis that the right hand side variables are
exogenous cannot be rejected at the standard level of
significance. Therefore, the results from the first
specification are emphasized.
The key coefficients for testing the parental
altruism hypothesis are the coefficients on the
income variables. Both parents’ income and child’s
income are measured in tens of thousands of dollars.
Therefore, the results in specification (1) indicate that
an increase in child’s income by $10 000 results in
a reduction in parental transfers of $846 while an
increase in parents’ income by the same amount
results in an increase in transfers of only $165.
Together, these estimated coefficients indicate that an
increase in child’s income by $10 000, along with a
simultaneous decrease in parents’ income by $10 000,
results in a reduction in parental transfers of only
$1011. This estimate is $8989 less than the reduction
of $10 000 implied by the parental altruism hypothesis,
suggesting that this hypothesis, and thus the
unitary preference model, be rejected. An F test that
the child’s income coefficient minus the parents’
income coefficient equals À$10 000 does in fact reject
the parental altruism hypothesis at the 1% level of
significance. Similar results are obtained for specification
(2).
One possible explanation for the rejection of the
parental altruism hypothesis is that measurement
error may be biasing the parents’ income coefficient
15
The estimate of the correlation between the error terms in the receipt and enrolment probits, ^, is not statistically
significant, suggesting that the two probit equations could have been estimated separately.
16
A similar caution to that regarding the validity of the high school dummies as instruments also applies here.
426 C. Kalenkoski
and thus the total reduction in transfers toward zero.
However, to bias a true total reduction of $10 000 to
the level of $1011 that is estimated in specification (1),
the measurement error variance of parents’ income
would have to account for 98% of the total variance
of parents’ income.17
This level of measurement error
is much larger than the 24% of the variation in
parents’ income that is unexplained by the CPS
parents’ income regression. Thus, even in the
presence of measurement error, the unitary preference
model can still be rejected.
Tables 3 and 4 show the transfer results disaggregated
by disagreement status. Table 3 shows the
results for specification (1) and Table 4 shows
the results for specification (2). While specification
(1) is the preferred specification given the Hausman
exogeneity test result presented in Table 2, Table 4 is
also included given the marginal p-value of 0.1571 on
the exogeneity test. Recall that a child is asked how
much schooling his or her parents want him or her to
obtain and how much schooling he or she expects to
obtain. In each table, column (1) gives the estimates
of the transfer regression for the group of students
whose parents want more schooling for them than
they expect to obtain for themselves. Column (2)
gives the estimates for those students who expect to
obtain the level of schooling their parents desire.
Finally, column (3) gives the estimates for those
Table 3. Transfers: comparisons by conflict status-double selection correction only
Parents want more No disagreement Parents want less
Explanatory variables Coefficient t-Stat Coefficient t-Stat Coefficient t-Stat
Intercept 3584.36 0.87 À351.57 À0.18 8231.36* 1.66
Price 0.60*** 7.54 0.52*** 8.30 0.49*** 5.02
Scholarships and grants À0.70*** À6.18 À0.57*** À9.69 À0.28** À2.36
Child’s income (in $10 000s) À814.35** À2.13 À1105.45*** À3.92 822.10 0.97
Parents’ income (in $10 000s) 102.77 0.91 232.47*** 3.78 129.25 0.84
Standardized test score À16.51 À1.35 9.47* 1.66 À0.06 0.00
Standardized high school GPA 365.07 1.06 148.04 0.80 À921.63 À1.63
Gender dummy (1 ¼ male, 0 ¼ female) 896.21* 1.81 À102.59 À0.42 À145.58 À0.27
Hispanic dummy 19.79 0.05 À272.67 À1.11 À157.97 À0.27
Asian/Pacific Islander dummy À466.55 À0.93 598.87** 2.09 122.72 0.12
African American dummy 182.77 0.43 3.30 0.01 À915.41 À1.06
Number of siblings 164.99 0.67 À166.24 À1.34 133.88 0.46
Number of older siblings 19.43 0.17 61.57 0.84 À60.72 À0.32
Traditional family dummy À604.36 À1.38 173.54 0.78 À879.13 À1.29
Number of rooms in home 8.51 0.09 137.53*** 3.09 À0.30 0.00
Parents’ highest education dummies
High school graduate 814.82 1.02 24.97 0.08 À606.44 À0.92
Less than 2 years vocational school À60.30 À0.13 À78.00 À0.30 À1365.97* À1.67
2þ years vocational school 222.78 0.47 À259.55 À1.13 À1396.77** À2.10
Less than 2 years college 46.69 0.12 À99.48 À0.39 À1271.93* À1.66
2 or more years college 576.41 1.09 315.93 1.16 À745.40 À1.14
4 or 5 year college degree 5.50 0.01 À155.60 À0.54 À581.78 À0.79
Master’s degree À61.89 À0.09 À132.83 À0.35 À53.50 À0.06
1 À4164.62 À1.31 326.76 0.20 À3979.76 À1.01
2 567.31 0.49 À291.99 À0.53 À1075.50 À0.73
No. observations 341 1207 203
R-squared 0.47 0.40 0.40
Test of altruism hypothesis
F-stat [1,317] p-Value F-stat [1,1183] p-Value F-stat [1,179] p-Value
507.75 0.0000 848.89 0.0000 157.81 0.0000
Source: High School and Beyond Survey data, National Center for Education Statistics, US Department of Education.
***indicates significance at 1% level.
**indicates significance at 5% level.
*indicates significance at 10% level.
17
In specification (2), to bias a true total reduction of $10 000 to the level of $2229 that is estimated, the measurement error
variance of parents’ income would have to account for 93% of the total variance of parents’ income.
Parent–child bargaining, parental transfers, and post-secondary education 427
students whose parents want less schooling for them
than they expect for themselves.
For each specification the parental altruism
hypothesis, and thus the unitary preference model,
is rejected for all three groups. However, while the
rejection of the unitary preference model was
expected for the parents want more and parents
want less groups, it was unexpected for the no
disagreement group. One possibility is that some
students may be improperly classified into the no
disagreement subgroup. Recall that students are
asked how much schooling they expect to obtain,
rather than how much they wish to obtain. If a child
reports that he expects to obtain more schooling than
he would wish given that he expects to bow to
parental pressure (parents have all or most of the
bargaining power), then a disagreement variable
based on these survey responses is biased against
indicating disagreement. Another possibility is that
the level of post-secondary schooling is not the
relevant source of disagreement. Rather, schoolingrelated
transfers may be affected by disagreement
over the total expenditures on schooling, which may
depend on school quality and prestige, or the
financing of the child’s post-secondary education.
Thus, if the source of disagreement is something other
than the level of schooling, students may be
improperly classified.
Years of post-secondary schooling
Recall that the years of post-secondary schooling
variable is defined as the number of years of postsecondary
schooling attained, given that some
Table 4. Transfers: comparisons by conflict status – predicted values and double selection correction
Parents want more No disagreement Parents want less
Explanatory variables Coefficient t-Stat Coefficient t-Stat Coefficient t-Stat
Intercept À7312.72 À0.79 À14345.19*** À2.69 À3110.32 À0.22
Predicted price 0.95*** 3.28 1.01*** 4.75 0.74* 1.84
Predicted scholarships and grants À0.96*** À2.96 À0.89*** À3.20 À0.64 À1.37
Predicted child’s income (in $10 000s) À1755.84 À1.17 À1241.39 À1.12 À1385.93 À0.68
Parents’ income (in $10 000s) 435.40* 1.70 566.26*** 3.65 408.41 1.04
Standardized test score 11.62 0.48 37.13** 2.47 37.75 1.14
Standardized high school GPA 805.71 1.22 728.01 1.49 À577.79 À0.50
Gender dummy (1 ¼ male, 0 ¼ female) À114.14 À0.11 À1594.95** À2.54 À1092.13 À0.74
Hispanic dummy 972.63 1.06 738.01 1.34 540.22 0.40
Asian/Pacific Islander dummy 141.99 0.12 1287.96 1.45 618.88 0.26
African American dummy 543.25 0.65 392.93 0.54 À423.67 À0.29
Number of siblings À297.97 À0.51 À924.32*** À3.05 À430.78 À0.58
Number of older siblings 168.02 0.63 303.37* 1.79 83.99 0.22
Traditional family dummy À143.10 À0.16 1360.61** 2.26 À415.50 À0.29
Number of rooms in home 152.37 0.85 301.08*** 2.87 196.47 0.78
Parents’ highest education dummies:
High school graduate 1081.78 0.89 377.10 0.45 À208.32 À0.13
Less than 2 years vocational school À366.56 À0.45 À705.69 À0.98 À769.59 À0.56
2þ years vocational school 807.45 0.90 À147.23 À0.21 À862.18 À0.62
Less than 2 years college À94.14 À0.11 À379.12 À0.59 À921.76 À0.70
2 or more years college 1079.97 1.04 1196.69* 1.66 À156.94 À0.11
4 or 5 year college degree 678.07 0.62 729.40 0.97 466.08 0.30
Master’s degree 707.64 0.53 1490.73* 1.81 922.83 0.39
1 5233.75 0.63 13294.93*** 2.79 5730.31 0.45
2 208.30 0.10 À1257.16 À1.01 À1087.03 À0.35
No. observations 341 1207 203
R-squared 0.32 0.25 0.30
Test of altruism hypothesis
t-stat [317] p-value t-stat [1183] p-value t-stat [179] p-value
4.60 0.0000 6.92 0.0000 3.59 0.0004
Source: High School and Beyond Survey data, National Center for Education Statistics, US Department of Education.
***indicates significance at 1% level.
**indicates significance at 5% level.
*indicates significance at 10% level.
428 C. Kalenkoski
post-secondary schooling is undertaken, and that the
years of post-secondary schooling regression is
estimated for the sample of post-secondary students
who receive a transfer (i.e. are cooperating with their
parents). Table 5 presents the results from two
different specifications of the years of post-secondary
schooling regression. Column (1) reports least
squares results that correct for two sources of
sample selection and column (2) reports the results
of a least squares specification that includes predicted
variables in addition to selectivity correction terms.
Robust SEs are used in calculating the t-statistics
presented in the first specification and bootstrapped
SEs are used in the second specification. One of the
Table 5. Years of post-secondary schooling: regression results and hypothesis tests
Double selection correction only
Predicted values and double
selection correction
Explanatory variables Coefficient t-Stat Coefficient t-Stat
Intercept À0.363170 À0.28 À5.575134* À1.70
Price 0.000008 0.41 – –
Predicted price – – 0.000202** 2.03
Scholarships and grants 0.000034 1.06 – –
Predicted scholarships and grants – – À0.000118 À0.76
Child’s income (in $10 000s) À0.568690*** À3.30 – –
Predicted child’s income (in $10 000s) – – À0.423878 À0.68
Parents’ income (in $10 000s) 0.024203 0.65 0.144606 1.51
Standardized test score 0.020382*** 4.72 0.031507*** 3.60
Standardized high school GPA 0.521078*** 4.11 0.751508*** 2.68
Gender dummy (1 ¼ male, 0 ¼ female) 0.344029** 2.29 À0.190982 À0.59
Hispanic dummy 0.326101* 1.93 0.699417* 1.94
Native American dummy 1.545911* 1.67 1.076848 0.62
Asian/Pacific Islander dummy 0.453772* 1.95 0.764994 1.57
African American dummy 0.438651** 2.02 0.588456 1.44
Number of siblings À0.038406 À0.53 À0.293174 À1.59
Number of older siblings À0.001072 À0.02 0.088359 0.92
Traditional family dummy 0.093257 0.62 0.489848 1.33
Number of rooms in home 0.038331 1.18 0.081199 1.34
Parents’ highest education dummies
High school graduate À0.022518 À0.11 0.143329 0.32
Less than 2 years vocational school 0.229822 1.07 0.043881 0.10
2þ years vocational school 0.438398** 2.37 0.564531 1.43
Less than 2 years college 0.614364*** 3.35 0.541032 1.36
2 or more years college 0.695015*** 3.79 1.025734*** 2.63
4 or 5 year college degree 0.797317*** 3.89 1.182412*** 2.60
Master’s degree 0.869828*** 3.47 1.451648*** 2.58
1 0.504403 0.52 5.130094* 1.70
2 À0.102374 À0.25 À0.386840 À0.52
No. observations 1330 1330
R-squared 0.22 0.21
Test of income pooling hypothesis
F-Stat [1, 1305] p-Value t-Stat [1305] p-Value
10.96 0.0010 À0.83 0.4056
Specification tests
Exogeneity test X2
[19] p-value Overidentification test X2
[502] p-value
10.16 0.9489 533.49 0.1600
Source: High School and Beyond Survey data, National Center for Education Statistics, US Department of Education.
***indicates significance at 1% level.
**indicates significance at 5% level.
*indicates significance at 10% level.
Parent–child bargaining, parental transfers, and post-secondary education 429
selectivity correction terms is marginally significant
in specification (2), but neither is significant in
specification (1). A Hausman exogeneity test indicates
that specification (1) cannot be rejected with a
p-value of 0.9489. Thus, the results from specification
(1) are emphasized.
The estimated income coefficients from this regression
are used to test the income pooling hypothesis.
In specification (1), the coefficient on child’s income
is negative and equal to À0.57, indicating that an
increase in child’s income of $10 000 reduces the
child’s years of schooling by over half a year. This
result is statistically significant at the 1% level. The
coefficient on parents’ income, however, is positive
but not statistically significant. An F-test rejects the
income-pooling hypothesis and thus the unitary
preference model at the 1% level of significance.
The estimated negative and significant child’s
income coefficient is an interesting result. While a
positive coefficient is predicted by the unitary
preference model, the negative coefficient is consistent
with bargaining. Another interesting result is the
positive and significant coefficient on the predicted
price of schooling in specification (2) which implies
that an increase of $1000 in the price of postsecondary
schooling increases the number of years of
post-secondary schooling obtained by 0.2. If the
predicted price variable is measuring a true price of
schooling, then such a positive effect is inconsistent
with the unitary preference model but is consistent
with the bargaining model. According to the bargaining
model, an increase in the price of schooling
decreases the child’s threat point and thus increases
the relative bargaining power of his parents.
A positive bargaining effect occurs if parents use
this increase in relative bargaining power to increase
the level of schooling obtained. Given a large enough
bargaining effect, the standard negative price effect
can be overwhelmed, resulting in an overall positive
effect of price on schooling as seen here. Another
possibility, however, is that the predicted price
variable is really a predicted schooling expenditure
variable that incorporates education quality. As the
predicted schooling expenditure increases, the years
of schooling increases, perhaps because parents and
children who spend more per year on education value
education more and hence choose more of it.
However, while the price coefficient is also positive
in specification (1), it is much smaller and not
significant in that specification.
Table 6 shows the results for years of postsecondary
schooling disaggregated by disagreement
status. Because of the inability to even marginally
reject the exogeneity of the potentially endogenous
variables, only the results from specification (1) are
presented. For the parents want more group, neither
the child’s income nor the parents’ income has a
statistically significant effect on years of postsecondary
schooling, and an F-test indicates that
the income pooling hypothesis cannot be rejected.
Note, however, that the estimated coefficient on
child’s income is negative, a sign consistent with
bargaining. Recall that an increase in child’s income
increases a child’s bargaining power and that a child
whose parents want more schooling uses this increase
in power to decrease the level of schooling. While not
significant, the t-statistic is over one and statistical
insignificance may be due to the small sample size of
this subgroup.
For the no disagreement group, child’s income is
negative and highly significant, indicating that a
$10 000 increase in child’s income decreases years of
post-secondary schooling attained by 0.76 years,
while parents’ income is positive but statistically
insignificant. An F-test rejects income pooling for this
group, and thus also rejects the unitary preference
model. Like the transfer results for the no disagreement
subgroup, this rejection was unexpected.
However, as discussed earlier, this may be a result
of improperly classifying respondents into disagreement
subgroups or incorrectly identifying the source
of disagreement between parents and children.
For the parents want less group, the coefficient on
child’s income is positive but insignificant, while the
coefficient on parents’ income is negative and
insignificant. The absolute value of the t-statistic on
parents’ income is over one, however, and may simply
be insignificant due to the small sample size of the
parents want less group. Its sign is consistent
with bargaining. Recall that an increase in parents’
income increases parents’ bargaining power, and
because parents in this group prefer less schooling
than their children, these parents use their bargaining
power to decrease the level of post-secondary
schooling, thus leading to an overall negative effect
of parents’ income on the level of post-secondary
schooling.
Sensitivity analyses
The results of the preferred specifications in
Tables 2 and 5 reject both the parental altruism
hypothesis and the income pooling hypothesis and
thus the unitary preference model. In order to
determine whether these results are sensitive to
alternative dependent and explanatory variables as
well as an alternative assumption regarding
preferences, several sensitivity analyses are
performed.
430 C. Kalenkoski
Recall that the disadvantage of using the years of
post-secondary schooling variable is the potential
time inconsistency problem. Because the model
presented in Section III is a static model, such a
problem arises if post-secondary decisions are made
at several different points in time rather than all at
once. Therefore, an alternative level of schooling
variable that takes on a value of 1 if a 4-year postsecondary
programme is chosen and a value of 0 if
a 1-year post-secondary programme is chosen, given
that either a 1-year or a 4-year programme is chosen,
is used to test the sensitivity of the results. In a linear
probability model specification with this alternative
dependent variable, the estimated coefficient on the
child’s income variable is significant while the
estimated coefficient on parents’ income is not and
income pooling is marginally rejected with a p-value
of 0.14. Thus the main conclusions drawn regarding
the effects of individuals’ incomes on post-secondary
schooling are robust to the particular schooling
variable that is chosen.
Because parents’ income and child’s income are key
explanatory variables, it is necessary to test the
robustness of the estimates and hypothesis tests to
alternative constructions of these variables. Recall
that the parents’ income variable used in the primary
analysis is predicted using the CPS coefficients in
Appendix Table A2. An alternative variable that
could be used, however, is constructed in a cruder
manner by subtracting child’s income from the
midpoint of the family income range. While some
of the point estimates in the transfer regression are
Table 6. Years of post-secondary schooling: comparisons by conflict status
Parents want more No disagreement Parents want less
Explanatory variables Coefficient t-Stat Coefficient t-Stat Coefficient t-Stat
Intercept À0.431491 À0.10 À1.327593 À0.71 2.279070 0.72
Price À0.000099 À1.51 0.000013 0.49 À0.000029 À0.54
Scholarships and grants 0.000049 0.43 0.000023 0.66 0.000161 1.40
Child’s income (in $10 000s) À0.648101 À1.11 À0.757796*** À3.26 0.212048 0.32
Parents’ income (in $10 000s) À0.001606 À0.01 0.056330 1.15 À0.091941 À1.06
Standardized test score 0.015599 1.24 0.022627*** 3.73 0.014124 1.22
Standardized high school GPA 0.812533** 2.32 0.508269*** 2.91 0.001206 0.00
Gender dummy (1 ¼ male, 0 ¼ female) 0.444189 0.85 0.233830 1.19 0.236893 0.64
Hispanic dummy 0.652394 1.27 0.420353* 1.89 À0.283805 À0.64
Asian/Pacific Islander dummy 0.498899 1.04 0.579862* 1.86 À0.042248 À0.06
African American dummy 0.240821 0.50 0.659855** 2.39 À0.494968 À0.79
Number of siblings À0.147971 À0.62 À0.116691 À1.24 0.381936** 2.05
Number of older siblings 0.124438 0.85 0.022994 0.39 À0.378861*** À2.67
Traditional family dummy À0.061278 À0.13 0.188455 1.04 0.722354 1.57
Number of rooms in home 0.067575 0.74 0.071917* 1.69 À0.022515 À0.28
Parents’ highest education dummies
High school graduate 0.139955 0.21 0.094728 0.36 À0.161759 À0.26
Less than 2 years vocational school À0.307552 À0.46 0.347643 1.34 À0.450936 À0.72
2þ years vocational school 0.537090 0.95 0.344140 1.47 1.742976*** 2.92
Less than 2 years college 0.771486 1.38 0.530779** 2.38 À0.003650 À0.01
2 or more years college 1.099961* 1.80 0.613434** 2.48 0.326695 0.64
4 or 5 year college degree 0.916519 1.37 0.771509*** 2.82 0.902656* 1.78
Master’s degree 1.087598 1.33 0.990922*** 2.94 0.641516 0.96
1 À0.816925 À0.25 1.853085 1.37 À0.078512 À0.03
2 1.332262 1.17 À0.575468 À1.02 À1.344546 À1.00
No. observations 226 867 140
R-squared 0.18 0.23 0.39
Test of income pooling hypothesis
F-Stat [1, 202] p-Value F-Stat [1, 843] p-Value F-Stat [1, 116] p-Value
1.13 0.2881 11.38 0.0008 0.21 0.6482
Source: High School and Beyond Survey data, National Center for Education Statistics, US Department of Education.
*** Indicates significance at 1% level.
** Indicates significance at 5% level.
* Indicates significance at 10% level.
Parent–child bargaining, parental transfers, and post-secondary education 431
affected by the use of this alternative parents’ income
variable, the parental altruism hypothesis is still
rejected. Similarly, although some coefficient estimates
in the schooling regression are affected, the
income pooling hypothesis is still rejected. Thus,
using the alternative parents’ income variable does
not affect the hypothesis test results.
The child’s income variable used in the primary
analysis is the child’s annual 1982 income. However,
an alternative variable that could be used is the
average of the child’s 1982 and 1983 annual incomes.
Both the transfer and the schooling results indicate
that while the point estimates differ somewhat
between the two alternatives, the hypothesis test
results do not. With respect to transfers, the altruism
hypothesis of the unitary preference model is rejected
by the data. With respect to the years of postsecondary
schooling regression, income pooling is
rejected. Thus, using this alternative child’s income
variable does not affect the hypothesis test results.
The final sensitivity analysis concerns the assumption
that equates parent–child cooperation with
positive parental transfers. It is conceivable that
parents may make zero transfers or even negative
transfers to their child (i.e. transfers flow from child
to parent) and still be making decisions jointly
with their child. In order to determine whether
this assumption affects the hypothesis test results,
the years of schooling regression is re-estimated using
the entire sample of post-secondary students, not
just those receiving transfers. While some of the
coefficient estimates differ, the conclusions drawn
from the income pooling hypothesis test does not.
The income pooling hypothesis is rejected.
VII. Conclusions
This article introduces parent–child conflict and
cooperative bargaining as a means of resolving this
conflict into the modelling of post-secondary education
decisions. The implications of a cooperative
bargaining model are compared to those of the
corresponding unitary preference model, suggesting
testable hypotheses regarding parental altruism and
income pooling.
The results strongly reject the unitary preference
model. Both the parental altruism and income
pooling hypotheses are rejected by the data, and
these results are robust to several different specifications
of the relevant equations. In addition, some
negative income and positive price effects are
obtained, evidence that calls into question the unitary
preference model but is consistent with bargaining,
suggesting further exploration of bargaining models
in this context.
An interesting result is that both the altruism and
income pooling hypotheses are rejected for students
in the ‘no disagreement’ subgroup. This may be due
to misclassification of students into the disagreement
status subgroups due to survey question wording or
to misidentification of the true source of parent–child
conflict. If the latter, this suggests further opportunity
to study other potential sources of disagreement.
Perhaps the initial decision to enrol or whether or not
the student attends a public or private institution is
the important source of disagreement. Alternatively,
it may be how a child’s post-secondary education is
financed, i.e. how much parents pay for schooling
and whether or not a child works and/or borrows to
pay for school. Future research should focus on these
potential alternative sources of disagreement.
Acknowledgements
The author thanks Brian Boulier, Shelly Lundberg,
Donald Parsons, David Ribar, Anthony Yezer, and
seminar participants at the Center for Economic
Studies, U.S. Bureau of the Census, the Labor
Studies Workshop at The George Washington
University, the Society of Government Economists’
Labor and Human Resources Brown Bag, and the
Initiative in Population Research at The Ohio State
University for their invaluable comments and
suggestions.
References
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Parent–child bargaining, parental transfers, and post-secondary education 433
Appendix
Table A1. Full and analysis sample means
Variable name Full sample
Analysis
sample
Gender (male ¼ 1, female ¼ 0) 0.50 0.47
Hispanic 0.22 0.16
Native American 0.02 0.01
Asian/Pacific Islander 0.03 0.03
African American 0.14 0.09
Mid-Atlantic 0.18 0.20
East North Central 0.19 0.22
West North Central 0.07 0.09
South Atlantic 0.16 0.12
East South Central 0.04 0.04
West South Central 0.11 0.08
Mountain 0.05 0.04
Pacific 0.14 0.14
Urban 0.24 0.19
Rural 0.25 0.27
Not urban, not rural 0.51 0.54
Number of observations 14 825 5015
Source: High School and Beyond Survey data, National Center for Education Statistics, US
Department of Education.
Table A2. CPS parents’ income regressiona
Explanatory variable Parameter estimate t-Stat
Intercept 3458.40** 2.27
Urban 635.90** 2.34
Gender À451.46* À1.89
Traditional family dummy 2735.07*** 8.36
Siblings À984.02*** À11.19
Family income categories
$8000–$14 999 5122.61*** 9.89
$15 000–$19 999 8960.31*** 16.18
$20 000–$24 999 13069.00*** 23.41
$25 000–$29 999 17206.00*** 30.22
$30 000–$39 999 22662.00*** 43.07
$40 000–$49 999 29480.00*** 51.55
$50 000 or more 48692.00*** 84.18
Parents’ highest education categories
High school graduate 1181.94*** 3.45
Less than 2 years post-secondary 2043.49*** 3.58
2–3 years post-secondary 1965.46*** 4.15
4–5 year college degree 5964.93*** 12.80
6 or more years post-secondary 11574.00*** 20.85
(50 state dummies not reported)
No. observations 6937
R-squared 0.76
Source: March Supplement to the Current Population Survey (internal version), US Bureau of the Census.
***indicates significance at 1% level.
**indicates significance at 5% level.
*indicates significance at 10% level.
a
The dependent variable is measured in dollars.
434 C. Kalenkoski
Table A3. Key variable sample statistics
Variable name No. observations Mean SD
Enrolment dummy (enrol ¼ 1, not enrol ¼ 0) 5015 0.66 0.48
Price 3287 2417.20 2623.10
Predicted price 5015 2238.59 1570.67
Scholarships and grants 3287 881.42 1686.88
Predicted scholarships and grants 5015 843.85 971.38
Child’s income (in $10 000s) 5015 0.36 0.53
Predicted child’s income (in $10 000s) 5015 0.36 0.24
Parents’ income (in $10 000s) 5015 2.18 1.80
Transfer receipt dummy (receipt ¼ 1, no receipt ¼ 0) 3287 0.57 0.49
Transfer amount 1886 2871.70 2713.53
Years of post-secondary schooling 2337 3.67 1.83
Initial programme choice: (four-year ¼ 1, two-year ¼ 0) 2936 0.70 0.46
Source: High School and Beyond Survey data, National Center for Education Statistics, US Department of
Education.
Table A4. Probit for selection correction of predicting equations
Enrolment
Explanatory variables Coefficient 2
Intercept À3.5498*** 38.45
Parents’ income (in $10 000s) 0.01800 1.25
Standardized test score 0.01190*** 91.88
Standardized high school GPA 0.96450*** 344.98
Gender dummy (1 ¼ male, 0 ¼ female) À0.01290 0.05
Hispanic dummy 0.17930** 5.05
Native American dummy À0.02280 0.01
Asian/Pacific Islander dummy 0.77560*** 13.91
African American dummy 0.64380*** 33.83
Number of siblings À0.13750*** 38.30
Number of older siblings 0.06730*** 9.82
Traditional family dummy 0.17600*** 9.53
Number of rooms in home 0.05500*** 14.26
Parents’ highest education dummies
High school graduate 0.08940 0.68
Less than 2 years vocational school 0.20350 5.65
2þ years vocational school 0.44530*** 25.46
Less than 2 years college 0.38780*** 20.54
2 or more years college 0.69310*** 72.22
4 or 5 year college degree 0.88870*** 73.19
Master’s degree (654 school dummies not reported) 0.63020*** 27.83
Log-likelihood À2103
No. observations 5015
Source: High School and Beyond Survey data, National Center for Education Statistics, US Department of Education.
***indicates significance at 1% level.
**indicates significance at 5% level.
Parent–child bargaining, parental transfers, and post-secondary education 435
Table A5. Conditional bivariate probit for double selection correction
Receipt (probit equation) Enrolment (selection equation)
Explanatory variables Coefficient z Coefficient z
Intercept À0.75112** À2.08 À2.78688*** À17.93
Predicted price 0.00006*** 3.31 0.00001 À0.55
Predicted scholarships and grants À0.00006* À1.70 À0.00004 À1.41
Predicted child’s income (in $10 000s) À0.21004 À1.58 À0.45172*** À4.60
Parents’ income (in $10 000s) 0.05065*** 3.44 0.01729 1.23
Standardized test score 0.00487*** 2.93 0.01128*** 10.81
Standardized high school GPA 0.11962* 1.83 0.67075*** 16.78
Gender dummy (1 ¼ male, 0 ¼ female) À0.19658*** À4.06 À0.01655 À0.37
Hispanic dummy 0.15915** 2.26 0.15409** 2.56
Native American dummy À0.15313 À0.65 0.01696 0.10
Asian/Pacific Islander dummy 0.13077 0.99 0.50254*** 3.14
African American dummy 0.08732 0.89 0.47171*** 5.75
Number of siblings À0.10151*** À4.58 À0.08844*** À4.71
Number of older siblings 0.03600* 1.72 0.04802*** 2.61
Traditional family dummy 0.14876** 2.54 0.13985*** 2.84
Number of rooms in home 0.02215 1.62 0.03207*** 2.67
Percent of high school class of 78–79
attending post-secondary school in 1980 – – 0.00904*** 8.90
Parents’ highest education dummies
High school graduate 0.07232 0.63 0.06187 0.67
Less than 2 years vocational school À0.04443 À0.48 0.23892*** 3.24
2þ years vocational school 0.05896 0.65 0.33979*** 4.59
Less than 2 years college À0.01782 À0.20 0.33272*** 4.56
2 or more years college 0.16794* 1.92 0.58932*** 8.56
4 or 5 year college degree 0.19041* 1.90 0.70591*** 7.99
Master’s degree 0.30161*** 2.75 0.56585*** 5.47
Log likelihood À4533
No. observations 5015
Censored observations 1728
Uncensored observations 3287
95% Confidence interval
 0.05808 À0.29608 0.39821
LR test of independent equations ( ¼ 0) 2
¼ 0.10 Prob > 2
¼ 0.7515
Source: High School and Beyond Survey data, National Center for Education Statistics, US Department of Education.
***indicates significance at 1% level.
**indicates significance at 5% level.
*indicates significance at 10% level.
436 C. Kalenkoski