Children as Public Goods
From the parent’s point of view, the care of children is a public good. Providing services to the
child will not only increase the father’s utility, but also the mothers. The issue is how to reach the
efficient allocation while free riding exists. The 3 topics discussed are: the efficient provisions of
public goods, the potential for free riding, and that free riding can be mitigated through repeated
interactions of spouses with each other.
Budget constraint: c = e – q
Utility function: U(c, q)
where e = mother’s endowment
q = child’s consumption
c = mother’s consumption
Solve for q max H(q) = U(e-q,q)
Solution U ce-q*, q*) = U (q-q*, q*)
Optimal own consumption c* = e – q* U* = U(c*, q*)
The solution to the mother’s optimization problem, says that she will want to choose q such that
she is equating her marginal utility of own consumption with her marginal utility of child’s
When q =q*, the gain in utility from increasing her child’s consumption by ∆ marginal units is
exactly equal to the loss in utility from decreasing her own consumption by ∆ marginal units.
MOTHER MARRIED TO A FATHER
Assume: neither parents cares about the welfare of the other parent
Both parents will obtain higher utility than if they were to remain single because child
consumption is higher than what was feasible for each of them as a single (q + q*). ɜ
Utility function: V(g, q)
Budget constraint: U(e + h – g – q, q) ≥ U r
where U = reservation utility for marrying him, U ≥ U* or she will not marry him
h = father’s endowment
g = father’s consumption
Father’s optimization problem L(g, q, λ) = V(g, q) + λ(U(e + h – g – q, q) – U ) r
Solution V-hat q (U-hat /Uqhat )V-cat = Vghat g FREE RIDING WITHIN A HOUSEHOLD
Non-cooperative parents allocate too little consumption to their children relative to cooperating
EFFICIENCY WITH REPEATED PARENT INTERACTION Lundberg Pollak Wales
Do husbands and wives pool their resources?
In this paper, we present an alternative test based on a “natural experiment” – a policy change
in the United Kingdom that transferred a substantial child allowance to wives in the late 1970s.
Using Family Expenditure Survey data, we find strong evidence that a shift toward greater
expenditures on women’s clothing and children’s clothing relative to men’s clothing coincided
with this income redistribution.
A unitary model of family behavior predicts that such a shift in the child allowance policy would
have no effect on consumption patterns, while an individual preference model predicts that
consumption may shift toward goods more highly valued or private to, the spouse receiving the
child allowance. Thus, one could test the pooling hypothesis by comparing expenditure patterns
before and after the policy change.
We break the sample into 3 periods: 1973-1976 to represent the consumption regime before the
policy change, drop the intermediate years 1977-79, and use the period 1980-90 to represent
the regime after the policy change.
The FES provides data on expenditures on women’s, men’s, and children’s clothing.
Table 3 (pg. 9/19) shows that the means of both these ratios (children’s clothing to current
expenditures on men’s clothing; women’s clothing to current expenditures on men’s clothing)
are higher in the period after the policy change than in the period before the policy change, at
least for families with more than one child.
Holding constant total family income, the income received by each spouse has substantial and
significant effects on family expenditure patterns. These findings are consistent with the notion
that children do better when their mothers control a larger fraction of family resources.
This is evidence for the Collective Model of the Family. Duflo
This paper studies whether the impact of a cash transfer on child nutritional status is affected by
the gender of its recipient. My estimates suggest that pensions received by women had a large
impact on the anthropometric status of girls (it improved their weight given height by 1.19
standard deviations and their height given age by 1.16 standard deviations), but little effect on
that of boys. In contrast I found no similar effect for pensions received by men (not associated).
This suggests that the household does not function as a unitary entity, and that the efficiency of
public transfer programs may depend on the gender of the recipient.
Low levels of investment in child health therefore have far-reaching consequences on economic
growth, distribution, and welfare. The evidence suggests that, compared to income or assets in
the hands of men, income or assets in the hands of women are associated with larger
improvements in child health.
An example of such a change is the expansion of the South African Old Age Pension program –
a universal, non-contributory, age-tested and means-tested scheme (one of the few successful
cash transfer programs in the developing world). At the end of the Apartheid era, the
government committed to achieving parity of benefits and eligibility requirements for Whites and
Blacks. This was achieved mostly by increasing the benefits received by the Africans. All women
above 60 and men above 65 are entitled to benefits, subject to a means test (370 rands per
Living arrangements in South Africa are such that grandparents often live in extended
households, with their children and grandchildren.
This paper addresses this identification problem in two steps. First, I compare a flow measure of
nutritional status, weight for height, of children living in households where there is no eligible
members, households where there is an eligible man, and households where there is an eligible
woman, after controlling for the presence of a man or woman who is old, but not old enough to
be eligible. In a second step, I make use of the fact that height for age reflects past as well as
current investments. If the pension had an effect, children born after the expansion of the
program have spent a larger fraction of their lives well-nourished if they live with a pension
recipient. Thus, I compare the differences in height between young children and older children
across households, according to whether there is an age-qualified woman, an age-qualified
man, or no eligible member living in the household.
A permanent shock to the non-labor income of a household member that was not expected at
the time of household formation can be used to test the unitary model of the household.
Weight for height of children reflects short run nutrition and illnesses and recovers quickly after
periods of malnutrition when proper nutrition is resumed.
For girls, the coefficient is positive, but insignificant without controlling for the presence of non-
eligible members above 50. The controls are introduced, the coefficient more than doubles, and becomes significant. The evidence points in the direction of rejecting the unitary model of the
CAVEATS (POTENTIAL PROBLEMS):
1. The presence of an elderly grandparent may actually be the sign of a relatively healthy
household: The grandmother is old, which indicates that she, the mother, or both, did not
have children very early. In addition, she is old but still alive, which could indicate that
household members are, in general, healthy.
2. The pension program led to changes in the composition of the household. Endogenous
household composition could create a positive correlation between unobserved
characteristics of the household and the presence of an eligible member. A difference
between the coefficient of a woman’s and a man’s pension could then be obtained even
with the absence of any causal effect of the additional income on nutrition. Family
composition may have changed as a result of the program, and this could invalidate the
identification strategy proposed in this paper, if families where children are more (or less)
likely to send their children to live with their grandparents or to have the grandparents
These could be addressed by comparing health status in household with or without
eligible members, before and after the expansion of the program. There were no
representative surveys of Black households before the end of Apartheid. However, we
can take advantage of the fact that height is a stock, which reflects accumulated
investment in child health and nutrition since birth.
The basic idea of the identification strategy is thus to compare the differences between the
height of children in eligible and in non-eligible households and between children exposed to the
program for a fraction of their lives and children exposed all their lives.
For girls, living with an eligible member is associated with an increase of 0.68 standard
deviations in height for age, with control variables. For boys, the effect of eligibility is small
(0.11) and not significant.
Two interpretations of this difference are possible. The first interpretation is that the same
resources are spent differently when they are received by a woman and when they are received
by a man. Another interpretation, however, could be that, in terms of permanent income, a rand
of pension received by a man represents much less than a rand of pension received by a
woman because men are expected to receive the pension for a shorter time. The point
estimates suggest that the propensity to save out of a man’s pension income is actually lower
than the propensity to save out of a woman’s non-pension income. Differences not likely to be
due to their different life cycle properties. Li, Rosenzweig, and Zhang (sophie’s choice)
- The key distinction between altruism and guilt is that for the former the utility of the age