LA A DOLE S CE N CIA Y LA EDA D ADULT A
E S T UDIOS G ENÉ T IC OS
We consider the static framework developed by DLP and extend it to include health investment decisions. We use subscripts to index goods and superscripts to index individuals. We consider three types of individuals: t∈ {m, f , c} indicating father, mother, and children, and focus only on households composed by one mother, one father, and one to four children aged 0 to 14. The two parents are the relevant
decision makersin the household, whereas children receive a share of the resources but do not participate in the decision making process. Households differ in many other attributes such as age of members, residency, and several socioeconomic characteristics that may affect preferences. We suppress these arguments in the theoretical section but we will take this heterogeneity into account when we estimate the model empirically.
Each household consumes K types of goods with prices p= (p1, ..., pK). y is the household income.
z = (z1, ..., zK) is the vector of observed quantities of goods purchased by each household, while qt = (qt
1..., q
t
K) is the vector of unobserved quantities of goods consumed by an individual t. We allow for
economies of scale in consumption through a linear consumption technology, which converts purchased quantities by the household, h, in private good equivalents, x.8 Let ut(qt) denote the utility that an individual of type t would attain if she consumed the bundle of goods qt. We refer to the latter as
materialwelfare. Each decision maker has caring preferences toward her children and her spouse, that is, her individual total utility depends, in a weakly separable manner, on the material welfare of the other household members, i.e. the utility they derive from consumption (u−t(q−t)). For children, uc(qc) can be interpreted as the child’s actual utility function over the bundle of goods qcthat the child consumes, or the utility function that parents believe the child has. For simplicity, it is assumed that each child of the same family is assigned the same utility function.9
In addition, we assume that each parent attaches some value to the health status of household mem- ber’s j∈ {m, f , c1, . . . , cs
}, where j now identifies either herself, her spouse, or the children, and therefore to the decision of investing in j’s health. These decisions are summarized by the J -dimensional vector H (J= s + 2), whose elements indicate whether the parents decide to invest or not to invest in j’s health. We model the utility parents get from each member’s health as an expenditure in a public good. Hence
H is interpreted as the outcome of a joint decision of expenditure on a good which has public good fea- tures. For simplicity, parents are assumed to make single period (myopic) decisions about to what extent to invest in j’s health. This is a restrictive assumption in general, but it is quite sensible in our framework as we focus on poor or constrained households. Moreover, we assume that each health investment deci- sion is independent of another. In other words, given any two family members, the decision of investing in one’s health affects the decision of investing in the other one only through the budget constraint.
In line with the collective modeling of household behavior, we assume that household decisions result from a cooperative bargaining process among the decision makers, which leads to a Pareto efficient outcome. The collective framework implies that households will choose consumption levels and health investments in order to maximize a weighted sum of parents’ utilities:
UH= RUm(um, uf, uc, H) + (1 − R)Uf(uf, um, uc, H) (2.1)
9It is straightforward to extend the model to allow each child to have a different utility function. What we need is information
where R= R(p, y, D) is the Pareto weight, which may depend on prices p, total expenditures y, and on a vector of distribution factors D. The latter are defined as variables with no direct impact on preferences or budget constraint, but that may influence the decision process. From a bargaining point of view, R can be seen as a measure of the mother’s influence in the decision process: the larger R, the greater is the weight that m’s preferences receive in the resulting household’s allocation of resources.
Each parent’s preferences in (2.1) are assumed to be separable in both the material well-being of the other family members and the utility derived from H. For simplicity, we parametrize the individual parents’ utilities as follows:
Um= um(qm) + δmf uf(qf) + δmcuc(qc) + H0αm Uf = uf(qf) + δmfum(qm) + δcfuc(qc) + H0αf
whereαmandαf are vector of parameters, whose elements,αm
j andα
f
j, describe how much additional utility each parent m or f attaches to the health investment on j. We can rearrange equation (2.1) as follows:
UH= UC ons+ RH0αm+ (1 − R)H0αf (2.2)
where UC ons is the total utility obtained from consumption by the household. Choosing H consists of deciding whether to invest or not in each family member’s health. The choice must be optimal in the sense that it maximizes (2.2) subject to the following budget constraint:
y≤ z0p+ KH (2.3)
where KHis the total cost of health investment. Under the assumption that each decision maker’s power
a common welfare index. Alternatively, we can assume that the decision power is in the hands of one individual (i.e., R(p, y, D) = 0) and that this benevolent dictator makes optimal decisions for all members of the household. These are the common restrictions implied by the unitary model of the household.10 Our collective model framework is more general and allows us to analyze the role played by the decision makers’ bargaining power in the health investment decisions, especially when there is disagreement. The following example may help clarifying this point.