During the past decade, the United States and other governments have focused increased attention on protecting children from environmental health risks (Scapecchi 2003). Economic analysis of policies responding to pertinent executive (Federal Register 1997) and legislative (7 U.S. Code 136) mandates is hindered, however, by the limited available evidence on the economic value of improved child health. Information about parents' valuation of their children's health would be particularly useful in examining the effectiveness and economic efficiency of policies affecting the health of children. Parental valuations provide an important foundation for estimating economic benefits of policies that improve children's health (Bergstrom 2003), and to the extent that parental resource allocations influence the health of family members, the valuations will partly determine the health outcomes that children experience. But little is known about parental valuations, and evidence about how parental resource allocations affect the health of children beyond infancy also is less than exhaustive, at least for developed countries.
This paper applies a model of parental decision making to examine how family resource allocations affect children's health and to estimate the implied parental willingness to pay for reduced acute illness in children. Data on individual children and on pairs of siblings, from the Child Development Supplement of the Panel Study of Income Dynamics (Hoefferth et al. 1998), are used to estimate a health production function for the number of days a child experiences illness-induced school absence. The number of school absences is a commonly measured indicator of children's acute illness that is closely linked to ambient air pollution concentrations (Castillejos et al. 1992; Ransom and Pope 1992; Romieu et al. 1992; Gilleland et al. 2001). Estimation methods account for the endogeneity of parental resource allocations using instrumental-variables estimation of a count data model (Mullahy 1997) and family-specific fixed effects.
Results underline the importance of accounting for the joint determination of parents' investments in children's health and the health outcomes experienced by children. Estimates suggest that children with greater stocks of health capital whose parents invest in preventive and remedial medical care experience fewer days of illness. Estimated parental willingness to pay to avoid one day of illness-induced school loss is about $100 to $150. This range is broadly consistent with the limited existing evidence on the value of reducing children's acute illness but is substantially more than values applied in medical economics and in recent environmental policy analyses. The implied aggregate benefits of reductions in children's sick time associated with air pollution control may be substantial. Holding income and other factors constant, single parents and those whose children lack health insurance coverage are willing to pay more than married parents or those with insurance, and the estimated income elasticity of willingness to pay is a relatively modest 0.14.
Previous research about how parental behavior affects child health often has focused on infant health (Kenkel 2003) and on obtaining consistent estimators of the effect of prenatal care or other maternal behaviors (Rosenzweig and Shultz 1983; Grossman and Joyce 1990; Warner 1998), sometimes with the aim of inferring parents' willingness to pay for improved infant health (Joyce, Grossman, and Goldman 1989; Nastis and Crocker 2003). Research on the impact of parental resource allocations on the health of older children is less common and often has involved families in developing countries (Pitt and Rosenzweig 1990). Studies of parents' valuations of the health of children beyond infancy have mainly attempted to infer the value of reduced mortality risk from the purchase or use of safety-related goods (Carlin and Sandy 1991; Blomquist, Miller, and Levy 1996; Jenkins, Owens, and Wiggins 2001; Mount, Schulze, and Zhang 2003), although a few studies have considered nonfatal health outcomes (Viscusi, Magat, and Huber 1987; Agee and Crocker 1996; Liu et al. 2000; Dickie and Messman 2004).
Research on parental behavior and child health has drawn heavily on Becker's (1993) unitary model of family decision making and Grossman's (1972) model of health production. In the unitary model, family resources are allocated to maximize a single utility function subject to a budget determined by pooled family income. Grossman's model focused on investment in health as a durable capital stock, but variations on his model often have been applied in one-period settings (Kenkel 2003) and to examine willingness to pay for improved health or reduced health risk (Berger et al. 1987; Dickie and Gerking 1991).
This section presents a unitary model of parents' resource allocations and children's health. Extensions to more complex models of family decision making are considered elsewhere (Jacobson 2000; Bolin, Jacobson, and Lindgren 2001). To avoid separate consideration of all possible types of families, the model envisions an employed single parent. Other types of families are considered in the empirical analysis, and the model can be adapted easily to consider dual-parent or dual-income families (Dickie and Salois 2003). A one-period setting is taken to focus on short-term illnesses; thus, parental resource allocations are assumed to influence the number of days a child is ill, but the stock of health capital is held constant.
The ith family's resources are allocated to maximize the parental utility function
(1) U = U([Z.sub.i], [h.sub.i1], [h.sub.i2], ..., [h.sub.iN], [N.sub.i]),
where [Z.sub.i] represents family consumption of a composite good and [h.sub.ik], k = 1, ..., [N.sub.i], represents the flow of healthy time consumed by one of the parent's [N.sub.i] children. Healthy time equals total time available T less time spent sick [S.sub.ik]. Time spent ill in turn is produced according to the health production function
(2) [S.sub.ik] = [S.sub.ik] ([M.sub.ik], [X.sub.ik], [[upsilon].sub.ik], [N.sub.i]),
where use of medical care [M.sub.ik] reduces sick time; [differential][S.sub.ik]/[differential][M.sub.ik] [less than or equal to] 0, [X.sub.ik] represents a vector of observable exogenous factors directly affecting the child's flow of healthy time, and [[upsilon].sub.ik] denotes the health "endowment" or inherent healthiness of the child. The vector [X.sub.ik] includes measurable indicators of the child's long-term health status or "stock of health capital," such as presence of preexisting chronic diseases. In contrast, the health endowment [[upsilon].sub.ik] summarizes effects of unmeasured factors known to the parental decision maker. Finally, parents' fertility decisions represented by the number of children may affect the production of child health.
Constraints on time and expenditures are combined to derive a full-income budget constraint (for details, see Becker 1965; Grossman 1972):
(3) [R.sub.i] = [w.sub.i]T + [A.sub.i] = [Z.sub.i][q.sub.zi] + [N.summation over k=1] [M.sub.ik][q.sub.ik] + [w.sub.i]G([S.sub.i1], ..., [S.sub.iN]).
Full income [R.sub.i] equals total time available T evaluated at the parental wage rate [w.sub.i] plus any asset or other nonlabor income, [A.sub.i]. Full income is spent on partly consumption [Z.sub.i], whose full or time-inclusive price is [q.sub.iz] = [p.sub.z] + [w.sub.i][t.sub.z], where [p.sub.z] denotes the money price and [t.sub.z] denotes the time required to consume a unit of Z, both of which are assumed constant over families. Full income also is spent purchasing medical care for children at full prices [q.sub.ik] = [p.sub.ik] + [w.sub.i][t.sub.ik], where [p.sub.ik] denotes the out-of-pocket monetary cost of a medical visit for child k and [t.sub.ik] denotes the time required. The out-of-pocket money price and the time requirement for medical care may vary between children, perhaps even within the same family, because of potential differences in insurance arrangements and locations of medical services. Finally, a sick child may detract from full income by reducing time available for market and nonmarket activities. The time lost by the parent depends on the time children spend ill: G([S.sub.i1], ..., [S.sub.iN]), where [differential]G/[differential][S.sub.ik] [greater than or equal to] 0.
Maximization of the utility function 1 subject to constraints 2 and 3 implies that parental willingness to pay for a marginal reduction in a child's sick time is given by
(4) [differential]U/[differential][h.sub.ik]/[[lambda].sub.i] + [w.sub.i]([differential]G/[differential][S.sub.ik]) = -[q.sub.ik]/[differential][S.sub.ik]/[differential][M.sub.ik],
where [[lambda].sub.i] denotes the marginal utility of full income and the equality follows from first-order conditions (for additional discussion, see Dickie 2003). According to Equation 4, willingness to pay to reduce children's sick time equals the monetized marginal utility or consumption value of a healthier child plus the increase in parental time for market and nonmarket activities made possible by a healthier child. Maximizing behavior implies that this marginal benefit of improved health equals the marginal cost of producing it, given by -[q.sub.ik]/([differential][S.sub.ik]/[differential][M.sub.ik]).
While Equation 4 gives the private willingness to pay of family i, social benefits may exceed the sum of these values over all families if the child's illness is contagious or if some costs of illness are borne by persons outside the family. First, contagion creates a classic public health externality in which a parent's valuation of her child avoiding illness is less than social benefits. (1) Second, institutions that shift some costs of children's illnesses from the family to other members of society, such as health insurance or paid leave from...
Parental behavior and the value of children's health: a health production approach.
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