The model of fertility and child investment outlined above suggests that infant health is a function of (i) maternal choice variables (e.g., smoking while pregnant) and (ii) maternal endowments (e.g., genetic makeup). A general health production function takes the form Y = f (X, W), where Y is a measure of the health of a particular mother’s newborn child, X is a vector of maternal choice variables, and W is a vector of maternal endowments. Elements of W are fixed from the mother’s perspective. However, a mother’s schooling could affect her health inputs, elements of X. Demand for health inputs may be expressed as a general function of resources, endowments, and the demand for schooling, X = g(S,I, W), where S denotes schooling and I denotes resources. Resources are meant to be interpreted broadly as non-schooling factors that affect a mother’s choice of health inputs. One such resource is income, which may lead to higher quality prenatal care, for example. Combining, we have
This clarifies that the effect of education on infant health is inherently a reduced-form parameter summarizing (i) the impact of schooling on health inputs (Ц), (ii) the impact of schooling on resources (Ц), (iii) the impact of resources on health inputs (dg), and (iv) the impact of health inputs on infant health (dX).
The first term of equation is the focus of Grossman’s model of health capital. In particular, it is the effect of education on health inputs via health knowledge and the ability to process information. The second term of equation represents the indirect effect of education via resources. A woman’s education may affect her income and her choice of mate, which in turn could alter her choice of health inputs.
In this paper, we are unable to distinguish between the direct/Grossman effect and the indirect effect. Nevertheless, this distinction is important. It highlights the potential for heterogeneous education effects as there are several mechanisms by which education could potentially improve infant health. In the present case, the effect of education may differ considerably based on whether the mother is still enrolled in school, as discussed above. Before proceeding, we note that analogous expressions may be developed relating female education to fertility decisions. A key difference is that a woman may be able to exercise choice over her fertility more readily than choice over the health of her offspring. This may be captured in the model above by ascribing a more limited role for genetic factors regarding fertility than regarding infant health.