H^ijt - a^i + r^j + d^t + (b)MEMP^it + (g)CCARE^it + (L)Z^ijt + e^ijt
In this equation, H^ijt represents the health of child i in site j at age t, which is measured in months. In our simplified specification of the production function, child health depends on an individual-specific effect, a^i (an unchanging characteristic of the child-mother pair, for example, the child's health endowment or his race); site effects, r^j; age effects, d^t; maternal employment at age t, MEMP; time spent in child care at age t, CCARE; and the quality of other health inputs, Z, at age t. In the empirical analysis, Z^ijt is a vector of possibly time-varying family and child characteristics (e.g., current family structure - number of siblings and adults - mother's age and education at the child's birth, and in some models, family income) that, along with site dummy variables, will be the proxy variables for more direct health inputs. We also control for calendar months and year. Month may be important for injuries because of seasonality in children's activity and for infectious disease because of seasonality in flue exposure. Finally, we include contemporaneous rather than lagged influences in child health because our health measures, injuries and infectious disease, have short gestational periods.
Can I hear a "Boo ya!" anyone?