discrete choice (full vaccination or no vaccination) or as a continuous choice with saturation (choose how many vaccines to get, with a maximum of 8). In practice, a majority of children get either full vaccination or no vaccination, so it seems that, to some extent, this is being treated like a discrete choice. However, in the empirical work I will report results both treating vaccination like a discrete choice (any vaccines versus no vaccines) and treating it as a continuous choice with saturation. Below I briefly outline the theory specific to each formulation.
Importantly, in both cases I assume that the effect of vaccinations is the same for boys and girls. If vaccination is more effective for boys, in particular, then we could get these effects not because of gender bias but because of a larger vaccination benefit. In general, however, there is little evidence that vaccinations are more effective for one gender and, if anything, papers that find a difference in efficacy tend to find that the vaccines to be more effective for girls (Aaby et al, 2002). In other work on this same data (Oster, 2008) I find that the relative value of vaccinations for mortality declines appears to be exactly the same for each gender. This does not, therefore, seem like a significant concern.
In this case, the family chooses to either vaccinate or not. Without vaccination, the child will live with probability p. With vaccination, the child lives with probability pˆ, where pˆ > p. The value of
the vaccination investment for boys is, therefore, φb(pˆ
p) and, for girls, φg(pˆ
provided by a number of sources, with a cost v + εi for family i, with the variation reflecting the fact that some families live closer to vaccination sources, or may have better access to transportation. The program analyzed here lowers the average cost v by providing additional access to vaccination, often more conveniently located than existing sources. Note that even if we have a model in which each family has multiple children, we still expect the cost of vaccination to act for each child. Because children need vaccines at specific ages, it is not reasonable to take all of your children to be
vaccinated at once, so the cost of travel must be paid for each child (or, below, for each vaccine).
Returning to the notation above, denote φb(pˆ
p) = ΛA
a n d φ g ( pˆ
p) = ΛD.
the problem now maps identically into the basic model in Subsection 2.1, and the propositions are
We predict a non-monotonic relationship between access to vaccination and inequality, and
this relationship should be larger among families with stronger son preference (higher φb relative to φg).