health camps and inequality, and Section 5 shows the relationship between other measures of access and inequality. Finally, Section 6 shows the test for non-monotonicities in mortality, and Section 7 concludes.
Theory of Discriminatory Investment
This section presents a simple model of discriminatory investments. The question of interest is how changes in access to investments (health services, education, etc) will affect the difference in the level of those investments between an advantaged and disadvantaged group. In the first subsection I outline the basic model of a discrete investment, without being explicit about the type of investment or the decision maker involved. In the second subsection I discuss, more informally, generalizing the model to the case with substitutes and to continuous investments. The third subsection explicitly discusses the specific case of vaccinations in a world with gender bias, which is the primary focus of the empirical work.
Individuals in the model are of two types, advantaged and disadvantaged, with measure 1 of each type. There is a social planner who has access to some investment that would be beneficial to both types, and he makes decisions about investment for each individual. The investment is provided by some outside entity (for example, the government) at a cost of v + εi for an individual i, where ε ∼ N 0, σ2. This cost is not systematically different across the two types. In the model, the investment is assumed to be discrete.1
The social planner values the investment differently for the two types. Denote the value of the investment for the advantaged group ΛA and for the disadvantaged group ΛD. There are many reasons why these values might differ, and those reasons are likely to be different across different contexts. For this general model, I will simply assume that these values differ.
The investment will be chosen for the advantaged and disadvantaged groups, respectively, if the following inequalities hold.
v > εi
v > εi
1The next subsection discusses the issue of continuous investments.