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about risk sharing and adverse selection, but Medicare is nevertheless also thought to decrease inequality by providing a safety net for the poor. These issues of access and inequality are important throughout the developing world, where the policies of governments and NGOs often aim to improve the circumstances for disadvantaged groups (for example, women or ethnic minorities) and to increase overall levels of access.

The assumption behind the higher access-lower inequality link is that increasing overall access to social services will generate relatively more benefits for under-served groups. However, the evidence on the validity of this assumption is mixed. Some work on Medicare has argued that it actually acts as a transfer from the poor to the rich (McClellan and Skinner, 2006); others argue this is not the case (Bhattacharyaa and Lakdawalla, 2006). Evaluations of recent school accountability programs in the spirit of NCLB have found an increase in the black-white test score gap after accountability (although they also find a decrease in the hispanic-white gap) (Hanushek and Raymond, 2004 and 2005). Other evaluations of these programs have argued they are most beneficial for students in the middle of the class, not for those at the bottom (Neal and Schanzenbach, 2007). In a historical example, improvements in infant health care in the 1950s seemed to decrease white infant mortality rates, while leaving black infant mortality rates unchanged, effectively increasing the inequality in mortality. However, further improvements in health care in the 1960s lowered relative mortality rates of black infants, increasing equality (Almond et al, 2007; Chay and Greenstone, 2000).

In this paper I argue that this empirically ambiguous relationship between the level of access to social services and inequality is not surprising and, in fact, is what we would expect based on simple economic theory. I show a model relating the level of access to some investment (equivalently, the cost of the investment) to the difference in investment levels across two groups, one of whom faces discrimination or disadvantage. At very low levels of access (very high cost), there is little or no investment in either group, implying equality. As access increases, the more valued group gets access first, generating inequality. After some point, further increases in access will improve the situation of the less valued group, restoring equality. This model therefore predicts that the relationship between access and inequality may be non-monotonic: inequality increases with increases in access from low levels, but decreases with increases in access when starting at a high level.

I test the predictions of this model using data on vaccinations in India, analyzing the effect of changes in the availability of vaccinations on overall vaccination levels for boys (the advantaged group) and girls (the disadvantaged group). This context is well suited to test this theory for several reasons. First, there is clear evidence of gender discrimination in India. Sen (1990,1992) argued that

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