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We study the long-term effect of access to health care on individuals' health status by investigating the relationship between the proximity to a Protestant medical mission in colonial India and current health outcomes. We use individuals' anthropometric indicators to measure health status and geocoding tools to calculate the distance between the location of individuals today and Protestant health facilities founded in the nineteenth century. We exploit variation in activities of missionary societies and use an instrumental variable approach to show that proximity to a Protestant medical mission has a causal effect on individuals' health status. We find that a 50 percent reduction in the distance from a historical medical facility increases current individuals' body mass index by 0.4. We investigate some potential transmission channels and we find that the long-run effect of access to health care is not driven by persistence of infrastructure, but by improvements in individuals' health potential and changes in hygiene and health habits.

We show that a local average treatment effect (LATE) can sometimes be point identified and consistently estimated when treatment is mismeasured, or when treatment is estimated using a possibly misspecified structural model. Our associated estimator, which we call Mismeasurement Robust LATE (MR-LATE), is based on differencing two mismeasures of treatment. In our empirical application, treatment is women's empowerment: whether a wife has significant control of household resources. Due to measurement difficulties and sharing of goods within a household, this treatment cannot be directly observed without error, and so must be estimated. Our outcomes are health indicators of family members. We first estimate a structural model to obtain the otherwise unobserved treatment indicator. Then, using changes in inheritance laws in India as an instrument, we apply our new MR-LATE estimator. We find that women's empowerment substantially decreases their probability of being anemic or underweight, and children's likelihood to suffer from cough, fever or diarrhea. We find no significant positive or negative effects on men's health. JEL Codes: D13, D11, D12, C31, I32.

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