LATE with Mismeasured or Misspecified Treatment: An application to Women's Empowerment in India

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.