Bounding Causal Effects

Empirical researchers commonly use instrumental variable (IV) assumptions to identify treatment effects. However, the credibility of these assumptions are often questionable. In this paper, we consider what can be learned when the assumptions necessary for point identification are violated in two specific ways. First, we allow the data to be contaminated, meaning that the exclusion restrictions of the IV estimator hold for only a fraction of the sample. Second, we allow for the data to be censored. After relaxing these assumptions point identification is no longer feasible, but we are able to construct sharp bounds of the treatment effect. In particular, we show that miscarriages can be seen as generating a contaminated and censored sample with which to analyze the impact of a mother’s age at conception on the subsequent development of her child. Utilizing the aforementioned bounds, we are able to demonstrate that for non-black children, a delay in their mother’s age at first birth is detrimental to their well being. * Department of Economics, Vanderbilt University, Nashville, TN 37235. Email comments to: [email protected]. This research was supported by a grant from the National Institute of Child Health and Human Development and by a predoctoral fellowship from the National Institutes of Health.