Beyond plausibly exogenous

We synthesize two recent advances in the literature on instrumental variable (IV) estimation that test and relax the exclusion restriction. Our approach first estimates the direct effect of the IV on the outcome in a subsample for which the IV does not affect the treatment variable. Subsequently, this estimate for the direct effect is used as input for the plausibly exogenous method developed by Conley, Hansen and Rossi. This two-step procedure provides a novel and informed sensitivity analysis for IV estimation. We illustrate the practical use by estimating the causal effect of (a) attending Catholic high school on schooling outcomes and (b) the number of children on female labour supply.