Decomposing identification gains and evaluating instrument identification power for partially identified average treatment effects

In this article, we synthesize and review existing results on the roles of instrumental variables (IVs) in average treatment effect (ATE) partial identification analysis. We provide a novel decomposition of identification gains in ATE bounds and offer insights for understanding the complex role of IVs in conjunction with model features and covariates. An empirical example of childbearing and women’s labor supply, with two IVs of ‘twins’ and ‘same-sex siblings’, demonstrates that ‘twins’ has significantly greater identification power than ‘same-sex siblings’, and the identification power of both IVs is heterogeneous across covariates. Our analysis can also be useful in IV selection in future program experiment designs.