Decomposing Identification Gains and Evaluating Instrument Identification Power for Partially

This paper studies the instrument identification power for the average treatment effect (ATE) in partially identified binary outcome models with an endogenous binary treatment. We propose a novel approach to measure the instrument identification power by their ability to reduce the width of the ATE bounds. We show that instrument strength, as determined by the extreme values of the conditional propensity score, and its interplays with the degree of endogeneity and the exogenous covariates all play a role in bounding the ATE. We decompose the ATE identification gains into a sequence of measurable components, and construct a standardized quantitative measure for the instrument identification power (IIP). The decomposition and the IIP evaluation are illustrated with finite-sample simulation studies and an empirical example of childbearing and women's labor supply. Our simulations show that the IIP is a useful tool for detecting irrelevant instruments.