  The effect of the full treatment is a primary parameter of interest in policy evaluation, while often only the effect of a subset of treatment is estimated. We partially identify the local average treatment effect of receiving full treatment (LAFTE) using an instrumental variable that may induce individuals into only a subset of treatment (movers). We show that movers violate the standard exclusion restriction, necessary conditions on the presence of movers are testable, and partial identification holds under a double exclusion restriction. We identify movers in four empirical applications and estimate informative bounds on the LAFTE in three of them. 
Instrument-based estimation of full treatment effects with movers