The interpretation of the IV models is the local average treatment effect
, or in this case, the effect of medical homes on the outcomes for those individuals with SMI who enroll because of county infrastructure or level of interest in medical homes.
If the exclusion restriction holds, along with assumptions 1, 2 and 3, it is possible to point and identify the average causal effect of D on Y for compliers using the local average treatment effect
They motivate their interest in the local average treatment effect
by stressing that this quantity is identified in circumstances where the effect of treatment on compliers is not identified.
Instead, we show how models differ in several measures of treatment effects, including the local average treatment effect
(LATE), the average treatment effect on the treated (ATET), and the sample distribution of incremental effects.
"Identification and Estimation of Local Average Treatment Effects
." Econometrica, 62, 1994, 467-75.