I am interested in a strategy to calculate heterogeneous treatment effects with an IV strategy for local average treatment effects (LATE).
I am estimating the effect of postsecondary educational selectivity on adult wages using an instrumental variables identification strategy. The instrument is linear distance to a selective institution and should identify the LATE, or the effect of the treatment on compliers.
In this case, the compliers would be those induced to attend a more selective institution due to closer proximity to a selective college or university. It is likely that the effect for students on the margin of attending a selective college (those who would not have otherwise attended a selective school) differs from the effect of those who would be an always-taker (not constrained by geography in choosing a college).
If the likelihood of being a complier is related with family socioeconomic background, what might be a valid strategy for estimating if the effect for low-SES students differs from high-SES students? Is it valid to run separate 2SLS models for students of low and high SES and then compare the LATE for each subgroup?
I understand that there are recent developments in strategies for marginal treatment effects. But, short of implementing a MTE strategy, would stratified models in a 2SLS framework be valid?