Leti This is such an interesting example. I agree it's really hard to study rigorously, for all the reasons you note. Sometimes in this type of setting people find a regression discontinuity strategy for a rigorous design. For example, if there is an arbitrary age cutoff or year of entry cutoff in the eligibility rules, you would expect that children right above and right below the age threshold would have different outcomes: this type of "discontinuity" can be used to estimate the effect of eligibility. The design really depends on identifying arbitrary features of the policy - features that do not correspond with human biology or the values of other confounders - and using those things as a discontinuity. This design is pretty popular in econometrics because it is more convincing than most observational approaches. Do you know if there is any such discontinuity in DACA that might be used for such an approach?
Maria