  Randomized controlled trials (RCTs) frequently utilize covariate-adaptive
randomization (CAR) (e.g., stratified block randomization) and commonly suffer
from imperfect compliance. This paper studies the identification and inference
for the average treatment effect (ATE) and the average treatment effect on the
treated (ATT) in such RCTs with a binary treatment.
  We first develop characterizations of the identified sets for both estimands.
Since data are generally not i.i.d. under CAR, these characterizations do not
follow from existing results. We then provide consistent estimators of the
identified sets and asymptotically valid confidence intervals for the
parameters. Our asymptotic analysis leads to concrete practical recommendations
regarding how to estimate the treatment assignment probabilities that enter in
estimated bounds. In the case of the ATE, using sample analog assignment
frequencies is more efficient than using the true assignment probabilities. On
the contrary, using the true assignment probabilities is preferable for the
ATT.
