  This paper studies the identifying power of an instrumental variable in the
nonparametric heterogeneous treatment effect framework when a binary treatment
is mismeasured and endogenous. Using a binary instrumental variable, I
characterize the sharp identified set for the local average treatment effect
under the exclusion restriction of an instrument and the deterministic
monotonicity of the true treatment in the instrument. Even allowing for general
measurement error (e.g., the measurement error is endogenous), it is still
possible to obtain finite bounds on the local average treatment effect.
Notably, the Wald estimand is an upper bound on the local average treatment
effect, but it is not the sharp bound in general. I also provide a confidence
interval for the local average treatment effect with uniformly asymptotically
valid size control. Furthermore, I demonstrate that the identification strategy
of this paper offers a new use of repeated measurements for tightening the
identified set.
