  This paper provides partial identification of various binary choice models
with misreported dependent variables. We propose two distinct approaches by
exploiting different instrumental variables respectively. In the first
approach, the instrument is assumed to only affect the true dependent variable
but not misreporting probabilities. The second approach uses an instrument that
influences misreporting probabilities monotonically while having no effect on
the true dependent variable. Moreover, we derive identification results under
additional restrictions on misreporting, including bounded/monotone
misreporting probabilities. We use simulations to demonstrate the robust
performance of our approaches, and apply the method to study educational
attainment.
