Instead of IV, can I simply run an OLS with the compliers?

[Rubens Lopes]

Imagine that I have a dummy variable that is a proper instrument. It identifies which observations of my dataset received the treatment randomly (or as good as). With IV, the effect I will obtain will be only for the compliers, anyway.
So why wouldn't I simply run an OLS with the compliers subset? Why doesn't everyone with a binary instrument do this?

[Bert Lloyd]

You don't know who the compliers are, since you would have to observe their treatment status for both states of the instrument.