Suppose you are running a randomized experiment to assess the effect of $X$, say some training program for unemployed people, on $Y$, say the chance of finding a job in the coming year. Suppose also that $X$ takes time : maybe it lasts for several month.
Because you randomize, you do not need to worry about self-selection bias initially. But during the course of $X$, some people will likely realize that $X$ is beneficial to them, and others may realize that they are wasting their time.
As a result, one might expect that among people who drop from the program, there is a higher proportion of agents for which the treatment effect would have been smaller. This might induce an over-estimation bias of the treatment effect.
My questions are :
- Is this kind of bias discussed in the literature on randomized experiments?
- Does it have a canonical name ?
- Do researcher try to control for this, and if yes, how?