Suppose I run a RCT where the treatment is educating high school students. Outcome variable of interest $y$ is the wage the student will earn after graduating from high school. Suppose there is no non-compliance, and SUTVA is satisfied. I am interesting in obtaining Average Treatment Effect (ATE). However, wage is only observed for individuals who are employed, and suppose also that the treatment also increases the probability of individual being hired.
How should I estimate the treatment effect on individual wage? To be specific, is the following regression what I want?
$y = \alpha + \beta D + \varepsilon$, where $D$ is the dummy for treated group.
This regression will include individuals whose wage is 0 because it includes individuals who are not hired. My instinct tells me that I need to somehow instrument for the treatment effect on the probability of being hired, but I am unsure what I should do.