Defining a binary treatment based on a proportion I want to explore the effect of bringing in more female students into a classroom on the existing individual students' performance using a panel dataset. However, there is no particular policy change or clear cutoff. Could I define the treatment as a binary variable that equals one when the percentage of new students who are female > 80% and use that to define treatment (where post-treatment is based on the first year that passing this threshold happens) in a typical difference-in-differences (DD) model?
In this specification, I would interpret the treatment as a "shift" to more gender diversity. Does this approach complicate identification? I am mainly leaning towards DD because I also want to do an event study analysis, but the threshold aspect also makes me think about using a regression discontinuity design.
Other ways I've thought of getting at this question is using a simple two-way fixed effects regression that includes year and individual fixed effects, while using the percentage of new students who are female as the key explanatory variable.
What are the potential problems with these approaches?
 A: I see a few potential problems.

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*The cutoff seems arbitrary; it's defined by you. In fact, you're in complete control of the treatment assignment process, whereas in most difference-in-differences applications the process is outside the control of the evaluator.


*You're losing information. Binarizing the treatment in this way is saying a classroom with .79 female representation isn't a diverse environment, yet a classroom with .81 female representation is. Discretization ignores the gradations off new female representation over time.


*The irregular exposure patterns will make your event study difficult to interpret. Say you're observing students over many years. A typical student may be in a classroom with .7 representation in one year and .9 in the next. The binary treatment indicator would 'turn on' (i.e., switch from 0 to 1) once the threshold is crossed, but you've given no indication that the treatment is permanent. In a subsequent period, a student is just as likely to be nested within a group just under the demarcation line, in which case the binary treatment indicator should now 'turn off' (i.e., switch from 1 back to 0). Unless you're making the claim that once the threshold is reached that entities stay treated in all subsequent periods, then you should account for all 'on' and 'off' periods of treatment.
It will be difficult to advise you further without knowing more information. I would be interested in seeing a treatment variation plot to see when entities move into (out of) of a treated condition across time. Since you're ignoring the continuous nature of your diversification variable, your treatment effect is reduced to variation in treatment timing.
I suppose the principal question is why did you choose female representation in excess of .8 as the cutoff? Why not .5? What does theory tell you about the relationship between female enrollment and scholastic achievement? I would hope your assignment process has some theoretical grounding. And what about classrooms where male representation goes to 0 over time? The cohort is above .8 so it's "treated" according to your definition, but is it still diverse?
You've also given little information about the nested nature of your data. Do you have students nested within classrooms, nested within schools, nested within school districts? And what about the characteristics of the classrooms or the schools? Is the dataset a mixture of public and private schools? If it's universities, what about exploiting differences across disciplines? Do you consider student-teacher ratios? And what about mobility patterns? Can a student switch classrooms or school districts over time?
I didn't pose these questions to confuse you. Rather, I did it to show you how difficult it is to advise you given the finite information provided in your post. Since you're interested in how the diversification of the "group" (i.e., classroom, school, district, etc.) affects individual level academic outcomes, then perhaps a multilevel model is more appropriate.
