I'm currently starting to write my undergrad thesis, which I plan to use as my writing sample when applying to PhD programs/predocs/etc., and I think I have a pretty interesting and achievable topic. I've read a bunch of papers that find educational attainment to be countercyclical, specifically during the Great Depression and Great Recession, and they theorize that the underlying mechanism has to do with the opportunity cost of education being lower during times where the labor market is not strong (dropping out doesn't have a good chance of getting any job, so might as well stay in school).

I want to verify this mechanism in part by seeing if the opposite is true - if dropout rates rise (or if graduation rates lower, similar idea) during times of strong labor markets. I'd also hypothesize that this effect is higher for low income individuals or students that are less likely to go to college even if they graduate high school.

However, in reading some literature and thinking about the model I plan on building, I believe a logistic regression (or some variation on a binary dependent variable, like one paper uses a LPM) is what most papers seem to use. Is this complex enough for the paper? Coming into the class, I was hoping to use a more sophisticated econometric model like DiD or RDD or some other causal framework, but I'm not sure they apply to my topic.

I've thought about trying to find say, a local unemployment shock and using that as an intervention to apply to a DiD or event study and use areas with consistently low unemployment as a control group, but I'm not sure. I know I shouldn't write a paper with the purpose of shoehorning in a fancy model, but I'm worried using a logistic regression isn't "complex" enough for PhD programs to see my ability to write academic papers/economic research.