I have panel data and wish to estimate the differential effect of a policy on a group of people having a disease (assume people can recover and get the disease again) relative to everyone else. My model is as such: Y_ijt = person fe + time fe + region fe + policy + policy*subpopulation + year*policy*subpopulation + time varying characteristics. I plan to use cmp (Roodman 2009), assuming disease is endogenous. I wish to model disease = Z X, where Z is exogenous but relevant (analogous to an IV) and X are predictors. Since I don't care about time invariant individual characteristics in my outcome equation but think the assumptions for random effects are satisfied for my predictor equation, and also believe that the errors in this SUR are correlated, what is the best course of action? My outcome variable is binary and my disease variable is an ordered logit.
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