Suppose I observe high school graduates applying to a certain college.
I want to model the probability to get admitted on the basis of individual characteristics (cognitive ability, test score, GPA, exchange experiences, interviewer's scores, etc.) with a logistic or a probit regression.
Suppose I observe 10 years of applications, i.e., 10 cohorts of applicants. In year 2010 some students apply to college, and in year 2011 some other students apply to college. This looks like a pooled cross-section (different individuals observed at different points in time).
But, some persons, like 0.5% of the total observed population, applied to college multiple times. For example, Mr. Joe Sixpack applied to college in 2010, didn't get admitted, and re-applied in 2011 (and still didn't get admitted).
Does this make my dataset a (highly) unbalanced panel dataset, rather than a pooled cross-section dataset? How to take into account autocorrelation?
I have an analogous objection from a referee for a paper I'm writing.
Related (without an answer).