I might be misunderstanding something, but are poisson or negative binomial models with an offset term for population size (rate models) and independent variables that are rates as well endogenous? In other words, is the denominator directly correlated with all of the independent variables concerning population? Probably an examples makes this clear.
Example: Imagine the dependent variable is the number of homicides and the offset is the population size so that I am essentially modeling the homicide rate (i.e. homicides divided by population size). Some of the independent variables are the proportion African-American, proportion white, proportion poor etc. Are these variables all endogenous because they are defined as x divided by population size (same denominator as outcome)? What are alternative ways to specify the model?