We are trying to decide between using crime per capita as a dependent variable in our model versus including population on the right hand side. The basic analysis is about crime's relationship with economic activity (business revenues, etc).
Our crime data is yearly, but our population data is decennial so the yearly numbers in between are interpolated. Since they are interpolated, I feel more comfortable using pop on the right hand side, since it is my understanding that interpolated data causes less bias when used as a control than when used as a dependent variable (mismeasurement in a dependent variable being more serious than in a control). If both are logged, shouldn't they be exactly the same anyway? (ln(crime/pop)=ln(crime)-ln(pop), so ln(pop) can be moved to the rhs).
The model is a fixed effects model with both year and geographic fixed effects. Also, population is just nighttime population (ie, people who live there), whereas our analysis is about daytime population (people who shop there, work there, etc). Any suggestions on which way to go?
Thanks in advance!