We have panel data on immigration stocks, immigration flows, and immigration policy for 30 countries and 10-30 years. We would like to test the theory that the effect of immigration flows (i.e., annual numbers of incoming immigrants as % of pop) on immigration policy depends on immigrant stocks (i.e., non-citizens as % of pop). In other words, immigration flows affect policy, but only when there are few existing immigrants to begin with.
It seems to me that an interaction between immigration stocks and flows will allow a test of this theory. However, while our dependent variable (immigration policy) and our main independent variable (immigration flows) appear to be stationary, immigrant stocks is not. Standard solutions like first-differencing immigrant stocks won’t help because that would transform stocks into another measure of annual flows, which will not allow us to test the theory.
Another way of putting this is to ask: does stationarity matter only for the dependent variable? Or also for all independent variables?
Advice on how to proceed will be greatly appreciated!