If not, is there a possibility of integrating a static variable in a dynamic model and what effect will it have on the model results?

In particular, the paper titles "Recognition Rates for Refugees in Scandinavia: What explains the difference" by Kristin Djerv and Alveng uses a similar model to that used by Eric Neymar which also in his paper "Asylum Recognition Rates in Western Europe: Their Determinants, Variation, and Lack of Convergence" which models recognition rates as the dependent variable yet in a dynamic model.

I want to use the recognition rates as my dependent variable, however, the independent variable which I want to see its effect is of a static binary nature, I do not want to construct a whole new model and would prefer to build on what is already existent.