As far as I know, war in V1 does not directly lead to migration. It might raise the militancy if it's not going well for a country but I mean directly. So when a province is on the frontlines (static like in WWI or if many battles are fought over it) it should make the POPs in that province want to migrate either to somewhere more peaceful in the country or abroad. If you're a poor North French farmer in Verdun you'd pack up your things and move to your relatives in the Provence, at least until the war ended. Or even to the US. So warfare should promote the (e)migration in a province. This could be a constant factor during all wars. Only the really big ones like the Great War or perhaps the ACW would lead to any large migrations.
Secondly, civilian casualties. War always costs some civilian casualties and warfare should activate an attrition factor in the province that is being ravaged by war.
Secondly, civilian casualties. War always costs some civilian casualties and warfare should activate an attrition factor in the province that is being ravaged by war.