I want to revive this thread, because I want to address the economic side of things (which I don't think have been addressed yet) and the recent history/impact on culture side in more depth.
I don't think there are numbers anywhere for import/export between Empires, but the are Caldari Megacorps with a big presence in the Republic in space, already (NOH, Ishukone, KK - 1 of each for the Caldari political factions, perhaps not coincidentally).
The Republic represents a market for Megacorps, and good will in the large Minmatar population in the Federation, perhaps, as well.
For the Republic, goods from the State represent a way to get away from some of the reliance (if there is any) on Federation produced goods.
Additionally, if the State still has problems getting enough labor (I'm not sure if it is clearly established whether they do, at this point in time, still?) then the Republic might be an attractive outsourcing option, with underemployment and a huge mix of skill-sets apparently just sitting there.
On the subject of recent history, just covering more 'common ground' the Republic is rebuilding a culture in the place where they came from, while the Caldari are adapting an old culture to a new place. Just has a certain symmetry, to me.