Is it even possible to establish the direction of causality? Like if you compare areas, then the areas with more immigrants usually see more economic growth. But, also, areas with economic growth is what attracts immigrants. I can’t think of a way to tease those apart. Is there one?
This is usually what's known in Econometrics as Identification. Any applied econ paper written in the last two or three decades has at least a short section discussing causality and making the case for its identification strategy.
