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.
Yes, they do. Just ctrl+F "identification" if you don't feel like reading the whole thing.
In fact, this is such a common practice that it's nigh impossible to publich an empirical paper without discussing identification and employing an identification strategy.
You can always tell people who are not familiar with modern Economics because of it too, they will bring "but correlation is no causation" up and feel pretty good with themselves. Then you mention the identification strategy, and they just stare at you blankly without getting what you mean by that. I've seen this happen so many times.
