https://poseidon01.ssrn.com/delivery.php?ID=8201061010270271...
I have only skimmed through the paper, but I am a bit skeptical about their conclusions. The authors first showed that the attacks-on-refugees time series is strongly correlated to the anti-refugee-posts time series. This part is very basic and is OK.
Then they tried to exhibit a causal relationship between the two series, and it is the trend of posts that drives the trend of attacks but not the other way around. This is where I have doubts. Apparently, the authors didn't try something basic first --- like a Granger causality test --- but applied a somewhat obscure regression procedure to establish causality.
This procedure, which they called a Bartik-type approach, was invented only in 1991. Now I'm not familiar enough with time series analysis to know the merits of this Bartik-type approach and why Granger test is not useful in this case, but from the graph in the Economist article, it seems that the trend of attacks is leading the trend of posts, so I wonder if they were deliberately omitting a Granger causality test that might refute their conclusions.