Does hate speech lead to hate crime?

That it does is a constant Leftist assumption. So it is no surprise that the authors below have tried to prove it.  And they claim that they have proved it.
    
According to their Table 4, however, the correlations found between speech and incidents are quite low.  A correlation of .236, for instance, indicates only 5.5% of common variance. 

The biggest problem however is that they ignore the ancient statistical dictum that correlation is not causation.  That dictum tells you that there might be somewhere a third variable that is causing the correlation between the two variables you are looking at.

And in this case there is a very obvious third variable:  The incidence of refugee misbehavior.  When refugess go on Jihad and kill people (etc.) you would expect that other people would both comment disapprovingly and in some cases retaliate.  So it is not the speech causing attacks on refugees, it is the behaviour of the refugees themselves

The authors below were rather hard-working.  They gathered data from both Germany and the USA in their attempt to prove their hypothesis. I have looked only at the German data but their methodology for their U.S. excursion seems to be the same as in Germany so the same criticisms apply.  Americans are certainly not short of deplorable behaviour from immigrants to complain about.

So to be a bit Scottish about it, their claim is "not proven".  Abstract follows:



Fanning the Flames of Hate: Social Media and Hate Crime

Karsten Müller et al.

Abstract

This paper investigates the link between social media and hate crime using hand-collected data from Facebook and Twitter. We study the case of Germany, where the recently emerged right-wing party Alternative für Deutschland (AfD) has developed a major social media presence. Using a difference-in-differences design, we show that right-wing anti-refugee sentiment on Facebook predicts violent crimes against refugees in otherwise similar municipalities with higher social media usage. Consistent with social media being the driving force, the effect decreases with internet outages; increases with user network interactions; is not driven by the news cycle; and does not hold for posts unrelated to refugees. We find similar evidence for the United States, where President Trump's twitter activity strongly predicts hate crimes against the minorities targeted in his tweets, but not other minorities. We find no effect for the period before Trump's presidential campaign or measures of general anti-minority sentiment.

SOURCE