I suspect this is one of the cases where “correlation does not equal causation” should be mentioned. It certainly might be causative, but it also might not be.
As the other commenter mentioned, you really need to look at the actual murders themselves. No amount of stop and frisk is going to reduce domestic murders.
The author suggests it’s fewer police out and about policing. It might be that.
This is a really card situation to prove causation since it’s retrospective observational. But maybe more researchers can try to isolate variables and find controls, etc.
For me, it’s trying to find a reasonable story so I can stop wondering. I imagine that police waking and driving around arresting people doesn’t stop murders, but fewer police being around doing stuff might result in more violence.
The authors used changes in the terror alert level (which caused increases in police presence) as a natural experiment, and found that crime dropped significantly in the area when the terror level increased.
I think the explanation here is probably quite simple: an increase in the number of police officers in an area means that calls are responded to more quickly and for any given crime the criminal has a higher chance of being arrested. As we'd expect, a high likelihood of negative consequences deters crime.