We have a member on the Aussie thread that was being driven insane by their cawing constantly just outside her window. (A bunch of them made it their home nesting tree) So encourage them but careful how closely lol
Over here I've never seen a crow chasing a hawk but I will often notice one above us because of the pee wees giving it a hard time and moving it on. Now that's a brave bird when you consider their size!
I'm going to take a wild guess here and assume you don't call them pee wees because they are huge. Right?