Their rejoinder, which I am responding to, is here. I'm really miffed at how they approached this - particularly since I spoke to all of their concerns in my response to the referee report (a response which isn't reflected at all in this rejoinder). It's a very weak rejoinder in my view. If it doesn't get published, I'll post my reply here. But QJAE seems to give wide latitude to dialogues, so hopefully it will.