Why does a wagtail wag its tail?

It’s thought that tail wagging in birds may help flush out insects, or act as a signal, either to others in the group, maybe as a dominance display, or to potential predators (“I’m alert: you won’t catch me”). Evidence from other tail-wagging species supports each hypothesis, but in wagtails specifically it’s unclear. Recent observations support the idea of it being a predator signal, which seems reasonable.