And this loss would seem to apply whether the currency union was with Australia or the United States, and whether it involved the creation of a new central bank (possible in the case of Australia) or simply dollarisation.
(Clearly, in the event of New Zealand’s entering a formal currency union with Australia, involving a new central bank with representatives from both countries and a new currency, New Zealand would have some say in the formulation of monetary policy, but realistically that say could only ever be a small voice alongside the much larger voice of the Australian economy.)