By taxing consumption instead of income we increase the price of everything, and thereby lower incomes. If people HAD to consume in the same place where they worked then this would have no impact on immigration incentives at all!!
If people could decide to save (which we could) then shifting from income tax to consumption tax gives people, at the margin, the incentive to work in New Zealand – but to move away and use this income somewhere else.
When the shift is introduced we are increasing the cost of consumption domestically – so people who have saved will want to move away (at the margin) and people who have borrowed will be more likely to stay in the country.
The net impact on migration is going to be ambiguous, but on the margin we can tell that there will be more incentive to work here and less incentive to spend here.
Of course this ignores one major thing, the dollar will fall to compensate for the change in the price level – implying that an “unexpected” increase in GST could have no impact at all at the margin for those with savings or borrowing (as the lower dollar reduces the value of domestic income overseas and makes consumption here cheaper for those with foreign income – thereby increasing the incentive for people who have saved to move here, and reducing the incentive for those who have borrowed to move here)