Although I am not convinced the change was a good idea, precisely because you probably want to keep as many pension-receiving seniors around as possible, I doubt it has had a huge effect up to now. Seniors in their late 60's or above aren't taxed on their public pension income [[like SS) at all, and aren't taxed on their private pension income until they reach about 45K for an individual or 90K for a couple. There aren't that many seniors with pensions at that level, and those people only pay on the excess, so unless they have very large pensions the amount of additional tax is pretty small. However, as the phase-in phases in, more pensioners will face the higher taxes, and some people who would have stayed may well move.
On the other hand, huge numbers of retirees moved from Michigan to Florida and other warm-weather states before the pension tax change; if the change is a factor, it is only one among many.
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