Over the years, we've seen corporations shift their headquarters to lower tax regimes in order to escape the notoriously high U.S. corporate tax, so it would stand to reason that high-earning individuals would also pick up and move themselves to states with low-or-no income tax once they hit it big, right?

Wrong.

According to a recent study, Americans who earn at least $1 million annually don't move away from high-tax states such as New York, New Jersey, and California any more frequently than the general population.

Of all of the households making over a million dollars, only about 12,000 change their state of residency each year. That's a rate of migration of 2.4 percent, and it's slightly lower than the national average of 2.9 percent.

"Persistent millionaires," those who made a million dollars multiple years as opposed to just one, were even less likely to move. The migration rate of one-time millionaire earners was 3.2 percent compared 1.9 percent for persistent millionaires.

I recently spoke to the author of this study, Cristobal Young, a professor in the Department of Sociology at Stanford University. Young is an economic sociologist and statistician, and he studies how public policies affect income inequality. He told me that high earners in America are the "working rich," and their livelihood keeps them grounded to the state where they developed their wealth.

"Migration is a young person's game. People move when they are starting out, and their incomes are pretty low. In fact, the people most likely to leave a state are those earning $10,000 or less annually," Young said. "It's just not something people do when they're millionaires because, by the time people are at the very top of their game, there is a lot of social capital in place. So unless you're retiring, it doesn't really make sense."

Young explains that, even though technology has allowed the world to shrink, allowing many aspects of business to be done remotely, there's still a need for the human connection. Working millionaires like lawyers, doctors, and entrepreneurs need to foster the relationships that got them to the top in order to ensure that they stay there.

"All of our work is collaborative today, especially at the very top of the income scale," Young explained. "We do our best work when we're connected to the very best people. This is why high income is like a marriage. We need to stay connected to top talent and collaborators, and that means people are tied to the places where they became successful."

When millionaires do move, they do have one state they prefer: the Sunshine State.

Young told me that, of all millionaire migration, 30 percent is into and out of Florida (20 percent in, 10 percent out). Largely, he says that has to do with the tropical climate Florida offers, while still being accessible to most major cities via a two-to-three hour flight (unlike Hawaii, for example, which is at least five hours from the mainland, and ten hours from New York). But not coincidentally, Florida also has no state income tax. That tax advantage, Young says, is surely part of Florida's appeal.

So as local legislatures look to replenish their coffers, could other warm climate states take a cue from Florida and attract millionaires by lowering their tax rate for top earners? Young says not to bet on it.

"No state will ever make money by cutting taxes for high income earners. Tax revenues are determined by the tax rate on non-movers," he explained. "The typical state has about 10,000 people in the millionaire bracket. So if you cut taxes on high income earners, you're going to be cutting taxes on 10,000 people to try to attract maybe a dozen or so millionaires that would be tempted to move. The population that stays is about a thousand times larger than the people who migrate.

"If states were thinking about this purely based on how much tax revenue they could generate, the simple answer would be to set the tax rate much, much higher."

That's not going to be music to any millionaire's ears.