Millionaires are mobile. Millionaires are used to zapping their money across borders and asset classes in perpetual pursuit of higher returns. Millionaires would rather give up their Gulfstreams than pay one cent more in taxes than they must, which is why if rates rise in one locale they react by directing their pilot to the nearest tax haven.

At least that's a common perception when it comes to America's rich, who are seen as being more attached to money than to place. And elements of that narrative are true, notably the near-frictionless flight of capital around the globe these days. But one strand of the story is dead wrong, it turns out: Millionaires in the U.S. are neither likely to pick up stakes nor to flee their state of residence just to lower their taxes.

"The general impression that top income earners are very geographically mobile is really untrue," said Cristobal Young, a professor of sociology at Stanford University and co-author of a new study that examines whether higher tax rates in one state lead millionaires to decamp for tax-friendlier states.

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Young and his fellow researchers -- Charles Varner, a sociologist and an associate director of Stanford's Center on Poverty and Inequality, and Ithai Lurie and Richard Prisinzano, financial economists at the U.S. Department of Treasury -- found that the six-zero set is, in fact, less likely to migrate to other parts of the country than people lower down the income ladder.

"The most striking finding of this research is how little elites seem willing to move to exploit tax advantages across state lines in the United States," they wrote in the study, published Thursday in the June issue of the American Sociological Review.

A number of U.S. states, their coffers drained by the recession, have imposed so-called millionaire taxes to boost revenue. Globally, some countries have sought to counteract the effects of rising income inequality by lifting taxes on millionaires, while both Hillary Clinton and Sen. Bernie Sanders have proposed hiking rates on top earners.

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Opponents of these policies say higher tax rates have unintended consequences, driving wealthy people away and, especially at the state level, reducing revenue and causing fiscal havoc. That was the claim recently when billionaire hedge fund manager David Tepper left New Jersey, which has the fifth-highest state income tax in the nation, and relocated to zero-tax Florida.

But Young's research -- which examined the tax records of every U.S. millionaire over more than a decade, some 3.7 million filers -- makes clear just how rarely millionaires in the U.S. actually move, whether to take advantage of lower taxes or for any other reason. Of the roughly 500,000 households per year that report at least $1 million in income on their tax returns, only 2.4 percent, or 12,000 millionaires, migrate to another state; that compares with 2.9 percent for the population at large.

Of the top income earners who do leave a state, only a sliver -- just over 2 percent -- seem to be spurred by a wish to cut their taxes, according to the study.

Why don't more rich people follow Tepper's lead and head to Florida or one of the eight other states in the U.S. that make do without a state income tax? Because for most millionaires, getting and staying rich is intimately connected to where they live.

Precious professional and social connections, often nurtured over years in a given industry, tend to bind the wealthy to where they live. So does family, since 90 percent of millionaires are married (compared with 58 percent for the general population) and are more likely to have children.

Perhaps it's not surprising, then, that millionaires who own a business have a migration rate of only 2 percent, versus 2.6 percent for non-business owners.

"When you reach this level of success, moving to a different state is a disruption," Young said. He also notes that corporate executives, doctors and other high-paid professionals, who make up the lion's share of millionaires in the U.S., typically reach their maximum income only for a few years. "It's a small window when they're at the peak of their careers, and to make a big, potentially disruptive move is not something that makes a lot of sense."

Not that millionaires never fly the coop in search of lower taxes. The study found that in the average state, which on an annual basis has a millionaire population of about 9,000, a 1 percent income tax increase could be expected to result in 23 top earners high-tailing it to a lower-tax state.

But the vast majority, tethered to their communities by the same links that tie less wealthy people to their humbler abodes, remain firmly grounded.

It follows, then, that states with higher tax rates don't have fewer millionaires. On the contrary, the state with the highest density of millionaires is Connecticut, which ranks No. 13 in state income taxes (rounding out the top five jurisdictions: the District of Columbia, New York, New Jersey and Massachusetts).

The one state that does seem to attract millionaires from higher-tax states is Florida; other low-tax states, such as New Hampshire, Nevada and Texas, don't have that drawing power.

What should we make of such findings? First, the specter of millionaire tax flight is largely a myth. That suggests state policymakers have little to fear in raising taxes on the wealthiest Americans as one way to close budget gaps and reduce inequality.

Second, the study challenges ingrained cultural beliefs about America as a land of of endless opportunity for anyone with the gumption -- and a bus ticket -- to go after it. If that's the country we once had, we inhabit it no longer.

After all, one group does show a greater inclination to move than the rest of us -- the poor. The highest rate of migration in the U.S., at nearly double the rate of millionaires, is found among people who earn around $10,000, the study shows.

If trying to escape poverty often means moving away, in other words, then getting rich usually means staying put.

Said Young: "We have this idea of mobility and migration as part of America, but it's less and less true."