The real estate market in some of the richest pockets of the Northeast is flooded with sellers, as homeowners try to unload gorgeous properties — and their high tax rates.

There also is evidence that Americans are not just moving to smaller homes in town but fleeing high-tax states altogether as they search for more frugal digs.

“Tax the rich. Tax the rich. Tax the rich. The rich leave,” New York Gov. Andrew M. Cuomo, a Democrat, lamented in February as he announced an anticipated revenue plunge in the Empire State. “And now what do you do?”

The population of New York and other high-tax states has posted a demonstrable decline in recent years, sparking a debate on whether there are limits to how much the taxman can squeeze from residents.

The issue is particularly acute as the April 15 income tax filing deadline approaches — the first since the Republicans’ tax overhaul capped the amount of state and local taxes that can be deducted on federal returns.

The $10,000 limit has left governors in high-tax states steaming and has sent Democratic politicians scrambling to try to offer breaks to the same wealthy Americans they usually demand pay their fair share.

“It is having a big impact,” said Chris Edwards, tax policy director at the Cato Institute. “There was migration before, but there has always been disputes about the causes with the data. Now I suspect a lot of people are just getting fed up.”

Mr. Edwards’ data shows a net outflow in 2016 of almost 600,000 people from the 25 highest-tax states to the 25 lowest, and they took with them roughly $33 billion in income.

For the 2018 tax year, the combined state and local tax bill that won’t be deductible comes to $323 billion, according to the Treasury Department’s estimate, and that whopping total will be borne by fewer than 11 million taxpayers.

Most of the affected taxpayers are higher earners who already pay most of the nation’s income taxes. The cap on state and local tax deductions affects only those who itemize their returns, which in the past accounted for 27% of filers, according to the IRS.

When Republicans pushed through the tax changes in late 2017, they suggested that high-tax states could cut their own taxes, thus saving residents the pain.

Maryland Gov. Larry Hogan, a Republican, tried. He proposed a bill to try to reduce taxes for retirees because many have been leaving over high tax bills.

Democrat-led states, meanwhile, attempted quirky workarounds, such as giving wealthy taxpayers an option of paying some of their taxes as charitable contributions, thus offering a break to offset the cap on state and local tax deductions. The IRS said it would reject those maneuvers.

Migration is one sure way to dodge the hit. The median home price now in Summit, New Jersey, is $868,200 but tops $1.3 million in Darien, Connecticut.

Just how many people avail themselves of that option, however, is not clear.

Moody’s, a financial analysis firm, concluded this week that the limit on state and local tax deductions “isn’t causing people to flee New York.” Moody’s analysts said that although Democratic politicians in the Northeast are laying the blame for a population decline on the tax change, demography is a bigger contributing factor.

Bloomberg News echoed that view last year by declaring: “Many from tri-state talk of fleeing to Sunshine State to avoid high taxes, but few actually do.”

But Mr. Cuomo and other politicians say they do see the evidence. The emergence of online advice for moving to low-tax states suggests a market for such decisions.

“Tax planning: How to claim Florida as your state of residence to save on taxes,” blared a recent advice piece from Kiplinger’s.

“The easiest way to do that is to sell your place up north and move down south,” the website said. “Of course, for many retirees, it’s not that simple. You may want to keep the northern home in your family or return there during the summer months.”

Vigilant state collectors are increasingly aware of the advantages a lower-tax state confers on homeowners and consequently gives such returns additional scrutiny, analysts say.

At least one app available helps high earners keep track of the number of days they spend in a low-tax locale so they can prove their claim that they live in the lower-tax jurisdiction, even if they maintain multiple homes.

“If you’re going to move, you really have to do it. You can’t pretend,” said Verenda Smith, deputy director of the Federation of Tax Administrators.

Mr. Edwards insists that high-tax states are worried about high earners leaving and blowing huge holes in state budgets, but Ms. Smith said auditors are taking steps to fight back.

“Believe it or not, most of the activity in the past has been in Iowa, where you had people selling farms,” she said. “But tax authorities in New York state in particular have invested heavily in nonresident audits. They’ve found it’s a very lucrative place to look.”

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