Sean Hannity, the Fox News prime-time host, threatened last month to leave New York for a tax haven down south. Tiger Woods transplanted himself from California to Florida for the same reason. The actor Gerard Depardieu decamped from France and sought citizenship in Russia after complaining that 85 percent of his income was consumed by taxes.

“I can’t wait to pay no state income tax down in Florida or Texas,” Mr. Hannity, who lives in Nassau County, said. “I haven’t decided yet, but I’m leaning Florida because I like the water and I like to fish.”

But a new analysis being released Monday undermines the frequent assertion that wealthy people reflexively flee New York City — where Mayor Bill de Blasio campaigned to raise taxes on those who make more than $500,000 — for low-tax states.

The study, by the city’s Independent Budget Office, found that the share of higher-income households that moved from the city in 2012, 1.8 percent, equaled the share of lower-income households that left.