The Department of Revenue won’t certify the official amount raised until later this year. But the estimates immediately buoyed supporters’ claims that the surtax would deliver much-needed revenue for the state despite fears it could drive out some of the state’s wealthiest residents.

“Opponents of the Fair Share Amendment claimed that multi-millionaires would flee Massachusetts rather than pay the new tax, and they are being proven wrong every day,” said Andrew Farnitano, a spokesperson for Raise Up Massachusetts, the union-backed group which pushed the 2022 ballot initiative.

“With this money from the ultra-rich, we can do even more to improve our public schools and colleges, invest in roads, bridges, and public transit, and start building an economy that works for everyone,” Farnitano said.

Voters approved the measure in 2022 to levy an additional 4 percent tax on annual earnings over $1 million. At the time, the Massachusetts Budget and Policy Center, a left-leaning think tank, projected it could generate at least $2 billion a year.

State officials last year put their estimates slightly lower at up to $1.7 billion, and lawmakers embraced calls from economists to cap what it initially spends from the surtax, given it may be too volatile to rely upon in its first year.

So far, it’s vastly exceeded those expectations, generating nearly $1.4 billion alone last quarter, which coincided with a better-than-expected April for tax collections overall.

State officials said that they raked in $1 billion more in tax revenue overall than they had projected in April. That marked a stark reversal from earlier in the fiscal year, when collections lagged expectations for months, prompting state officials to slash spending, downgrade their revenue forecast, and, last month, freeze some state hiring.

Matt Gorzkowicz, Healey’s budget chief, said at the time that officials believe most of the unexpected revenue was generated by the “millionaires tax” and collections from capital gains, all money that state officials largely can’t use to balance the budget.

Revenue from the surtax is constitutionally mandated to go toward education and transportation initiatives, while excess revenue from capital gains must flow to the state’s emergency savings account. Nevertheless, Gorzkowicz said then that state officials believe they’re on track to close the fiscal year at the end of June in line with projections.

Massachusetts has struggled with residents leaving the state in recent years.

In 2021 — before the “millionaires tax” took effect — Massachusetts said goodbye to taxpayers with a collective $4.3 billion in adjusted gross income, an increase of 40 percent from the prior year, according to an analysis by the Pioneer Institute. Nearly 25,200 more tax filers moved out of Massachusetts than moved in, the data show.

A recent analysis by Boston Indicators, the research arm of the Boston Foundation found that the people moving out of Massachusetts across 2021 and 2022 were predominantly middle- and high-income earners, and college-educated.

Particularly dire: Working-age adults are leaving in droves. On net, Massachusetts lost an average of 22,631 people ages 25 to 44 across 2021 and 2022 — the largest number of any age group and a marked increase over previous years, according to the report.

Exactly why — and how much the tax environment may have contributed — wasn’t completely clear, as the state has also struggled with a housing crisis that has pushed families and others to seek more affordable locales.

The same analysis found that the state’s population rebounded last year, with a gain of nearly 11,500 residents from July 1, 2022, to July 1, 2023, as immigration numbers rebounded from pandemic-era lows.

“Whatever short term financial benefit the state will receive from the income surtax will be outweighed by the long-term negative effect this tax is having on the state,” said Paul Craney, a spokesperson for the conservative-leaning Massachusetts Fiscal Alliance.

Phineas Baxandall, the Mass. Budget and Policy Center’s interim president, said Monday that the take from the tax shouldn’t be shocking. A state analysis five years ago predicted that the “millionaires tax” could generate nearly $2 billion, he said, and “income has further concentrated at the top since then.”

“This isn’t surprising,” he said.

State Senator Michael Rodrigues, the state’s budget chief, said on the Senate floor Monday that excess revenue from the tax could ultimately come close to $1 billion for this fiscal year. Under language lawmakers passed last year, 85 percent of any “excess” revenue is transferred to an account reserved for one-time projects or spending, such as road maintenance, school building projects, or major public transportation work.

“We will not have any problems identifying those,” Rodrigues said. “As we all know, [transportation and education] are two areas of immense need.”

Material from the State House News Service was used in this report.

Matt Stout can be reached at matt.stout@globe.com. Follow him @mattpstout.