Photo: Ted Shaffrey, Associated Press

California lost a very small but statistically significant percentage of high-income residents after voters approved Proposition 30 — the 2012 ballot measure that raised the top state income tax rate to 13.3 percent, the highest in the nation — according to a new working paper from three researchers.

The state lost an estimated 138 high-income individuals, or about 0.04 percent of the roughly 312,000 people subject to the tax increase, said co-author Charles Varner, associate director of the Stanford Center on Poverty and Inequality.

The research comes at a time when more Californians are at least threatening to leave the state because of high taxes and housing costs. The rumblings have escalated since the federal tax law that passed in December capped the previously unlimited federal itemized deduction for state and local taxes at $10,000.

“It remains to be seen what kind of effect (that change) might have, and we will be looking at that as the numbers come in,” said Varner, adding that he expects any effect on migration to be small.

The new paper updates a study on migrating millionaires that Varner and Stanford sociology Professor Cristobal Young published in 2012. That report looked at the movement of millionaires into and out of California after voters in 2004 approved a 1 percent tax on income over $1 million to fund mental health services.

Contrary to expectations, they found that the net migration of millionaires into California — millionaires moving in minus those moving out — increased slightly after that tax increase.

“In other words, the highest-income Californians were less likely to leave the state after the millionaire tax was passed,” their report said.

The tax increase approved in November 2012, however, was much larger than the mental health surcharge.

“One reason we wanted to update our previous paper is that this tax change in 2012 is the largest state tax change that we have seen in the U.S. for the last three decades,” Varner said.

For singles, Prop. 30 raised the rate by one percentage point on income between $250,000 and $300,000; by two points on income between $300,000 and $500,000; and by three points on income over $500,000. The income thresholds are doubled for married couples and indexed to inflation.

This brought California’s top rate, including the mental health tax, to 13.3 percent. (These increases were supposed to expire in 2019, but in 2016 voters extended them to 2030.)

The new working paper looked at taxpayers who were and were not subject to those rate hikes and found that in the two years before the increase (2011 and 2012), net in-migration for both groups “was positive and roughly constant.”

However, after 2012, net in-migration declined for those facing an effective tax increase of 0.5 percent or higher. The drop was largest for the group facing the highest effective tax increase, wrote the authors, who included Allen Prohofsky of the California Franchise Tax Board.

They noted that domestic migration accounts for a tiny portion of the change in the state’s millionaire ranks. That population fluctuates by more than 10,000 people from year to year, and migration accounts for 50 to 120 people, or about 1 percent. The remaining 99 percent “is due to income dynamics at the top — California residents growing into the millionaire bracket, or falling out of it again.”

The millionaire population is highly correlated to the financial markets. The researchers found that the median person who earned at least $1 million in a given year earned at least $1 million in only seven of the 13 years before and after that year.

That could be one reason people don’t pull up stakes after a tax increase. Another reason: It’s hard to move when you have a high-paying job, a spouse who may work and kids. The report found that married people with children are less sensitive to the tax increase than married people without children.

One thing that tends to make people of all income levels leave the state is divorce.

“In the year of divorce, the migration rate (for all taxpayers) more than doubles, and remains slightly elevated for two years after the event,” the report said.

The “core question” of both studies “is whether raising taxes on the rich reduces their net migration into the state,” the paper said.

Although the first study showed a counterintuitive result (more rich people coming than leaving), after the 2012 tax increase, “we observe a statistically significant effect in the expected direction,” albeit a small one, the authors wrote. “We estimate that California lost 0.04 percent of its top earner population over the two years following the tax change.”

The latter result was “consistent with what we found” in a 2011 study that examined the migration response to a tax increase in New Jersey, which raised its top rate by 2.6 percentage points, Varner said.

This year, Massachusetts voters will decide whether to increase its tax on income over $1 million by 4 percentage points. Its current rate is 5.1 percent.

The Pioneer Institute, a free-market think tank in Massachusetts, published a paper citing eight reasons why it thinks Young and Varner’s previous paper underestimates millionaire migration. Young published a rebuttal to those assertions.

Among other things, Young noted that only 11 percent of millionaires in the study made their money primarily from capital gains and that most “are the working rich.” He found no difference in tax flight among the two groups but is still doing research on capital gains.

“What we found is that net migration of millionaires to California was positive over the whole period we studied,” from 2007 to 2014, Varner said. “This suggests that the state has consistently become a more attractive place for top income earners to live.”

That echoes the results of another recent study conducted by Beacon Economics for San Francisco think tank Next 10. It tried to explain why California lost nearly 1.1 million more people to other states than it gained between 2006 and 2016.

It concluded that “the main driver for net out-migration appears to be high housing costs,” not high state income taxes. That’s because the “vast majority of people who moved out of California were concentrated in lower-skilled, lower-paying fields.” People moving out probably paid little or no state income tax because California’s tax structure is highly progressive, it said.

Kathleen Pender is a San Francisco Chronicle columnist. Email: kpender@sfchronicle.com Twitter: @kathpender