Still, two of the state’s largest insurers, MAPFRE and Liberty Mutual, increased their rates by 3 percent, well above the average.

The state Division of Insurance required all insurers to take into consideration the reduced driving of policyholders in 2020 and 2021 in the rates that are now in effect.

An analysis by the DOI shows an increase in average rates of “only .43 percent, with most filings reflecting a decrease in rates,” the DOI said this week.

In a statement, the DOI cited as a factor in moderating rate increases its “work to ensure rates are actuarially appropriate and reflect 2020 and 2021 driving habits.”

Among the state’s five largest auto insurers, which together represent more than 60 percent of the market, MAPFRE (about 22 percent of market) and Liberty Mutual (9 percent) were the only ones to implement rate increases, according to DOI data.

GEICO (15 percent of market) made no change in its rates; Arbella (8 percent) lowered its rate by one-half of 1 percent; and Safety Insurance (8 percent) lowered its rates by 2.3 percent, according to DOI.

About 40 companies write auto insurance in Massachusetts.

But big increases in auto insurance rates may be coming.

“Inflationary trends continue unabated in 2022 and MAPFRE will adjust its rates as may be needed to reflect increased auto claim costs,” the company said in a statement this week.

Tom Wilson, CEO of Allstate, one of the country’s largest auto insurers, said in an interview on Bloomberg Television this week that premiums will have to climb for insurers to recoup some of the expenses lost to inflation.

“We have to raise our prices,” he said, referring to Allstate and its competitors.

MAPFRE’s rate increase came despite objections from the Office of Attorney General Maura Healey, which has no control over the DOI but reviews proposed rate increases as required under state law.

In December, the attorney general’s office called upon the DOI to reject the MAPFRE rate increase, calling it “excessive.”

The DOI did not respond to that letter and the rate increase went into effect in January.

Companies that sell auto insurance in Massachusetts are free to set their own rates, but the state insurance commissioner has the authority to review them to make sure they aren’t excessive, in which case approval can be withheld.

Insurance companies are also free to file for rate changes whenever they choose. The DOI, however, made an exception last year when it required all insurers to make one-time rate filings that took into consideration the impact of reduced driving during the pandemic. Those filings resulted in the rates now in effect.

Since the pandemic began, the attorney general’s office has fired off a half-dozen letters to the DOI, arguing policyholders deserve substantial refunds or reductions in premiums to drivers.

In March 2021, the attorney general’s office said auto insurers reaped about $700 million in extra profit during the pandemic, and urged the DOI to “stop” insurers from “continuing” to “overcharge” consumers.

The most recent letter from the attorney general’s office came in December, following the DOI’s decision not to object to MAPFRE’s pandemic-impacted rate filing.

In that letter, Glenn Kaplan, chief of the unit in the attorney general’s office that deals with insurance matters, objected to MAPFRE’s proposed rate increase and asked the DOI to “take a further look at the company’s proposal.”

“Since April of 2020, we have written to you a number of times regarding the need for insurers to reduce auto premiums in light of the pandemic,” Kaplan wrote in the letter to the DOI.

“Instead of dropping rates, [MAPFRE] is now seeking to increase them. The company’s filing contains an overall increase of 3 percent, with some policyholders receiving increases as high as 13 percent.”

Kaplan wrote that MAPFRE’s rate filing assumed “that nothing has changed as a result of the pandemic.” But, Kaplan continued, “the ongoing presence of COVID-related behavioral changes, especially in light of recent virus variants developments, shows that things are not simply continuing from 2019 as if the pandemic never occurred.”

In a statement released this week, MAPFRE said it “respectfully disagrees” with Kaplan.

“MAPFRE’s rates and premiums are based upon data, and the effect of the pandemic was reflected in the company’s rate filing,” the company said.

“In 2021, we saw a continued increase in the severity of accidents and a substantial upturn in the cost of repairs due to the inflationary environment and supply chain pressure,” MAPFRE said.

“MAPFRE took an overall increase of 3 percent effective January 2022, which took into account changes in driving frequency and patterns, and sought to address the rapid increase in loss costs,” the company said.

A spokesperson for Liberty Mutual also defended its rate increase.

“A significant rise in claims severity, driven largely by sharp inflationary increases in labor rates, and repair, used car and medical costs, is impacting auto insurance costs,” the spokesperson said. “For the first time since 2017, we requested and were approved for a Liberty Mutual rate increase in Massachusetts.”

Got a problem? Send your consumer issue to sean.murphy@globe.com. Follow him on Twitter @spmurphyboston.