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Massachusetts drivers are starting to see higher auto insurance rates, four years after they tumbled when the state opened the market to more competition.

Many of the state’s largest auto insurers have raised rates in each of the past two years, citing the need to keep pace with the rising cost of claims for car accidents, theft, and injuries.

Some companies say they could not make enough money after they dropped rates in 2008 to compete with rival insurers or to gain market share.

The Boston Globe reported last month that major insurers have raised rates by a median of 4.3 percent so far this year after a median increase of 4.5 percent last year, outpacing the overall rate of inflation. Auto insurance rates used to be set by the state.

Topics Trends Personal Auto Pricing Trends Massachusetts