Massachusetts will be responsible for at least $162 million in new costs over the next decade to fund the federal expansion of health insurance coverage, according to a new report.

The paper from the Pioneer Institute, a free-market-oriented Boston think tank, said that additional spending will squeeze the state budget and divert money from other priorities such as education and transportation.

The costs come in the form of a fee that is part of the Affordable Care Act, which extended insurance coverage to millions of people. The law makes more Americans eligible for Medicaid and provides subsidies to many people on private insurance plans, depending on their level of income. Pioneer said it is the first organization to calculate the long-term costs of the fee.

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State and federal officials have negotiated a deal to delay a federal policy that threatened to destabilize health insurance rates at small businesses across Massachusetts.

Governor Charlie Baker’s administration said Tuesday that the agreement will postpone for one year a piece of the Affordable Care Act that requires a change in the way small businesses’ insurance rates are calculated. Massachusetts will have to phase out its current rules and switch to the federal formula by 2019.

The rules apply to businesses with 50 or fewer employees.

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The Affordable Care Act is now six years old. Perhaps more important for Massachusetts, this month marks the 10th anniversary of “Romneycare,” making it a good time to review that law’s impact.

Governor Mitt Romney’s original proposal was simple: Stop subsidizing hospital care and redirect the money to ensure that all residents have “minimum coverage”—in his mind, catastrophic insurance. Individuals could choose and pay for anything beyond that. The premise was that taxpayers should not have to cover the cost of care for those unwilling to pay for it.

A Health Connector was to serve as an exchange where individuals could buy insurance directly and which would test-drive market reforms. Unlike President Obama, Romney did not implement his creation.

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When President Obama’s landmark health care law ushered in a slew of new insurance options in 2013, the Andersons could not wait to sign up. But in April, when Roger Anderson fell while hiking and hurt his shoulder, he discovered, to his dismay, that simply being insured was not enough. The Andersons’ mid-tier health care plan costs them $875 a month and requires them to meet a $7,000 deductible before insurance payments kick in. Their experience echoes that of hundreds of thousands of newly insured Americans facing sticker shock over out-of-pocket costs.