Under the GOP plan, the cap on these “Health Savings Accounts” would nearly double, from the current family limit of $6,750 to a proposed $13,100.

“Republicans have long said that we have to empower patients as consumers to spur competition and bring down costs,” House Speaker Paul D. Ryan (R-Wis.) wrote in an op-ed in USA Today. “That’s why we will also nearly double the amount of money you can contribute to health savings accounts to pay for out-of-pocket expenses. This will end Obamacare’s limits on how you save and spend your health care dollars.”

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Health policy specialists say the accounts in their current form tend to be attractive to higher-income people who face higher marginal tax rates and benefit more from taking a deduction. Treasury data shows that in 2014, more than half of the total amount directly contributed to health savings accounts came from households making more than $100,000 a year.

Doubling the contribution limit — which is $3,400 for an individual and $6,750 for a family — would make them more attractive mainly for people who have plenty of extra cash to increase their contributions.

Most of the attention to the Republican health-care bill has focused on the way it will cut taxes and redistribute subsidies in ways that could help younger and wealthier people at the expense of low-income and older people, particularly in areas of the country with high health- care costs. Those concerns triggered amendments, unveiled Monday, aimed at providing an additional $85 billion in aid to people between ages 50 and 64.

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But the proposed changes to health savings accounts, which can be used with qualifying high- deductible health plans, are another area where changes would increase benefits largely to higher-income people.

“These funds are nice tax shelters for high-income people,” said Linda Blumberg, a senior fellow at the Urban Institute. “If you are a modest-income person, the tax benefit is not very valuable to you because your tax rate is much lower, and you may very well not have the money to put in there.”

The accounts are what tax wonks call “triple tax advantaged,” meaning people: 1) pay no taxes on the money they put in, 2) pay no taxes on investment income and 3) get to withdraw money without paying taxes when they use it for health expenses. The accounts are a core part of a conservative vision of health reform, with the idea that they give consumers control and choice and will encourage greater competition as people shop around for the best care.

An analysis from the Tax Policy Center found that more than 16 percent of people who filed taxes with an income above $200,000 made contributions to a health savings account, compared with fewer than 2 percent of those who made less than $30,000. Data from the Treasury Department show that of those who make deposits into their accounts — and therefore receive the tax advantages of deducting the amount from their income — more than 60 percent make more than $75,000 a year.

The question then becomes whether the changes proposed in the Republican plan would expand the use of the program. The Republican plan would nearly double the contribution limits and halve the penalty for withdrawing money for non-health-care-related expenses, from 20 percent to 10 percent.

Tom Miller, a resident fellow at the American Enterprise Institute, said that increasing the limits on how much people can contribute was not likely to cause a huge surge in their use. The Joint Committee on Taxation estimated that changing the contribution limit would cost $19 billion over a decade.

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“It just doesn’t add a whole lot, where they’re increasing the limits on how much you can contribute," Miller said. "They tend to be more attractive to upper-income people."

An analysis from Devenir Group, a research firm, found that nearly half of the contributions to health savings accounts in 2016 came from employees, for an average contribution of $1,786, with an average employer contribution an $868. In accounts not associated with an employer, the average contribution was $1,713. That's far below the combined limit of $3,350 for an individual or $6,750 for a family for that year and suggests that many people are not rubbing up against the current limit.

“It’s likely a small percentage of individuals and families that actually maximize their contribution,” said Eric Remjeske, president of Devenir.

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Those who would benefit from the higher limits would need to have sufficient discretionary income to put even more money toward their future health-care needs.

“The current changes ... are focused on enhancing aspects of HSAs for existing account holders,” Mark Fendrick, director of the University of Michigan's Center for Value-Based Insurance Design, wrote in an email. “These tend to be higher-income earners. There is nothing I see that makes high-deductible health plans more attractive to those who are not already enrolled.”

Where the changes may make a big difference is for people who have maxed out other tax- advantaged retirement accounts — who tend to be wealthy people. For that group, halving the penalty for a withdrawal for a non-health reason may be an added reason to increase their contribution.

Edwin Park, vice president for health policy at the Center on Budget and Policy Priorities, said that people at the upper end of the income spectrum tend to end the year with big balances in their accounts, while lower income people are more likely to spend the money in the account each year.