WASHINGTON — People with health insurance saw increases in their medical costs slow from 2009 to 2011, signaling potential structural changes in the industry that could cut health-care inflation and save the U.S. government hundreds of billions of dollars, according to two studies.

The changes include greater use of generic drugs, higher out-of-pocket costs and more efficient care, a trend encouraged by the 2010 health-care overhaul, said David Cutler, a Harvard University health economist. If they permanently slow growth, the government may reap $770 billion in unexpected savings from projected expenditures by 2021, wiping out a fifth of the budget deficit, one of the studies found.

The studies, published Monday in the journal Health Affairs, suggest that while the recession accounted for almost 40 percent of the decline, hitting those who can’t afford medical care, other factors also were at work. The analysis will be part of the debate between President Barack Obama and Republicans over how to control spending growth for Medicare and Medicare.

“Folks have gotten the message: The money flows are going to be different, and they’re very much responding to that,” said Cutler, who co-authored one of the reports.

The two studies aim to shed light on why the annual growth of medical spending slowed from a high of about 8.8 percent in 2003 to an average of about 3 percent per capita from 2009 to 2011, according to data reported in January by the Centers for Medicare and Medicaid Services. Total health spending in the U.S. amounted to 17.9 percent of gross domestic product in 2011 or about $2.7 trillion, the agency said.

While neither study calculated a direct effect from the 2010 Affordable Care Act, Cutler, a former Obama adviser, said in a telephone interview that its influence is “gathering steam over time. It’s not a coincidence these things are happening at the very same time that policies are starting to penalize re- admissions, infections and things like that.”

Opponents of the 2010 law have said the slowdown is almost entirely attributable to the recession, and they expect when the law kicks in full force next year, spending growth will begin to surge again.

In one study, researchers analyzed health spending from 2007 to 2011 by employees with insurance supplied through 150 large companies. The growth of their medical spending dropped from more than 5 percent annually in 2009, adjusted for increases in out-of-pocket spending, to less than 3 percent in 2010 and 2011, the research found.

“I don’t want to downplay the importance of the recession,” said Michael Chernew, a professor of health-care policy at Harvard Medical School in Boston who also was an author of the study. “But even if you get rid of at least the direct effect of the recession, there was really something else going on.”

The indirect effect is harder to gauge, he said. While large firms maintained health insurance for their employees, the recession may have pressured them to work harder at holding down spending growth, he said.

“An alternative theory is that the slowdown in health-care spending growth reflected structural changes in the factors underlying the health-care system and that spending growth will remain low for some period of time, even after the economy fully recovers from the recession,” Cutler said in his paper.

Cutler’s research compared the U.S. government’s growth projections for health spending from 2004 to 2012 with actual increases in the period. It found that the real growth rate was about half of the government’s prediction, leading to a gap of more than $500 billion in 2012 between the projections and spending.

The paper calculates that the recession accounted for about 37 percent of the slowdown in health costs from 2003 to 2011. Declining private insurance coverage and cuts in payments by Medicare, the government health plan for the elderly and disabled, accounted for another 8 percent and the remaining 55 percent is “unexplained,” Cutler wrote. That’s where the structural changes come in, he said.

If the current lower-than-expected rate of growth continues, the country may reap savings of as much as $770 billion through 2021, the research found.

Keith Hennessey, a lecturer at the Stanford Graduate School of Business and former director of the U.S. National Economic Council under President George W. Bush, said he believes growth will increase again once the health-care overhaul kicks in starting next year.

Hospitals and doctors supported the law “because they thought the increased revenues they’d get from increased demand for their goods and services would exceed lower payments for those goods and services, which suggests to me total health spending will be increasing,” Hennessey said. “As a general rule in designing federal health programs, more coverage costs taxpayers more money.”

That Cutler data also contradicts an April 23 finding by health economists at the nonprofit Kaiser Family Foundation of Menlo Park, Calif., and the Altarum Institute of Ann Arbor, Mich., which said the recession accounted for about 77 percent of the slowdown.

“The one thing that is still clear is that I think we’re all in agreement that not all of the slowdown is attributable to the economy or to the recession,” said Charles Roehrig, the Altarum economist who was one of the authors of the earlier report.

Also in Health Affairs, research by the nonprofit Center for Studying Health System Change in Washington challenges the idea, promulgated by hospitals and insurers, that cuts in payments by public programs such as Medicare and Medicaid lead to a “cost-shift” to employers and other private payers.

Hospitals with relatively slow growth in Medicare payments from 1995 to 2009 also saw relatively slow growth in payments from private insurers, said Chapin White, a researcher at the center. A 10 percent reduction in Medicare payments led to a 3 to 8 percent reduction in private payment rates, he said.

“These payment rate spillovers may reflect an effort by hospitals to rein in their operating costs in the face of lower Medicare payment rates,” he wrote. “Alternatively, hospitals facing cuts in Medicare payment rates may also cut the payment rates they seek from private payers to attract more privately insured patients.”

The results argue against repealing cuts in Medicare payments, he said, because that may lead to increased charges to private payers as well.