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More than 9 million Americans have gotten health insurance for the first time thanks to Obamacare, according to a new report from the Rand Corporation.

Most of the people who got new insurance didn’t buy it on the Obamacare exchanges but rather signed up with an employer, the survey found. Rand says that 8.2 million people have gained insurance from an employer since September — more than 7 million of them who had no health insurance before.

“We see that of the 40.7 million who were uninsured in 2013, 14.5 million gained coverage, but 5.2 million lost coverage, for a net gain in coverage of approximately 9.3 million,” the Rand report reads. Only about 1 million lost their private plans, and another 2 million lost employer-sponsored coverage.

The report adds to a growing number of studies trying to determine just what effect the 2010 Affordable Care Act is having on rates of health insurance in the U.S. The law is designed to start transforming the U.S. healthcare system in part by getting insurance to more people.

Most Americans get their health coverage through an employer, and the law requires more employers to provide health insurance.

Two other reports published in the past week show the rate of people lacking health insurance has fallen to about 15 percent in recent months, and the Rand survey supports this.

The Obama administration says more than 7 million people have signed up for health insurance on the new, online exchanges. The Rand survey of 2,425 adults estimates a much lower number — 3.6 million — but the researchers say their findings do not reflect everyone who may have signed up in the final days of open enrollment in March.

“Although a total of 3.9 million people enrolled in marketplace plans, only 1.4 million of these individuals were previously uninsured,” Rand says in comments on its blog.

“Medicaid enrollment increased by 5.9 million,” it adds. The Obama administration has only claimed 3 million.

Rand also estimates that fewer than 1 million people who had private health insurance lost their coverage when the plans were cancelled because they did not meet the new requirements of the law for providing minimum coverage. “While the survey cannot tell if this latter group lost their insurance due to cancellation or because they simply felt the cost was too high, the overall number is very small, representing less than 1 percent of people between the ages of 18 and 64,” the report reads.

"Urban, Gallup, and RAND all say the number of uninsured is declining since the ACA went into effect. Now we can debate why and by how much," the Kaiser Family Foundation’s Larry Levitt said in a tweet.