The number of Americans without health insurance fell by 3.8 million in the first quarter of 2014, according to an official government report released Tuesday. The comprehensive data, collected by Center for Disease Control and Prevent for its National Health Interview Survey (NIHS), should give an accurate estimate of the number of uninsured Americans at the start of the year. However, it may not give a complete picture of the Affordable Care Act's impact.

The NIHS found that the uninsured rate among people of all ages fell from 14.4 percent in 2013 to 13.1 percent in the first three months of 2014. The estimates are based on data collected from January through March from 27,627 people.

In addition to tracking the uninsured rate, the study showed that 3.7 million people specifically said they obtained coverage through the new Obamacare marketplaces.

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The Obama administration earlier this year said that more than 8 million people signed up for insurance on the Obamacare marketplaces. Additionally, the government said more than 4.8 million people gained coverage through Medicaid and the Children's Health Insurance Program (CHIP), and more than 3 million young adults were able to stay on their parents' health plans due to the Affordable Care Act.

Some critics suggested the administration inflated the numbers by counting enrollees who already had insurance and simply switched plans, or by counting people who signed up for coverage without paying for it.

However, a portion of Obamacare enrollees who gained coverage this year may not have been counted yet by the NIHS. Given the significant technical issues with HealthCare.gov and some state-run Obamacare websites, a significant portion only signed up for plans at the tail end of the enrollment period. In fact, the administration reported that nearly 1 million of those who signed up for private insurance via Obamacare didn't select a plan until after March 31.

In May, Gallup released its own survey showing that more than 8.9 million adults gained health coverage this year.