The Republican decision to repeal Obamacare's penalties for going uninsured will result in 4 million fewer individuals choosing to purchase coverage over the next decade, according to a new actuarial analysis that sees a more modest impact from the elimination of the mandate than previous estimates.

The numbers are likely to create further debate over how effective Obamacare's individual mandate was in compelling people to buy health insurance, particularly among parts of the population who are able to obtain medical coverage at little or no cost to themselves.

The latest findings from the Office of the Actuary, which is part of the Centers for Medicare and Medicaid Services, differs sharply with the Congressional Budget Office, which projected that the repeal of the penalty in the Republican-backed tax law late last year would cause 13 million more people to become uninsured over a decade.

The CBO's higher estimates on the effect of the individual mandate played a crucial role in the two major legislative debates last year – healthcare and taxes. During the healthcare debate, CBO's assumptions about the mandate were a major part of its projections that Republican plans to repeal and replace the law would significantly increase the number of uninsured Americans. The projections became a central line of attack from Democrats and pro-Obamacare activists, and helped give centrist Republicans cold feet about unraveling the law. On the flip side, in crafting their tax law, Republicans took advantage of CBO's big assumptions about the mandate to help their budgetary math. CBO has been revisiting its analysis and has said that based on the information it has compiled it expects its future projections to be lower.

Throughout the healthcare debate, Republicans criticized CBO, questioning its assumptions that low income individuals who could qualify for free or near free care would forgo coverage just because the mandate would be going away.

The fine from Obamacare will go to zero in 2019 and CMS projects that uninsured rolls will rise by 3.5 million as a result of the mandate repeal by 2020, accounting for the bulk of the 4 million it predicts would choose to go uninsured by 2026.

CMS and CBO did agree that shortly after the repeal of the fine, roughly 2 million of those who will become uninsured will choose to forgo coverage their employer offers them. But the agencies primarily differ over their predictions about the impact the individual mandate will have in two other areas: Medicaid, which is almost fully paid for by the government, and the Obamacare exchanges, where certain customers can purchase private coverage subsidized by the federal government.

CBO projected that Medicaid rolls would fall by 5 million, while CMS actuaries indicated they believed Medicaid enrollment wouldn't have a noticeable impact.

"We do not expect an impact on the Medicaid enrollment trend at this time," said Gigi Cuckler, an economist for the Office of the Actuary.

CMS predicted that the roughly 2 million others, out of the 4 million total, would come from the pool of people who would choose not buy health insurance through the Obamacare exchanges, particularly those whose income is comparably higher than others. Under Obamacare, a person making more than $48,240 does not qualify for subsidies. The estimates suggest that people who receive subsidies from Obamacare, some of whom can purchase private coverage at no cost, are more likely to stay enrolled in coverage.

"These estimates assume that some younger and healthier people will choose to be uninsured, particularly those with comparatively higher incomes who would not qualify for premium subsidies in the marketplace," Cuckler said.

CBO forecasts, in contrast, puts more weight to non-financial factors. For instance, has noted that health insurers have threatened to leave the exchanges without a mandate, making coverage options unavailable.

In a presentation made public, CBO officials also revealed one of the reasons they believed fewer people would be enrolled in Medicaid: They presumed a portion of enrollees who think they have to buy health insurance because of the mandate head to the exchanges only to learn they qualify for no-cost Medicaid coverage instead.

The total number of people who are uninsured over time is expected to grow because of factors outside the individual mandate repeal, according to CMS. Its analysis projects that by 2026 the number of uninsured will rise to 37.7 million people, a 9.1 million increase from 2016, when the number of uninsured in the U.S. reached a historic low.

John Poisal, deputy director for the National Health Statistics Group, noted the expected trend showing a rise in the number of people who are uninsured is "influenced by economic factors, such as the impact of growth in GDP, and employment on private health insurance enrollment, as well as growth in population."

The projections, which come out annually by CMS, do not make any assumptions about what new legislation might influence enrollment and spending, meaning that they presume no other healthcare law will pass and acknowledge that this is a key uncertainty in laying out forecasts.

Editor's note: This story has been updated to clarify the breakdown of health insurance customers who would choose to be uninsured, and to add more details throughout.