The study predicts that the president’s actions will have only minimal effect on enrollment and premiums in 2015.

“We figured that enrollment would go down about 4 percent, or about a half a million, for 2015,” said Evan Saltzman, the study’s lead author and a project associate at Rand, a nonprofit research organization.

Rand projects that 12.2 million people will be enrolled in private health insurance plans by 2015, a figure that closely tracks the prediction of the Congressional Budget Office, which forecast that 13 million would be enrolled by 2015. The Rand study also projects a 1 percent increase in premiums that year due to Obama’s pledge.

Researchers used an economic model based on data about how people make insurance decisions and how firms decide to offer health coverage to employees and their families. The model predicted that people eligible for federal subsidies would tend to seek insurance on the marketplace in much larger numbers, even if they had the option of renewing their noncompliant plans. Researchers also found that older consumers would tend to move to the marketplace because of new protections that restrict insurance companies from charging a 64-year-old enrollee more than three times what they charge a 21-year-old enrollee.