“It was a trend that was happening; we noticed that trend; we took advantage of that trend,” said Jason L. Furman, the chairman of the White House’s Council of Economic Advisers. “Some of it was the Affordable Care Act catching up with the private sector, and some of it was pushing the private sector forward.”

Administration officials have pointed to falling hospital readmission rates as one strong sign that cost-control provisions in the Affordable Care Act are working. Also, they noted that a growing number of insurers and health care providers are agreeing to contracts that pay for the quality of care, rather than the quantity, another indication that the law’s encouragement on that front is starting to pay dividends.

But those are responsible for only a tiny portion of the slowing rise of health care costs; other changes, like rising deductibles and copays that discourage some people from seeking extra services, play a bigger role, analysts say. Still, the Kaiser Family Foundation, a nonprofit research group, estimates that the weak economy accounts for as much as three-quarters of the slowdown in the growth of spending on health care.

But even if only about a quarter of the savings is because of noneconomic factors, said Larry Levitt, a top official at the Kaiser Family Foundation, “that’s real change in the health system.”

Critics, however, say they see little evidence that the law will lead to significant cost savings.

“These claims are just as groundless as the ones that misled so many Americans to believe they would be able to keep their previous coverage,” argued Charles Blahous, a former Bush administration official now at the Mercatus Center at George Mason University.