But savings were not entirely driven by healthier people who switched to the plans. They were also achieved by more efficient use of the health system. Narrow network enrollees used the emergency department less, particularly for conditions treatable in office settings. The per-visit cost of outpatient care also fell for narrow network enrollees, which would be expected if the plans paid lower prices. The authors did not find evidence that patients in narrow network plans used lower-quality hospitals, consistent with other work that suggests networks can be narrowed without sacrificing quality.

The savings were concentrated among enrollees who retained their primary care physician as they switched plans. And the distance that narrow network enrollees traveled for primary care visits — but not for specialists — fell. This suggests that plans that narrow their networks of costly specialists but maintain or increase their network of primary care doctors are on the right track. Not only can primary care doctors help patients select specialists and hospitals — and advise them when they’re necessary at all — but retaining primary care physician relationships is also important to many patients.

That’s why the results of a recent study of new plans offered in California are especially troubling. Simon Haeder, a West Virginia University political scientist, and colleagues at the University of Wisconsin-Madison and the University of California, Irvine, found that access to primary care physicians was relatively poor for a sample of plans offered through California’s Affordable Care Act Marketplace in 2015. Most Obamacare marketplace plans in California, as well as in other states, are narrow network plans.

Using a “secret shopper” approach, the study found that only about 30 percent of attempts for appointments with specific primary care doctors were successful. In this approach, an individual pretending to be a patient seeking an appointment called the offices of over 700 primary care doctors listed in marketplace plan directories.

In about 15 percent of cases, the doctor did not accept the caller’s plan, despite being listed in its directory. In nearly 20 percent of cases, the directory included the wrong phone number or the number was busy in two calls on consecutive days. Ten percent of doctors called were not accepting new patients. And about 30 percent of doctors called were not primary care physicians, despite being listed as such in the directory.

When callers were able to make an appointment, the average waiting time for a physical exam was about three weeks. In cases for which the caller pretended to have acute symptoms, the average time until an appointment was about one and a half weeks.

“If patients struggle to obtain primary care appointments, narrow network plans may have a rocky future,” Mr. Haeder said. Consumers revolted against managed care in the 1990s, he notes, and they could very well revolt against poorly managed and loosely regulated narrow networks.