Privately run Medicare plans pay hospitals about 5 percent less for services than traditional Medicare, according to a new study that provides some insight into how the government could save money on healthcare for seniors.

Medicare Advantage plans, which are run by private insurers and cover about one-third of U.S. seniors, pay hospitals 5.6 percent less on average than the traditional Medicare program, which operates on what is known as a fee-for-service model, according to a study by Stanford researchers published Monday in the journal Health Affairs.