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.

Medicare Advantage versus traditional Medicare is a politically fraught topic, as President Obama's healthcare law exacted cuts from Medicare Advantage over Republican objections.

Democrats argued that they were reining in excess Medicare Advantage payments to bring them in line with what fee-for-service Medicare pays. But Republicans and other advocates for Medicare Advantage objected to cutting the popular program, which has steadily enrolled more seniors every year since its inception and prompts private insurers to compete against each other.

"If Medicare Advantage prices are lower than those of [fee-for-service] Medicare, then Medicare can obtain the same quantity of services for less money through Medicare Advantage," the study's authors wrote.

The researchers calculated the average price per admission for seniors with Medicare Advantage, traditional Medicare and private insurance. After taking into account differences in hospital networks and geography, they found Medicare Advantage plans paid 5.6 percent less on average for hospital services. When narrower provider networks weren't factored in, the difference was 8 percent.

The researchers also found that rates paid by commercial plans were much higher than those paid by Medicare Advantage and traditional Medicare.