The dramatic drop in the price of oil since 2014 has delivered only a muted boost to the U.S. economy, but that could change if households start figuring cheap oil is here to stay.

That conclusion, in research published Monday by the San Francisco Federal Reserve Bank, suggests that the longer the price of oil stays low, the better the news is for a recovery that has been moderate at best.

That's significant for a central bank that is seeking evidence that the economy is strong enough for it to continue to raise interest rates from their current level of 0.25 percent to 0.5 percent.

Oil currently sells near $40 a barrel, down from around $100 a barrel two years ago, but households have generally assumed the decline is temporary, wrote the Fed researchers. That's pared about 30 percent from the impact that would otherwise be expected, they concluded.

"Because the decline in oil prices is considered temporary, households with less information do not believe their future income will rise as much as they would if they had full information," the researchers said. "As a result of this less-informed perception, they choose to spend relatively less. In turn, the more muted consumption response translates into a more muted overall boost to economic activity."

Still, that muted effect could be temporary, if households begin to see cheap oil as permanent, they conclude.

"Continued low oil prices could change consumer perceptions, leading them to increase spending as they learn about this greater degree of persistence," they wrote.