On Thursday, Fed Chair Janet Yellen told bankers in Kansas City that the central bank might have the ability to help the U.S. economy in a future downturn if it could buy stocks and corporate bonds.
"It could be useful to be able to intervene directly in assets where the prices have a more direct link to spending decisions," she said.
Right now, the Fed is barred by law from buying corporate assets.
It's not the first time this has come up. During congressional testimony earlier this week, Yellen said unlike the European Central Bank and Bank of Japan, the Fed can't purchase equities. She suggested lawmakers may want to consider changing the law.
And in a speech in August at the central bank's annual Jackson Hole Summit in Wyoming, Yellen said, "Future policymakers may wish to explore the possibility of purchasing a broader range of assets."
However, Koesterich said the Fed has taken the wealth effect about as far is it can go.
"We've seen household wealth in the U.S. now at $89 trillion, relative to disposable income it's close to the highs of '07," he said. "It's not clear to me that pushing that up even higher is going to have the effect on the real economy."
Jim Bianco, president of Bianco Research, said he would be uncomfortable with the Fed buying stocks because it would allow them to cast proxy votes.
"When controversial CEO pay or mergers or some kind of other deal comes up … there's the Fed potentially making a critical decision on the management of a company," he said. "And that's not good for them to be in that position."
Plus, capitalism is about giving money to good ideas and taking it away from bad ideas, he said. The Fed doesn't want to make those choices because it doesn't want to be seen as political, and would therefore distort the process, he explained.
That said, Bianco doesn't see Congress passing a law that would give the Fed the power to buy stocks anytime soon.
—CNBC's Linda Sittenfeld, Steve Liesman and Reuters contributed to this report.