The United States and global markets alike are still plagued by the threat of financial institutions that are "too big to fail," Gary Stern, former president of the Minneapolis Federal Reserve Bank, told CNBC on Monday.

"We still have a 'too big to fail' problem," he said, referring to the theory that some financial institutions are so large that their collapse could send shock waves through the economy.



But Stern told "Closing Bell" that some of the steps taken by the Federal Deposit Insurance Corp. and the Federal Reserve have resulted in progress. For example, he said, the implementation of the so-called living will, or recovery and resolution plan, is a move toward increased transparency.



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"I think if that is done well ... if the regulators insist that it be done well and they get bank board of directors involved, we can rein in—not eliminate—but rein in too big to fail, diminish the scale of the problem, reduce the probability of severe financial crises," Stern said.



Economist Simon Johnson, speaking at the American Economic Association's annual meeting in Philadelphia this weekend, countered that the living will does not provide enough transparency, for instance, about which pension funds or global money market funds are exposed to a troubled bank.

Stern agreed with that assertion but said it's a good start.



"We've got to pay attention to who the counterparties are, who has the exposure, which markets do these institutions rely on for funding and so forth," he said. "Those are issues that require a fair amount of resources to really get your arms around. But it's not impossible, and I think good process is being made."



—By CNBC's Drew Sandholm. Follow him on Twitter @DrewSandholm