Janet Yellen has made it clear she wants to move the Federal Reserve away from a bank-centric regulatory model to one that appropriately tailors rules to the nonbanks that it now regulates. Whether she is able to succeed in this quest may determine the success of her likely chairmanship.

Yellen is only the second person nominated as chairman of the Fed since Alan Greenspan took the helm 25 years ago. Similar to her predecessor, Ben Bernanke, Yellen largely pledged continuity at the helm of the powerful central bank during her confirmation hearing. In Bernanke's 2005 nomination hearing, the most meaningful exchanges focused on two topics that would greatly define his chairmanship.

Bernanke was asked to respond to Warren Buffett, who had warned that the use of derivatives had become a "ticking time bomb" for the financial system. Bernanke responded with the consensus view at the time: "Derivatives, for the most part, are traded among very sophisticated financial institutions and individuals who have considerable incentive to understand them and use them properly. The Federal Reserve's responsibility is to make sure that the institutions it regulates have good systems and good procedures for ensuring their derivatives portfolios are well managed and do not create excessive risk."

Clearly, many of those systems and procedures were flawed. The institutions in question, however, were outside of the Fed's jurisdiction. For that we all paid a heavy price.

Senator Paul Sarbanes (D-MD) then asked about Bernanke's longstanding support for inflation targeting, a policy by which the central bank sets a public, numerical goal for inflation. This was a significant change for the conduct of monetary policy, as Greenspan opposed inflation targeting. Sarbanes questioned both the Fed's legal ability to set an inflation target without setting a corresponding employment target, and the wisdom of doing so, arguing it would be inconsistent with the Fed's dual mandate to focus on both inflation and employment.

Bernanke responded that an inflation target is the best way to achieve full employment: "Senator, I think it is a false dichotomy … I am entirely in favor of maximum employment. I believe that [inflation targeting] is a method to achieve it." Bernanke succeeded and the Federal Reserve adopted inflation targeting.

However, he changed course and also adopted an explicit employment target. In the current debate about when the Fed will taper its current monetary easing, the Fed has publicly given specific employment targets as to when it will act, without linking the action to any specific inflation target.

Confirmation hearings demonstrate both a nominee's worldview, and offer insight into how they may adjust it.

Yellen demonstrated both in her hearing. She reiterated the consensus view that quality regulation is critical to financial stability. Few argue with that premise, but what does it really mean? Is the Federal Reserve's economic model capable of prospectively gauging the level of stress in the financial system as necessary to guide monetary policy decisions? Will Chairman Yellen incorporate financial regulatory decisions, such as whether the Volcker Rule is working or having deleterious side effects, into monetary policy? The Fed's ability to put this thought into action in real-time may determine whether we are on a path to stable financial growth or are just floating between economic bubbles.

Yellen also heard an earful from senators like Jon Tester (D-MT) and Mark Kirk (R-IL) about the Fed's ability to transform itself from a regulator of financial holding companies, primarily banks, to a regulator of nonbank systemically important financial institutions. Can the Fed evolve from a bank-centric regulator into one that can tailor rules and regulations for nonbank entities such as broker-dealers, insurers and consumer finance institutions?

These thoughtful questions have been raised because of unease about what the Federal Reserve has done so far in tackling this new, broader mandate. Yellen appeared to understand the problem, responding that the Fed understands that insurance companies are "different from banks, and we are taking time to study what the best way would be to craft regulations for those organizations."

A significant set of challenges awaits the next Fed chairman on how to adapt the its regulatory rules to properly cover the growing number of nonbanks that it regulates. This may require revisiting prior assumptions, such as with inflation and employment targeting. We all should hope that the next Fed chairman will rise to the challenge and guide the Federal Reserve to landing at the right policy answers to these questions. Much rides on their success.

Aaron Klein is director of the Bipartisan Policy Center's Financial Regulatory Reform Initiative.  He served as a deputy assistant secretary for economic policy in the Obama administration and as the chief economist on the Senate Banking Committee from 2005 – 2009.