Republican presidential candidate, former Massachusetts Gov. Mitt Romney pauses during a campaign rally on Monday, Oct. 8, 2012 in Newport News, Va. (Evan Vucci/AP)

Many of the challenges Mitt Romney would face in choosing a Federal Reserve chairman, should he win the presidency, are the same as those that President Obama would encounter: the need to find someone with an exemplary mix of skills as an economist, communicator and financial regulator.

But he would have an added challenge. Romney would need to decide whether he fully buys in to the arguments he has made in favor of a tighter money supply. Is he willing to put the nation’s money where his mouth is?

“The American economy doesn’t need more artificial and ineffective measures,” Romney’s campaign said after the Fed announced its latest strategy to pump more money into the economy in September, a policy aimed at bringing down unemployment. “We should be creating wealth, not printing dollars.” Romney has said he would not reappoint Fed Chairman Ben S. Bernanke when his term expires Jan. 31, 2014, about one year into the new presidential term.

If Romney sticks to his embrace of hard money, it would be a rare event in economic history. Elected political leaders, at least outside of Germany, almost always favor lower interest rates to higher, and easier money to tighter. Aides to Richard M. Nixon, Ronald Reagan and George H.W. Bush pressured the Fed to ease monetary policy, at times of significantly higher inflation than what has been experienced recently. Bush is said to have blamed his loss in the 1992 election on Fed Chairman Alan Greenspan’s unwillingness to cut interest rates enough.

So, in selecting a replacement for Bernanke, Romney would have to weigh whether he wants someone who will push the Fed to raise interest rates and sell off the central bank’s holdings of assets sooner rather than later, in the interest of preventing potential inflation in the long term. Does he believe in tighter monetary policy deeply enough to endure the risk that those actions will slow the economy or even tip it into a new recession?

That answer will help determine whom he chooses for the top job at the Fed. Here are some of his primary options. As in Monday’s piece on Obama’s options for a Fed chairman, they are divided into “above the line” (people almost certain to receive serious consideration) and “below the line” (a longer list of individuals who could be worthy of discussion) candidates.

John B. Taylor

He is a Stanford University economist and a leading monetary economist. Central bankers the world over use his “Taylor rule” as a benchmark to help analyze where they should set short-term interest rates, given economic conditions in their nations. He has also emerged in recent years as a staunch critic of the Bernanke-led Fed’s easing policies and fiscal stimulus efforts. He would, barring a ­180-degree change of heart, steer the Fed away from its unconventional easing policies and try to withdraw its extensive stimulus efforts in place since 2008. Taylor does have high-level government experience as undersecretary of the Treasury for international affairs in the early years of the George W. Bush administration. He had a reputation then for a sharp independent streak, which can be a feature, not a bug, in a Fed chief.

Glenn Hubbard

The dean of Columbia Business School has advised Romney for years and served in the early years of the George W. Bush administration as chairman of the Council of Economic Advisers. His academic background is stronger in tax policy and corporate finance than in monetary policy and macroeconomics, but he has a sufficiently big brain — and credibility on Wall Street and in Washington. He has been more cautious than Taylor in his assessments of the Bernanke Fed, even defending Bernanke directly, saying he should “get every consideration” for another term in an interview with Reuters TV in August. In short, if Romney wants to see tighter money, Taylor is probably a safer bet, whereas it is less clear what monetary policy in a Hubbard Fed would look like.

●■The remaining candidates are below the line. Any could get a serious look for the job or even get the appointment, but they have significant disadvantages they would need to overcome.

Martin Feldstein

He is the dean of the conservative-leaning economists but one who has been passed over for the Fed chief job by the past three Republican presidents. A Harvard professor who was chairman of the Council of Economic Advisers in the Reagan White House, he is as credible a thinker on macroeconomics as they come. His downsides: Feldstein was a longtime board member of American International Group, the insurance giant that received a massive and massively unpopular bailout in 2008. And he turns 73 next month, making him a bit old for the job (though by all appearances he remains in good health).

Greg Mankiw

Chairman of Harvard’s economics department, he has advised Romney for years and was chairman of the Council of Economic Advisers in the George W. Bush White House. He has the economic smarts for the job, but the open question for Romney would be whether he has the political savvy. Also, Mankiw’s writing in recent years has seemed to advocate for Bernanke-style easy-money policies, which could put his views at odds with a new Republican administration.

Kevin Warsh

He was among Bernanke’s closest advisers during the financial crisis but has distanced himself from the Fed’s unconventional steps to ease policy in the aftermath, putting his views on monetary policy more in line with Romney’s positions. Warsh knows financial markets, politics, the international aspects of the job and the Fed as an institution, though he would be a non-economist in the job of the United States’s economist in chief. At 42, he is young for the job and may be a better fit for the Treasury Department in either the Romney or a future Republican administration.

Mystery executive

In last week’s analysis of who might serve as Romney’s Treasury secretary, we included the possibility of a “Mystery CEO,” a corporate executive who has Romney’s trust but is not on the radar as a potential political nominee. The same could be said for Fed chief. Call it “Mystery Financial Executive.” The challenge in appointing a Wall Street chieftain to the Fed chairmanship in this post-crisis era is that Senate confirmation would be tough for anyone from one of the banks that received a bailout. And really, anyone from the financial sector would face questions on whether he or she would be an adequately tough regulator of Wall Street. Fox, henhouse, etc.

Thomas Hoenig

If Romney wants to really send a message that he is committed to tight money and combating the too-big-to-fail problem in the banking system, he could consider an unconventional choice. Hoenig, the former president of the Kansas City Federal Reserve Bank and now a director of the Federal Deposit Insurance Corp., is among the most vigorous advocates of each: He dissented from all eight Fed policy meetings in 2010, preferring to raise interest rates, and has assailed the Wall Street banks that he sees as a receiving unfairly generous help from the government. Even if he makes Romney’s short list for consideration, the major banks (the executives of which have generally supported Romney) would scream bloody murder.