Federal Reserve Chair Janet Yellen testified before the House Financial Services committee in November. (Getty Images)

Debates over monetary policy normally play out through spreadsheets and statistics, but an argument between political activist and five-time presidential candidate Ralph Nader and Federal Reserve Chair Janet Yellen has turned personal -- and public.

Nader issued an open letter to Yellen last month arguing that low interest rates were unjustly hurting savers. The Fed has kept its target interest rate at zero since 2008 and is now weighing whether to start raising it. But the contention sounded odd coming from a liberal like Nader, as many Democrats and progressive groups have been urging the central bank to hold off on an increase until the job market is stronger. It's Republicans who have repeatedly criticized the Fed as punishing savers, many of whom are seniors.

Nader's letter was even more controversial for the personal sideswipe he took at Yellen, the first woman to lead the central bank in its 100-year history:

Chairwoman Yellen, I think you should sit down with your Nobel Prize winning husband, economist George Akerlof, who is known to be consumer-sensitive. Together, figure out what to do for tens of millions of Americans who, with more interest income, could stimulate the economy by spending toward the necessities of life.

After the letter was released, many commentators criticized Nader's remarks as sexist. "Ralph Nader mansplains monetary policy to Janet Yellen," said New York magazine.

On Monday, Yellen did something unusual. She responded in a missive of her own.

"Thank you for your recent letter," it began. But the tone quickly shifts: "It may help to review a few basic facts."

Yellen argued, as her predecessor Ben S. Bernanke did before her, that low interest rates have primarily reflected a weak economy. The Fed's efforts to revive the economy have helped create millions of jobs and fostered a stronger recovery overall.

Would savers have been better off if the Federal Reserve had not acted as forcefully as it did and had maintained a higher level of short-term interest rates, including rates paid to savers? I don't believe so. Unemployment would have risen to even higher levels, home prices would have collapsed further, even more businesses and individuals would have faced bankruptcy and foreclosure, and the stock market would not have recovered. True, savers could have seen higher returns on their federally-insured deposits, but these returns would hardly have offset the more dramatic declines they would have experienced in the value of their homes and retirement accounts. Many of these savers would have lost their jobs or pensions (or faced increased burdens from supporting unemployed children and grandchildren).

Yellen makes no mention of Nader's comment about her husband. But the letter is signed by just one person: Janet Yellen.