Can a woman effectively run the Federal Reserve? That shouldn’t even be a question. And Janet Yellen, the vice chairwoman of the Fed’s Board of Governors, isn’t just up to the job; by any objective standard, she’s the best-qualified person in America to take over when Ben Bernanke steps down as chairman.

Yet there are not one but two sexist campaigns under way against Ms. Yellen. One is a whisper campaign whose sexism is implicit, while the other involves raw misogyny. And both campaigns manage to combine sexism with very bad economic analysis.

Let’s start with the more extreme, open campaign. Last week, The New York Sun published an editorial attacking Ms. Yellen titled “The Female Dollar.” The editorial took it for granted that the Fed has been following disastrously inflationary monetary policies for years, even though actual inflation is at a 50-year low. And it warned that things would get even worse if the dollar were to become merely “gender-backed.” I am not making this up.

True, The Sun is a marginal publication, with strong gold-bug tendencies, and nobody would pay much attention if the rest of the right had ignored or distanced itself from that editorial. In fact, however, The Wall Street Journal immediately followed up with its own editorial along the same lines, in the course of which it approvingly quoted The Sun piece, female dollar and all.

The other campaign against Ms. Yellen has been subtler, involving repeated suggestions — almost always off the record — that she lacks the “gravitas” to lead the Fed. What does that mean? Well, suppose we were talking about a man with Ms. Yellen’s credentials: distinguished academic work, leader of the Council of Economic Advisers, six years as president of the San Francisco Fed, a record of working effectively with colleagues at the Board of Governors. Would anyone suggest that a man with those credentials was somehow unqualified for office?Sorry, but it’s hard to escape the conclusion that gravitas, in this context, mainly means possessing a Y chromosome.

Both anti-Yellen campaigns, then, involve unmistakable sexism, and should be condemned for that reason. As it happens, however, both campaigns have another problem, too: They’re based on bad economic analysis.

In the case of the “female dollar” types, the wrongheadedness of the economics is as raw and obvious as the sexism. The people shouting that the Fed is “debasing the dollar” have been warning of runaway inflation any day now for almost five years, and they have been wrong every step of the way. Worse, they have shown no willingness to admit having been wrong, let alone to revise their views in the face of experience. They are, in short, the last people in the world you should listen to when it comes to monetary policy.

The wrongheadedness of the gravitas crowd, like its sexism, is subtler. But to the extent that having gravitas means something other than being male, it means being what I like to call a Very Serious Person — the kind of person who talks a lot about the need to make tough decisions, which somehow always involves demanding sacrifices on the part of ordinary families while treating the wealthy with kid gloves. And here’s the thing: The Very Serious People have been almost as consistently wrong, although not as spectacularly, as the inflation hysterics.

This has been obviously true in the case of budget policy, where the Serious People hijacked the national conversation, shifting it away from job creation to deficits, on the grounds that we were facing an imminent fiscal crisis — which somehow keeps not coming.

But it has also been true for monetary policy. The Wall Street Journal (news department, not editorial) recently surveyed the forecasting records of top policy makers at the Fed, whom it divided into “hawks” (officials who keep warning that the Fed is doing too much to fight unemployment) and “doves” (who warn that it’s doing too little). It found that the doves made consistently better forecasts, with the best forecaster of all being the most prominent of the doves — Janet Yellen.

The point is that while the gravitas types like to think of themselves as serious men (and I do mean men) who are willing to do what needs to be done, recent history suggests that they’re actually men who are eager to prove their seriousness by doing what doesn’t need to be done, at the public’s expense.

Also, there was a time not along ago when almost everyone in the gravitas crowd, if asked who possessed that mystical quality in its purest form, would surely have answered “Alan Greenspan.” How well did that turn out?So is Janet Yellen the only possible candidate to be the next leader of the Fed? Of course not. But the case for someone else should be made on the merits — and, so far, that hasn’t been what’s happening.