But as easy as it is to tell a story about why Yellen should be Fed Chair, it's hard to tell one about Warsh. The Harvard Law-trained Warsh, whose father-in-law is a major Republican donor and the heir to the Estée Lauder fortune, got his start on Wall Street before taking a job in the Bush White House. From there, he was nominated to be a Fed governor despite lacking the kind of high-level academic or financial credentials that others have had. “Kevin Warsh is a bad idea,” former Fed vice chair and Reagan appointee Preston Martin said at the time, and “if I were on the Senate Banking Committee, I would vote against him.”

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They didn't. Instead, at 35 years old, Warsh became the youngest governor in the Fed's history.

(Keep in mind that a few years later, Senate Republicans would block Nobel Prize-winning economist Peter Diamond from taking the same position three separate times, despite the fact that he had also taught then-Fed Chair Ben Bernanke, on the grounds that he did “not possess the appropriate background, experience, or policy preferences to serve").

It's true that some of our best central bankers haven't had PhDs in economics, but that wasn't Warsh. His specialty was seeing inflation problems that didn't exist. He warned about inflation in 2006 when, excluding volatile food and energy prices, it was just 2.1 percent. Then he did in 2007 when it was 2 percent by the same measure. And again in 2008 when core prices were rising a relatively nonthreatening 2.3 percent, going so far as to say that he was “still not ready to relinquish my concerns on the inflation front” the day after Lehman Brothers failed.

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What Warsh wasn't worried about, though, were all the risks banks had been taking that would ultimately require them to be bailed out. A few months before the credit crunch began in 2007, Warsh even said that “an important source of strength has been financial innovation,” highlighting the purported benefits of credit default swaps and other derivatives that Warren Buffett would go on to call “financial weapons of mass destruction.” This was supposed to be Warsh's area of expertise.

Now, to be fair, everybody makes mistakes. Warsh, after all, was far from the only member of the Fed to be so blinded by inflation that they missed the ticking time bombs on bank balance sheets. Most of them were. And, as Bernanke put it in his memoir, Warsh's “many contacts on Wall Street” and “particularly good connections among Republican lawmakers” did “prove invaluable” when they were desperately trying to keep the entire financial system from melting down.

The bigger question, though, is whether you learn from your mistakes. Warsh didn't. He kept tilting at these inflationary windmills even as the prospect of a second Great Depression loomed as a real possibility. In April 2009, when the economy had just lost 539,000 jobs, the unemployment rate had ballooned to 8.9 percent, and core inflation was a mere 1.2 percent, Warsh told his colleagues at the Fed that “I continue to be more worried about upside risks to inflation than downside risks,” according to the transcripts the central bank has released of its meetings. He sang the same tune five months later when he said that the Fed should start removing its support for the economy even before it had “substantially returned to normal,” lest they let the inflationary genie out of the bottle. Core prices were only rising 1 percent at that time. And they were increasing even less than that when Warsh once again sounded the alarm about the dangers of trying to do too much to put people back to work in a speech a year later. Unemployment was 9.8 percent then.

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Warsh has never admitted that he was so wrong to lose so much sleep over an imaginary inflation problem when the economy was faced by a very real unemployment one. Instead, as Bloomberg View's Ramesh Ponnuru points out, Warsh has spent his time inventing new, incorrect rationales for his old, incorrect policies. After he left the Fed, he argued that it shouldn't be doing as much not because it was risking inflation, but rather because it was allegedly fueling inequality and allowing Congress to get away with not cutting Social Security.

Warsh was unavailable for comment, but two of his supporters, Heritage Foundation economist Stephen Moore and CNBC Senior Contributor Larry Kudlow, told me why they think he'd be a strong choice despite all of this. (For the record, they say the same about Stanford economist John Taylor. And Taylor, if Trump's comments Friday on Fox Business are any indication, has remained in the top tier of candidates, while Warsh seems to have slipped.)

"A lot of people were wrong about inflation after the crisis when we had a massive run-up in the money supply," Moore said. The more important thing, in Kudlow's opinion, is that Warsh "doesn't believe that faster growth and higher wages cause inflation." This, he explained, means that "if Trump gets his tax cuts, and the economy responds with higher growth" then "Warsh will let that run." This is what Moore hopes for as well, since, he believes, "the role of the Fed chair is not just to be the key person on monetary policy, but also to be a spokesperson for economic policy in general." He thinks that "Trump needs someone who will speak out in favor of his tax cuts," and that Warsh would fit that bill.

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To be clear, this is not what Fed chairs are supposed to do. They're supposed to stay out of politics entirely. They haven't always — Alan Greenspan, for one, seemed to endorse the Bush tax cuts in his typically Delphic way back in 2001 — but that's the ideal. Warsh, though, has a different view of things. During his time as a governor, he actually argued that the Fed should have done less despite still-high unemployment — in effect, ignoring its statutory mandate to keep joblessness as low as possible while also keeping inflation low — so as to "put the burden" on Congress to do the kind of things he thinks would be good for growth, like cutting entitlements and striking new free trade deals. It's a dangerously undemocratic idea that would be dangerous for the economy as well. That's true even in the opposite case where, say, the Fed "rewarded" the government for cutting taxes by keeping interest rates inappropriately low. We've already seen what happens when the Fed focuses on what is best for the president over what is best for the economy. It was called the Nixon administration, and it helped set the stage for a decade of stagflation.

In a rational world, Warsh's long and distinguished career of being wrong about just about everything would keep him from becoming Fed chair. But, as you may have noticed, this isn't exactly a rational world. It's one where Trump has reportedly all but ruled out appointing his National Economic Council Director Gary Cohn to lead the Fed after Cohn criticized Trump's statements about neo-Nazis and anti-Nazi protesters both being to blame for the violence in Charlottesville. Being easy on fascists isn't usually a criterion for central bankers, but being hard on them is apparently a disqualification for Trump. Which is to say that Trump might have other priorities than whether his most important economic policymaker is the best economic policymaker he can find — an opening if there ever was one for Warsh.