If it's possible to make a good decision that also makes no sense, President Trump has just done that.
But now she's going to be out of a job.
To put in perspective how crazy it is that someone with Yellen's track record isn't being kept on, take a look at the chart below. It shows what's known as a central banking “loss function,” basically how far the Fed is from achieving its stated goals of low unemployment and low inflation. (This is a simple one that weighs both equally, although recent research has suggested that central banks should maybe put more emphasis on unemployment). The closer it is to zero, the better the Fed is doing.
As you can see, the Fed has had its best performance under Yellen. Indeed, it has averaged a mere 0.9 “loss” during her tenure, compared to 1.4 for the runner-up in Greenspan. And the only reason her numbers aren't even better is that, according to this model, unemployment and inflation are both a little too low right now. That's a bit of a paradox, since lower unemployment is supposed to cause higher inflation, but it gives you an idea of the kind of nitpicking you have to do with Yellen. Things almost seem too good by traditional measures.
This isn't the whole story, though. Take Paul Volcker. It's not his fault that he inherited a high-inflation economy that makes his numbers look worse than everybody else's. Especially not when he ended up making things much, much better by the time he left the Fed. What you have to do, then, is also look at how much the Fed's “loss” changed over the course of a Fed chair's term. Although even that can be misleading if, say, a bubble built up during someone's time at the helm — let's call him “Alan Greenspan” — and only burst after he left. In any case, though, this measure says that Volcker was the most successful Fed chair of recent vintage, and Yellen maybe the second or third most (with Ben Bernanke sharing the credit for the recovery). Sure, she was bequeathed a pretty healthy economy, but it's gotten even more so under her direction and shows no signs of stopping. There isn't much more she could have done.
This really is an unprecedented situation. There's been an unofficial bipartisan tradition to reappoint a Fed chair as long as they're doing a good job and want to keep doing it. Reagan kept Carter-nominee Volcker, Clinton kept Reagan-nominee Greenspan, and Obama kept Bush-nominee Bernanke. Trump, though, apparently felt, as he put it, that “you want to make your own mark.” In other words, Yellen was Obama's pick, so she couldn't be Trump's no matter how perfectly she did her job.
None of this is to say that Powell isn't a solid choice himself. He is. In fact, he might be the second-best person for the job.
But what happened to only hiring the best?