It’s pretty easy to identify what we don’t want in a Federal Reserve Board member. So let’s talk about what we do want.

Last week, President Trump told us that one of his announced-though-never-formally-nominated choices for Fed, Stephen Moore, had withdrawn from consideration. This came just 10 days after another Fed pick, Herman Cain, bowed out.

Both men were unfit for one of the world's most powerful economic policymaking jobs. That was obvious from their confused and often self-refuting economic commentary, not to mention personal baggage and troubling attitudes toward women.

While some saw Moore and Cain as merely the latest in Trump's pattern of selecting the worst possible people for any given job, in a key way, they were a departure from trend.

Trump's earlier Fed nominees had actually been reasonable, competent professionals. Four of the five sitting Fed governors were selected by Trump (one, Jerome H. Powell, was originally appointed to the board by President Barack Obama and then elevated to chair by Trump). All four easily sailed through Senate confirmation.

Which means the Trump administration has proven itself capable of identifying and nominating qualified Fed candidates. So, what makes a qualified Fed candidate in 2019?

First — and I can’t believe this is controversial — expertise and experience.

Career-wise, good Fed candidates generally fall into one of two buckets. They're either serious economic researchers (not necessarily with a Ph.D., though it doesn't hurt) who spent their careers studying issues relevant to monetary policy or financial regulation and have been published in peer-reviewed journals. Or, alternatively, they have extensive experience as a financial market participant.

And sorry, my fellow greenroom denizens: playing an economist on TV does not count as sufficient experience.

Second, candidates should be consistent and intellectually honest in their reasoning, and transparent about their policy priorities.

If they've changed their minds on something significant (such as the risks of inflation), that's fine. Smart people change their minds all the time when new evidence warrants. But they need to be honest about any inconsistencies and be able to explain them.

An instructive example is Narayana Kocherlakota, who was not on the Fed board in D.C. but did vote on interest-rate policy while president of the Minneapolis Fed. In 2012, he underwent a very public intellectual transformation from inflation hawk to inflation dove. While some Fed watchers may have disagreed with his recommendations (some before that transformation, some after), he was open about his thinking.

And his reasoning had nothing to do with political convenience.

Speaking of which, third: Fed candidates must demonstrate that they prioritize the central bank's political independence. That means they'll resist arm-twisting from the White House, and they will do unpopular things when it's in the best interests of the economy. They should respond to good-faith criticism — the Fed does get things wrong, after all — but not to partisan pressure.

Alas, Trump's criteria for future Fed appointees will likely be different.

Presumably, the reason there has been such an abrupt change in the quality of Trump's Fed picks is that it dawned on him that the Fed wasn't his puppet. The Fed's independence was never an "obvious feature to the president," as another candidate who interviewed for Powell's job put it. But Trump never had cause to stress-test that presumption.

Then Trump grew angrier about Fed rate hikes, which all of his own appointees voted for. So he broke a multi-decade policy against White House comment on Fed decisions, a norm established to preserve the central bank's actual and perceived independence. When that didn't work, he began deliberately seeking out Fed candidates who had expressed personal loyalty to him and more pliancy in their views.

What's a president to do then?

Well, he could nominate an economist who leans dovish for reasons related to consistently held economic principles. But Trump also clearly prefers appointing Republicans, and the Venn-diagram overlap of economists who are both reliable inflation doves and reliable Republicans is small.

A name some White House officials have floated in recent days is Paul Winfree, a director at the conservative Heritage Foundation who previously served as a Trump budget and domestic policy aide. Winfree's work emphasizes fiscal policy, not monetary policy, so it's unclear how he'd approach the Fed's core responsibilities. If Trump ultimately nominates him, Winfree will have to give senators, and the public, a clearer view into his thinking.

Regardless, whomever Trump picks must, at minimum, meet the three criteria above. A record of sound judgment, strong character and intellectual open-mindedness would be nice, too.

Catherine Rampell

Catherine Rampell’s email address is crampell@washpost.com. Follow her on Twitter, @crampell.