THERE ARE two vacancies on the seven-member Federal Reserve Board of Governors, and President Trump has struggled mightily to fill them. His problems are largely of his own making. Mr. Trump has loudly and repeatedly criticized the Fed’s current chairman, Jerome H. Powell, for allegedly failing to keep interest rates sufficiently low — this despite having appointed the capable Mr. Powell himself in 2017. At times, he has even seemed to threaten to fire Mr. Powell, which probably would not be lawful. Given that context, Mr. Trump’s attempt to fill the two Fed spots with political loyalists of questionable qualifications, Herman Cain and Stephen Moore, struck many people as a bid for improper influence over the central bank. There was even pushback from Senate Republicans, albeit of varying degrees of forthrightness, and Mr. Cain and Mr. Moore dropped out of their confirmation bids.

Now Mr. Trump offers two new names, Christopher Waller and Judy Shelton, as likely nominees to the Fed. Mr. Waller is a former chair of the University of Notre Dame economics department who has been in charge of research at the Fed’s St. Louis branch since 2009. He is known to be a “dove” on interest rates, which is undoubtedly one reason Mr. Trump picked him, but he is a nonpolitical expert who wrote in 2011 that central bank independence “is the key tool to ensure a government will not misuse monetary policy for short-term political reasons.”

So far, so reassuring. Ms. Shelton presents a more complicated case. She has some strong academic credentials — a PhD in business administration — and has held public positions, including chair of the National Endowment for Democracy and her current Senate-confirmed post as the United States’ representative on the European Bank for Reconstruction and Development.

However, hers has been an eminently political career, including stints on Republican nominee Bob Dole’s campaign for president in 1996 as well as that of Ben Carson in 2016 before she signed up with Donald J. Trump for President and, later, with his Treasury Department transition team. Like Mr. Moore, think tank briefs and op-eds in the conservative press, not peer-reviewed research, have been her stock in trade.

She has heaped rhetorical abuse on the Fed over the years, likening it as recently as May to Gosplan, the notorious Soviet economic planning agency. She blasted the Fed for its loose monetary policy when Barack Obama was president, but now that Mr. Trump is in office and demanding lower interest rates, she has concluded that lower rates are in order. The great cause of her career has been a dubious one: the gold standard, which advocates such as Ms. Shelton see as a restraint on central bank currency manipulations, but which opponents — correctly — see as an arbitrary limitation on liquidity that almost strangled the world economy to death in the 1930s. “We make America great again by making America’s money great again,” she wrote last year.

A similar pattern of eccentric ideology, flip-flops and flattery doomed Mr. Moore’s bid for a Fed post. If Senate Republicans give her record the scrutiny it deserves, they might doom Ms. Shelton’s, too.

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