On Monday, President Biden announced that he was renominating Jerome H. Powell for another four-year term as chair of the Federal Reserve, resisting pressure from progressive Democrats who wanted a change at the top of the Fed and instead choosing policy continuity. But in a move that could appease some of those progressives, Mr. Biden said he would nominate Lael Brainard as vice chair. The role could give her the power to influence everything from the cost of money to the future of digital cash. Mr. Powell, who is expected to receive bipartisan support for his Senate confirmation, will face the task of dismantling the extraordinary efforts the Fed took last year to keep the economy going during the depths of the pandemic. Now, the Fed will need to determine how to start raising interest rates, which have been just above zero since March 2020, without sending the economy into a recession.