A new president takes office with big plans, and needs a booming economy to help underwrite his promises. A Federal Reserve chief sees an economy starting to overheat, and begins warning of the need for higher interest rates.

They were bound to clash: Lyndon B. Johnson, the new president, and William McChesney Martin, the longtime, fiscally conservative Fed chairman.

It is a conflict from the 1960s with echoes in the present day, as President Trump’s campaign talk of robust tax cuts, job growth and economic expansion is bumping up against calls by the Fed chairwoman, Janet L. Yellen, for a cautious rise in interest rates, lest inflation get out of control.

Today, when Ms. Yellen acts, we figure she is not doing Mr. Trump’s bidding. She and Fed policy makers are expected this week to increase the benchmark rate for the fourth time in less than two years. But that independence was not always assumed in the Fed’s early years, and Martin’s standoff with Johnson provided a template for interactions between the Federal Reserve and the White House for decades to come.