PAUL VOLCKER has repeatedly rescued the Reagan administration from the worst consequences of its economic mistakes. But his second term as chairman of the Federal Reserve Board is ending, and, as President Reagan announced yesterday, Mr. Volcker will not remain for a third. While that now exposes the administration to a degree of vulnerability, the president has chosen the next chairman well. He has put aside all the Reaganomics and funny business to nominate Alan Greenspan, an experienced economist who stands for sophisticated and orthodox financial conservatism. On inflation and the war against it, Mr. Greenspan's views are not likely to prove very different from Mr. Volcker's.

Why did Mr. Volcker decide to leave? The chairmanship is a grinding job, and eight years of it is long service. But it seems pretty clear that he would have remained if the president had been prepared to give him a measure of visible public support. That was more than Mr. Reagan was prepared to offer. He likes having it both ways. He likes the credit for a low inflation rate, but he prefers not to be associated with the financial discipline that produces it. More than most presidents, he likes to convey an impression that there is an enticing Reagan policy, dancing around somewhere out there in the mists beyond your line of sight, quite unrelated to the somber and unwelcome strictures that Mr. Volcker keeps reading to Congress.

Each of the president's last five appointments to the Federal Reserve Board has been advertised by his supporters as an anti-Volcker vote -- with accompanying speculation inspired by the White House regarding the exciting things that would happen when the Reagan votes got control of the board. They have had control, arithmetically, for some time and nothing much has happened. But Mr. Volcker was tired of the game and evidently felt that, to operate effectively, he needed more than a grudging and silent reappointment. Since the president was not prepared to extend it, Mr. Volcker now leaves it to Mr. Greenspan to deal with the White House and the president's ideas about economics.

Mr. Greenspan understands fully the perils of presidential policy that tolerates gigantic budget deficits. He knows a lot about Washington, where he has served with distinction before. But he has had less direct experience with the international financial system and the mechanisms that set, for example, the dollar's exchange rate. Dealing with the Latin debts may well prove to be the most difficult part of his new job. For the past five years the United States has managed its interests chiefly through the Federal Reserve. Mr. Volcker has often been the bridge between the commercial banks, on one hand, and the Latin governments, in which he has built up a wide range of personal associations, on the other.

A Federal Reserve Board chairman's successes are usually measured in the disasters that never happened. Under Mr. Volcker the inflation of the 1970s didn't return, the dollar's exchange rate didn't collapse and Latin America didn't drift off into default, isolation and depression. So far the world's financial system has kept its balance. For his part in that, he is owed the gratitude of this country -- beginning with President Reagan's.