PAUL VOLCKER'S second term as chairman of the Federal Reserve Board is likely to be even more difficult than his first. While President Reagan is entitled to applause for good sense in offering the appointment, Mr. Volcker demonstrates real courage in accepting it.

If he had left this spring, he would have been remembered as the central banker who brought inflation under control when a succession of presidents and Congresses had failed. The consumer price index was rising at a rate of 13 percent a year when he took office in the summer of 1979; so far this year it's been just over 3 percent. When Mexico's currency nearly collapsed under the weight of its foreign debts last year, a rapid and effective international response organized chiefly by Mr. Volcker prevented disaster. It would have been a very adequate record on which to retire.

And the next four years? It is easier to bring inflation down at the price of a severe recession than to keep it down while promoting a recovery. As for the foreign debts, since last summer governments and banks around the world have done a good deal of work to prevent, in the short term, the disaster of cumulative defaults. But for the longer haul nothing has improved. There are signs that the financial strains on some of the borrowers are increasing.

Everybody's favorite way out is, of course, steady economic growth and declining interest rates. But that won't happen as long as the United States continues to run budget deficits on the present scale. The Federal Reserve can't prevent those deficits. It can only try to cope with the consequences of their impacts on the world's financial markets.

Mr. Volcker was the candidate of, among others, many leading figures in those financial markets. Mr. Reagan may now feel that he has done enough for the financial crowd and, since all the economists tell him that a recovery is now assured, perhaps he will be tempted to turn to the more congenial pastime of a prolonged quarrel with Congress over the budget. The effect of a long quarrel will be to perpetuate those deficits and, as long as they run to 6 percent of American GNP, the Federal Reserve's days and nights are going to be devoted chiefly to damage control.

The Federal Reserve is in good hands. But the country can't run a balanced and productive economic policy through its central bank alone. Mr. Volcker and his colleagues can prevent certain kinds of catastrophe--for example, sustained inflation. But they can do it only at a cost. That cost depends on the skill with which economic policy--keep your eye on those deficits--is being managed by Congress and, most especially, by the president.