Reporters had a vested interest in the reappointment of Federal Reserve Board chairman Arthur F. Burns. Burns made good copy. It's doubtful that his successor, G. William Miller, chairman of Textron Inc., will do quite so well.

There was an almost theatrical air to Burn's stuffiness. His quiet pronouncements instantly acquired Zeus-like qualities that easily translated into headlines. The effect was to perpetuate the Fed's mystique as a place of enormous power. In this picture, the "independent" Fed emerges as the economy's secluded command center. And the White House and Congress dance to the Fed's tune or suffer its mistakes.

In fact, the truth is a lot less tantalizing. The Fed's independence is vastly exaggerated. Its actions are sharply circumscribed by a vague sense of what's politically feasible and intellectually correct. The Fed conforms more to what the public wants - or, at any rate, the public as represented by Congress and the White House - than the reverse. If the Fed has sinned, its sins belong to everyone.

Consider the most damning anti-Fed allegation: that it is responsible for inflation, having allowed excessive growth in the money supply. Too much money was sent chasing after too few goods, and inflation resulted.

Strictly as a matter of arithmetic, that's probably what happened. But, in the real world, the Fed simply accommodated the policies that the rest of society - either in its foolishness, selfishness or short-sightedness - willed.

In the 1960s, the Fed provided enough money and credit to permit the rapid expansion of the Kennedy-Johnson years, spurred by the Vietnam war. When food and energy price increases intensified the inflationary process, the Fed generally supplied the money to permit further inflationary wage and price increases that businesses and workers, themselves protected from the consequences of inflation by a myriad of institutional and political arrangements, could win.

Consequently, the country now seems locked into a 10 percent annual growth of the money supply, which roughly finances a 4 percent increase in real output and 6 percent inflation. (For technicians, the definition of "money" used here is M2: that is, currency in circulation, checking deposits and savings deposits at commercial banks.)

There is no doubt that the Fed could halt inflation. It could simply decree relatively low growth in the money supply (say, 4 percent for M2) and abide by that policy, some what might.

No one really knows what the results would be, but a massive recession (even a depression) is a good possibility. The credit needs of businesses, consumers and local governments would collide with the stingy money supply allowed by the Fed. Starved for credit, weak firms would collapse, new home construction would shrink and investment would shrivel.

Perhaps this discipline ultimately would prove healthy: shock treatment to destroy the inflationary mechanisms and psychology that perpetuate the wage-price spiral. Perhaps, in retrospect, the shock would not even be that damaging. The economy might be sufficiently resilient to absorb the blow with fewer bankruptcies, lower unemployment or less stagnation than might legitimately be feared.

But no one at the Fed, least of all Arthur Burns, has been willing to take that gamble. Instead, the Fed timidly (Burns would say prudently) has tried to nudge down increases in the money supply - with only slight success - to less inflationary levels. This policy accurately reflects public ambivalence about reducing inflation and professional confusion among economists about the best way to do it.

And that is how things should be. Nobody elects the Federal Reserve Board. More than the Supreme Court - whose justices have included eminent jurists and successful political leaders - its members boast neither great professional achievements nor varied personal backgrounds. Mostly, they have migrated upward through the banking system, the economics profession or some government bureaucracy and, through a fluke, have been appointed to the Fed.

The ambiguity of the Fed's "independence" is well understood by the Fed itself, the White House and Congress. And, politically at least, it serves them all well. It gives Congress and the White House a convenient scapegoat for unpopular but sometimes necessary actions. Meanwhile, the existing arrangement preserves the institutional autonomy of the Fed's decision making, which inflates the self-importance of Fed members.

There are, to be sure, genuine conflicts. In 1965-66, for example, Lyndon B. Johnson seethed when the Fed raised interest rates. But the Fed's action came as Johnson was attempting a sharp expansion of U.S. involvement in Vietnam without raising taxes to pay the bill. The Fed's move enjoyed grudging support among economists and, at that, was only temporary.

An even better example of the complicated interplay is the so-called accord between the Fed and the Treasury Department in 1951. Until then, the Fed had supported prices of Treasury securities by buying them in sufficient quantity to maintain their face value. Treasury naturally liked this arrangement, because it simplified the job of refinancing maturing dept. If no one else would buy, at least the Fed would. The Fed resented being Treasury's handmaiden and argued that the policy, committing it to pumping unlimited amounts of money into the economy, was inflationary.

The Fed, of course, was right, which probably made a change inevitable. But neither did the Fed flagrantly defy the White House. Fed chairman Thomas B. McCabe resigned, President Truman appointed William McChesney Martin Jr. - who had been a high Treasury official - and Martin only gradually retreated from price support Martin knew, as economist Robert Weintraub has said, "What the President wanted . . ."

In both 1951 and 1966, the Fed constituted a loose check on the White House. It may do so again in the future. But Miller steps into a job where the constraints and the forces for continuity are awesome. To think that the Fed is the economy's independent nerve center is to misunderstand both politics and economics.