G. William Miller is off and running as chairman of the Federal Reserve Board and, after five and a half weeks, Washington observers are still not sure what makes Miller run.

When President Carter nominated him to the post in late December to replace crusty old Arthur Bruns as chairman of the nation's central bank, a sigh of relief went up from the nation's liberals. Here was a man, they felt, who was not so downright scared of inflation that he would use tight money policies to thwart congressional attempts to stimulate economic growth and reduce unemployment, something they accused Burns of doing.

Neither Miller's record as a socially active business executive (he headed the National Alliance of Businessmen and was active in programs aimed at employing minorities and youth) nor his comments immediately after the president's announcement did anything to dispel that notion.

But with amazing ease, G. William Miller has donned the anti-inflation mantle that Arthur Burns wore so frightfully often in public.

While arguing that unemployment and inflation are twin problems that cannot be solved independent of one another, as soon as he was sworn in Miller was publicly worrying about the sudden surge of inflation and deterioration of the dollar and cautioning that inflation needs to be stressed more than umemployment at the present time. It was a position Treasury Secretary W. Michael Blumenthal had adopted within the administration and was beginning to take publicly as well.

By last week, Miller was calling inflation not merely a serious problem but a national "emergency."

While some observers are distressed that Miller seems to have adopted the same concern with price stability that all other central bankers share, others are not so sure. House Banking Committee Chairman Henry Reuss (D-Wis.) thinks Miller's vocal concern with inflation and the need for government and the private sector to take steps to fight rising prices reflects Miller's desire to keep the Fed from being the only inflation fighter in town.

Miller, for his part, has managed to talk both sides of the argument. He told Congress that the Fed cannot fight inflation alone nor wants to, that he is very concerned about inflation, but that he also wants to pursue a non-inflationary money policy that steadily would reduce the yearly increase in money growth. He also warns that, if the country does not get serious about inflaiton, the Fed will be prepared to take harsh measures to slow price increase.

It is too early to tell whether Miller, who talks an anti-inflation game similar to the one Burns talked, will follow the Burns approach to monetary policy. That policy - the liberals' protests notwithstanding - was not a particularly austere one. Although Burns frequently wagged an accusatory finger at those whose actions he considered inflationary, the monetary policy he pursed was for the most part liberal and often inflationary.

Miller the monetary policy chief is still an unknown. He has no track record. It was not until last Tuesday that the first major monetary policy decisions were made by the Miller-led Fed, when money supply growth targets for the next year were adopted by the agency.

But one thing is clear. In his brief term in office, Miller has adopted more than Burns' inflation rhetoric. Miller, like Burns, has a penchant for commenting on all matters of economic policy, whether it be the money policy the Fed controls or the taxing, spending and energy policies that are under the joint purview of Congress and the administration.

Already Miller has called for unilateral presidential action to curb oil imports unless Congress acts soon on the energy bill, has criticized the president's proposed tax cut as being too big and suggested its effective date be delayed, and has said he favors rescinding some Social Security tax increases Congress voted into effect last December and now may decide to roll back under heavy political pressures. The former Textron Corp. chairman also wants the government to under-take a broad program aimed at structural unemployment.

"It's something that disturb me about Miller," said Sen. William Prox-mire (D-Wis.) chairman of the Senate Banking Committee that overseas the Federal Reserve. "It was the same thing that disturbed me about Burns. Burns would come up here with a 20-page statement, 15 pages of which lectured everyone about things over which he had no control and only 5 pages of which were dedicated to the vaguest discussion of monetary policy."

In the 19 years that he headed the Federal Reserve, Burns' predecessor, William McChesney Martin, "picked carefully the occasions he would talk about anything but monetary policy," one observer noted.

By contrast, "Arthur (Burned) lectured about everything any chance he got. The thing that surprises me most about Miller is that he leans more toward Burns than toward Martin. He sounds off on a lot of things that are not concerned with monetary polict. If there's anything that got people at the White House mad at Burns, it was his constant picking at everything," he said.

"Maybe it's because Burns did it that way that he's doing it that way," another official observed.

Miller came from the large, Providence-based conglomerate eager to establish himself in Washington. He is at ease with people and, unlike the professional Burns, lectures little, listens a lot and banters good-naturedly with reporters and legislators.

He appears to have jumped into the role of chairman of the seven-member Federal Reserve Board of Governors, a job many consider the second most powerful in Washington, with two notions in mind.

First, Miller wants to establish himself as his own man. "He's one vote among seven on the board and one among 12 on the Federal Open Market Committee (which sets monetary policy) and he's in a den of Republican appointees. For tactical reasons, he's got to show he's not Mr. Carter's lackey," one economist noted.

"Second, he wants to establish himself as a take-charge guy," he continued. And Miller did not leave a $400,000-a-year job to be a narrow tecnican, another veteran economist noted.

Yet, at the same time, Miller is a puzzlement, and his independence troubles a few.

Two events last week have Fed watchers (who by definition are now Millers watchers) confused. On Tuesday, following the president's anti-inflation address, Miller issued an unsolicited statement to the press extolling the president's program and exhorting the nation to cooperate in helping to reduce the rate of inflation.

"It was almost as if he were a young congressman hoping to get his name in print," one flabbergasted observer said. "It certainly was not in the style of the Rederal Reserve chairman." The statement was also issued without consultation with the board.

But the next day, in a breakfast meeting with reporters, Miller reversed gears and was sharply critical of the $25 billion income tax cut the president proposed last January that is having problems in Congress. Miller suggested that the cut would be inflationary and might be postponed a few months to help balance the budget.

Later the same day, Treasury Secretary Blumenthal, who was Miller's prime sponsor for the Fed post, stoutly defended the tax package against not only congressional critics but Miller's critique, although privately administration members concede the size of the tax cut may have to be trimmed.

Some administration sources say, however, that there is no concern at the White House or the Treasury with Miller's outspokenness. "Maybe he hasn't yet learned that every word a Fed chairman utters is hung on," one official suggested. Others, however, are upset."He's got to learn he can't shoot his mouth off on everyting," another said.

Furthermore, one official said he's worried that Miller really believes postponing the tax cut will have any impact on inflation or business confidence. "We withdrew the $50 rebate last spring supposedly to help business confidence and the market fell. If we change the tax cut, it won't make a damned a bit of difference on inflaiton, but it will make us seem like we don't know what we're doing."

While it is still too early to judge Miller's brand of monetary policy - Proxmire criticized Miller for being a "rookie" in this area - Federal Reserve staffers apparently are pleased with Miller's openness and intelligence and his ability to digest complicated topics quickly.

Miller also has opened up the central bank to the public eye a little. While Burns spoke infrequently with reporters and then only with the self-important caveat that nothing he said could be attributed to him or the central bank (leading to attributions like sources in a posiiton to know what Burns thinks say . . ."), Miller has met informally and on the record with many groups of reporters in his five weeks on the job.

He also has consulted with reporters on whether the Fed needs to be quite so secret about all its documents and to release minutes of its important meetings with such a lag.

Through it all, however, there "does seem to be a man with the rhetoric and style of Arthur Burns," Prosmire said.

"But the rhetoric cuts both ways," another economist cautioned. "While he complains about inflaiton, he has not yet said that inflation-fighting is the Fed's number one business. If he really wanted to pursue a policy of slowing money growth (with would be anathema to many congressional liberals), he'd be saying what he's saying.

"If he wanted to follow the Burns-Nixon approach of worrying about inflation but pumping up the money supply, he's be saying the same thing year on this fellow."

A top official agrees. "After all," he said, only in part facetiously, "most of what Miller has said is in the job description of a Fed chairman. He's got to get up in the morning and inveigh against inflation twice in the mirror, then before he goes to bed at night he's got to critice profligate fiscal policy."