The Alan Greenspan era at the Federal Reserve Board has been ushered in with a boost in interest rates -- the first since 1984. Apparently, it was designed to tell the world that the Fed is worried about both the recent slump in the dollar and a perceived threat of inflation.

The stock market, historically fearful of an interest-rate spiral, thinks that the cure may be worse than the disease: this discount rate increase may be the first of a series of money-tightening moves.

Such a pattern had been predicted by those who felt that Greenspan, who succeeded the hard-nosed Paul Volcker at a time the dollar was weakening, would have to take some highly visible action to prove his manhood.

Of course, nothing that happens at the Fedis quite that simple. For one thing, it is nota one-man show. There are six other gover-nors (one vacancy exists at the moment), and a majority of four is needed to raise the discount rate.

Greenspan, less aloof than Volcker, has been busy cultivating good will among his fellow governors. And with two absent last Friday, he was able to garner the votes of the other three for a 4-0 boost in the discount rate. Gov. Martha Seger, one of the absentees, might have voted against Greenspan because she worries that the business expansion is fragile.

Bill Neikirk of the Chicago Tribune, in his new book "Volcker: Portrait of the Money Man," makes the point that financial markets loved Volcker "because of an undefinable quality that exuded confidence and trustworthiness, the same principles that stand behind a country's money."

Although Greenspan's public record over the past 20 years tells us that he is a highly conservative economist who has all of the proper "establishment" concerns about inflation and budget deficits, some expressed concern that he wasn't sufficiently worried about the dollar.

Just before his appointment to the Fed chairmanship, he forecast that the dollar would continue to decline -- and implied that such a drop would be the only way to ensure a significant reduction in the trade deficit.

So it was more or less natural for exchange markets to test Greenspan. At the end of August, as the dollar fell toward 140 yen after holding above 150 yen for much of the year, the markets interpreted the lack of American support for the dollar as proof the Reagan administration was not opposed to further slippage.

This would be a departure from "target zone" agreements made in Paris last February by Treasury Secretary James Baker and endorsed at the June summit in Venice. With the trade deficit stubbornly high, and Congress poised to pass protectionist legislation, a weaker dollar might be the only way to counter the trend.

But if the dollar continued to give ground, with nothing to brake it, Japanese and other foreign investors whose money is financing our budget deficit might hold back. Then, the shortage of funds would cause interest rates here to skyrocket, touching off an American recession for a certainty and a worldwide depression as a probability.

Therefore, Washington Fed-watchers assume, Greenspan seized his opportunity last Friday. With unemployment down to a 6 percent rate (which shows a certain strength and resiliency to the domestic economy), he persuaded the other three governors in town to send a signal to the markets: the dollar must not be allowed to fall out of bed.

However, a dollar-oriented, tight monetary policy carries with it dangers of another kind. Former Fed governor Emmett Rice said in an interview that he vigorously disagrees with the discount rate increase at this stage "because I don't see inflation as a threat." Rice thinks that Greenspan was too eager to show a Volcker-like toughness.

It is clearly legitimate to worry (as does the stock market) that higher interest rates will be a drag on the economy. As economist Henry Kaufman pointed out in recent congressional testimony, "Our financial system is going astray. Many deposit institutions are weak, and businesses and households have assumed massive debt burdens." A recession induced by high interest rates could push some of these over the brink. Kaufman's lament was underscored by a recent report of the Congressional Budget Office demonstrating that "a large number" of savings and loan institutions "are still extremely weak."

For Greenspan and the Fed, the dilemma is ever present. If the central bank is successful in reversing the dollar decline, the only remaining way of attacking the trade deficit will be through a deep downturn that cuts off the buying power of American consumers. Thus, the inaugural move of Greenspan's Fed offers no reason to cheer: if it achieves the stated objective, it can bring equally severe problems in its wake.