It's hard to envy Alan Greenspan, the new chairman of the Federal Reserve Board. The Fed regulates interest rates, but in the wake of the stock market crash, dangers lurk no matter how Greenspan moves rates. Higher rates could threaten an economic slowdown or recession. Lower rates could cause a collapse of the dollar and higher inflation. All Greenspan can do is make an educated guess and guard against the greatest danger. At the moment, that's visible inflation -- not an invisible recession.

Just how he reacts will help shape the world economy. In the weeks since the crash, the global dimensions of the economic impasse have become increasingly clear. For the first half of the 1980s, the world economy grew in a dangerously unstable way. The United States' huge appetite for imports propelled other economies. The immense U.S. trade deficit corresponded to the enormous trade surpluses of West Germany, Japan, Taiwan and other countries. The question now is whether this lopsided pattern of global growth can be gracefully reversed.

In some ways, Greenspan was one of the big winners of the stock market crash. It enabled him to escape quickly from the shadow of his predecessor, Paul Volcker. No one ever doubted Greenspan's intelligence or his credentials as an economist. But crisis management is an art -- not a science -- and everyone wondered whether Greenspan had the needed instincts and skills. For the moment, he has quieted the critics.

When the market dropped sharply, he acted decisively. The Federal Reserve made added credit available to banks, which could lend it to hard-pressed brokers or mutual funds. The move helped limit the panic. Without ample credit, traders and securities firms could have faced insolvency. They might have been forced to dump stocks to raise cash. For all its impressiveness, though, this performance still leaves unanswered the basic question of how Greenspan will handle the broader problems of inflation and recession.

His position is anomalous. Lower interest rates are the traditional medicine for an economic slowdown. Indeed, the Fed cut a key interest rate after the crash as a means of providing short-term emergency credit. The so-called Fed funds rate was reduced from about 7.5 to 6.75 percent. Greenspan's dilemma is that he can't go much further down this path -- maybe he's already gone too far -- without creating as many problems as he solves.

All the evidence so far points to continuing U.S. prosperity. There's already something of a mini-export boom. In the third quarter, gross national product grew at a brisk 4.1 percent annual rate. Of course, the stock market crash could change the outlook. Overburdened by debt and alarmed by the crash, consumers may delay spending. But unless the effect is dramatic, lower interest rates risk overheating the economy and worsening inflation.

The unemployment rate is now 6 percent. Factory utilization is rising sharply. The economy can't tolerate both an export boom and strong domestic spending without fostering inflationary pressures. All inflation indexes are rising faster than in 1986, and only part of the increase reflects erratic swings in oil prices (down last year, up this year). Corporate purchasing agents report lengthening delivery times for new goods. A lower dollar is raising import prices.

A belief that the United States will tolerate higher inflation could also become self-fulfilling by triggering a collapse of the dollar. Inflation fears would prompt investors to dump the dollar, and higher import prices would intensify inflation. The dollar is fated to depreciate, but it matters whether the drop is gradual or sudden. A slow decline would allow U.S. exporters to expand production capacity, while other countries try to speed up their economies. Foreign exporters can shift production to the United States and ease the risk of domestic scarcities.

But none of these changes can occur instantly. The inescapable conclusion is that Greenspan and the Fed should continue to resist inflation -- not because it is a riskless policy, but because the alternatives are worse. The inflationary impact of a sharp drop in the dollar would either lead to a permanent rise of inflation or, more likely, force the Fed to subdue inflation by causing a slump. Meanwhile, the dramatic loss of exports to the U.S. market could drive foreign economies into recession.

So this is a testing time for Greenspan. No one really knows how the stock market will affect the economy. The initial appraisals indicate a surprisingly modest impact. Before the crash, 49 economists surveyed by the Blue Chip Economic Indicators newsletter predicted average 1988 economic growth of 2.8 percent. After the crash, that dropped to 1.9 percent. Unemployment barely rises to 6.2 percent. But who knows? Maybe the forecasts are too optimistic.

Whatever gamble Greenspan takes, he must contend not only with economic uncertainties but also with the pressures of public opinion. Here, a comparison with the Crash of 1929 is apt. It engendered a lot of talk about the economy's fundamental strength and the crash's therapeutic effects. Speculators would be punished; the value of real work would be restored.

In 1987, this sort of moralizing has been minimal. The almost universal response has been: Oh my gosh, we can't let this lead to a recession. The reaction is more than a mood; it's also political pressure. In an interview with the Wall Street Journal, Treasury Secretary James A. Baker III pointedly warned that the Fed shouldn't do anything that might risk a recession in 1988, which just happens to be an election year.

The contrast between the two crashes is worth pondering. With hindsight, the 1929 reaction rationalized government passivity that contributed to the onset of the Great Depression. But today's reaction poses the opposite danger. The eagerness to avoid recession -- even if it initially succeeds -- could lead to more serious economic problems later.