When Alan Greenspan talks, people listen.

Trouble is, they don't always do what he would like.Greenspan, chairman of the Federal Reserve Board, warned in late 1996 that "irrational exuberance" was propelling stock prices. The Dow index soared another 3,000 points over the next year and a half.

But on Tuesday, Wall Street heeded some hints Greenspan had dropped on the eve of the long Labor Day weekend. The Dow Jones industrial average rebounded sharply, closing at 8,020.78, up 380.53.

Underlying the see-sawing markets is a question rarely asked: What business does Greenspan have sticking his nose into whether stock prices go up, down or sideways?

Answer: Plenty.

In the view of economists, Greenspan's job includes paying attention to a wide array of shadows and substance in economic activity. They range from the value of stocks on Wall Street to the cost of money in Germany to the price of tea in China.

Changes in the prices of stock, money or commodities, at home or abroad, can have long-term consequences on the rate of inflation and economic growth in the United States. Greenspan the stock watcher is also Greenspan the nation's top economist by virtue of his position.

Greenspan, appointed by the president to head an agency created by Congress, plays the parts of politician, scold and sage as well as economist in a job that many citizens who are affected by his work may not understand. While much of the action takes place behind the scenes, economic turmoil at home or abroad can vault him into a starring role.

While the chairman garners most of the attention, the Fed's Open Market Committee (FOMC) has the authority to set policies that affect the supply of money in the economy and influence interest rates. The 12-person committee is made up of members of the Fed's board of governors and the presidents of regional Fed banks, in rotating terms.

The Fed chairman is first among equals on the committee, a leader who seeks consensus on whether to pursue policies that tend to accelerate or slow economic growth. Part of his influence stems from having more than 100 economists reporting directly to him, which provides a base of knowledge his peers cannot claim.

In an era when efforts to contract federal budget deficits have reduced the power of Congress to change tax rates or government spending to sway the course of the U.S. economy, the authority of the Fed has risen. In effect, its tools to influence monetary growth and interest rates are the most potent Washington has to affect commerce and consumer spending.

Greenspan's "concern with stock prices, which may be correct or incorrect, is related to his overall concern for stability in the economy," said economist Allen Meltzer, chairman of the Shadow Open Market Committee, a panel of private economists who second-guess Fed policy.

"Probably his staff and he are concerned about stock prices and think one possible outcome would be a crash that would affect consumer spending."

Congress created the Fed in 1913 as a central authority charged with keeping the nation's banking system running smoothly and, by implication, keeping the country's economic fortunes on track.

It hasn't always done a stellar job.

In the Great Depression, economic historians say, the Fed botched the chance to rescue many large banks from insolvency - a mistake that deepened the economic downturn.

And in the 1970s, the Fed was blamed for fanning inflation with an "easy money" policy that ultimately led to a combination of spiraling prices and sluggish economic growth that was dubbed "stagflation."

But between 1977 and 1987, under Fed Chairman Paul Volker, inflation fell from double-digit levels to a rate of about 4 percent. Since Greenspan took the helm in 1987, inflation rates have been cut in half, to less than 2 percent in the past year.

The Fed has been quick to react in an emergency. As recently as 1987, after an October crash that knocked off 20 percent of the Dow's value in a single day, the Fed pumped money into New York banks to ensure that brokerage houses had the cash to pay customers who wanted to sell their stock or traders who needed money to settle accounts with one another.

More broadly, the Fed effort to briefly inflate the money supply was meant to offset broader economic consequences of a longer-run decline in stock prices - a worry that, as it turned out, did not become a reality.

Macroeconomic Advisers, a St. Louis economic consulting firm once headed by Fed Vice Chairman Laurence Meyer, estimates that for every dollar in value lost in household net worth in a market decline, consumers pull back on spending by about 4 cents in the months that follow. Those pennies add up when the market loses more than $1 trillion in value in a single day, as it did last week.

The Fed was just as worried about wealth gains pushing up consumer spending when the market was soaring. Indeed, one of the reasons Greenspan fretted about "irrational exuberance" was out of concern that the higher the market rose, the farther it would fall in a crash.

"Last year, in real terms, the increase in wealth was the largest we've seen in several decades," said Bill Melton, a Minnesota economic consultant who has written a book about the Fed. "All other things being equal, that would suggest consumer spending would be robust and the economy might continue to grow beyond its sustainable growth rate."

In the past, spurts of growth beyond an annual 3 percent rate have been followed by a rise in inflation. Greenspan has said again and again that pushing down inflation rates is the surest path to long-term, non-inflationary economic growth.

"During this decade, it's become more and more clear that if the Fed keeps inflation in check, other things will fall into place," said Peter Kretzer, economist at NationsBanc Montgomery Securities.

While the markets listen when Greenspan talks, it's not often that he gets many good lines. Vague language and droning speech patterns are a plus for the Federal Reserve, an institution that doesn't like to telegraph its actions in advance.

Take this gem from the Greenspan speech in California on Friday that some say lifted the spirits of stock traders Tuesday:

"In the spring and early summer, the Federal Open Market Committee was concerned that a rise in inflation was the primary threat to the continued expansion of the economy. By the time of the committee's August meeting, the risks had become balanced, and the committee will need to consider carefully the potential ramifications of ongoing developments since that meeting."

Translation: Interest rates may be as likely to go down as go up in the coming months, because of weaker economies abroad reducing demand for U.S. exports and U.S. companies reporting smaller profits from foreign operations.

One reason for obfuscation is that Greenspan and his colleagues sometimes don't know what they'll do next.

"The markets have been indicating monetary ease," Kretzner said, noting that interest rates on bonds that won't mature for decades have been falling faster than the interest rates on bonds with terms of only a few years.

To Kretzner, that means Greenspan will see the market signal as a sign to lower the interest rates the Fed controls. Both of those rates are for short-term loans: The federal fund rates - the price banks charge each other for overnight loans - and the discount rate, the price the Fed charges member banks for loans from its vault.

"Certainly, by controlling the federal funds rate, the Fed does not control the whole economy," Kretzner said. But lower interest rates mean a lower cost of doing business and the promise of higher corporate profits in the future.

The result, he said, would likely be a rise in stock prices, the very phenomenon that Greenspan lamented not too long ago. Whether a market rebound at the moment is good or bad, however, no one knows for sure. Not even Greenspan.