(FORTUNE Magazine) – The markets and the media laughed when Fed Chairman Alan Greenspan warned repeatedly during the past several months that the stock market's roaring growth couldn't continue forever. They rolled their eyes when he said, also repeatedly, that the Fed was concerned about the recurrence of rising inflation and needed to move to raise interest rates to vent inflationary pressures before they began pushing up the indexes.

Well, Greenspan's forecasting abilities are looking pretty good. On April 14 the Labor Department announced that the core inflation rate had risen an unexpectedly high 0.4% in March--suggesting that the first strong inflationary surge in several years may have begun. The stock market, already perturbed by the collapse of settlement talks in the Microsoft antitrust case (and suffering some morning-after remorse in the wake of its passionate dot-com lovefest), plunged on the inflation news and continued to stagger in the ensuing weeks. As FORTUNE went to press in late April, the Dow Jones industrial index was back to where it had been a year earlier, and the Nasdaq composite index had fallen 30% in a few weeks, careering into territory it hadn't visited since last fall.

You might think the markets and the media would now cut the Fed chairman a little slack--admitting that maybe he does know a thing or two about the economy, and that, just maybe, he was right to begin raising short-term interest rates last June, even though there was no obvious evidence of inflation. (The Fed has pushed rates from 4.75% back then to 6% now and is expected to raise them again when it meets May 16.)

You might also think that Greenspan could draw on the store of credibility he has built up since he became chairman in the summer of 1987. Since then there has been just one recession--in 1990-91. It was barely a recession at all: The economy contracted by a mere 0.2% (in the 1982-83 recession, for comparison's sake, it shrank two whole percentage points). And since 1991's bump in the macroeconomic road, we have been experiencing the longest economic expansion in U.S. history, with no obvious end in sight.

You might think all that, but you'd be wrong: In a pattern that has unfolded again and again in Greenspan's 12-year reign, the markets and media are--at best--treating him as if he were an unproven beginner. At worst they regard him with outright suspicion. Back in 1993, Fed watchers seized on the fact that Greenspan was seated next to First Lady Hillary Clinton at her husband's first State of the Union address, speculating that he had joined forces with the Clinton Administration and would conduct monetary policy according to its interests. When Greenspan concluded in early 1994 that a recurrence of inflation was likely (even though there was no hard evidence at that time), he began pushing up short-term interest rates--doubling them from 3% to 6% between early 1994 and mid-1995--and was criticized widely for doing so. He turned out to be right: The economy cooled (GDP growth fell from more than 6% in the fourth quarter of 1993 to less than 1% in second-quarter 1995), and then growth resumed, avoiding the typical boom-bust cycle of expansion and recession that had characterized previous decades. This policy episode--referred to as "the soft landing"--is considered by the monetary-policy cognoscenti to be among the most successful central-bank actions in history.

Today the publisher of Forbes (once a close rival of FORTUNE's) ridicules Greenspan as "the world's most inflated central banker." Business Week concludes that the Fed has "painted itself into a corner" and worries that the "nine-year-old economic expansion [will] come to a screeching halt." Most egregiously, the venerable New Yorker devoted 12 densely packed pages of its April 24-May 1 issue to a profile of Greenspan. It reviews his career from grade school to the present, dwelling at length on various events in his life both before and at the Fed. The profile ventures, "If Greenspan succeeds in slowing down the economy without provoking a recession, he will, surely, go down as one of the great Fed chairmen." But there is no mention in the profile of the soft landing of 1994-95, the high point of his career, in which he did exactly that.

Can he do it again? Sure, the threat of a stock market meltdown makes the task trickier, but the economy is far stronger today than it was six years ago. Based on Greenspan's record--and contrary to what you may read or hear elsewhere--there's every reason to think he can do it again.

REPORTER ASSOCIATE Lenore Schiff