With almost choreographed precision, Mr. Greenspan presided over his last policy meeting at the Fed shortly before the Senate voted this afternoon to confirm Ben S. Bernanke as his successor.
As expected, the Fed increased short-term interest rates today, with the benchmark federal funds rate on overnight bank loans rising another quarter point today, to 4.5 percent. This is its 14th straight increase since June 2004.
But the Fed, in a statement, effectively gave Mr. Bernanke a wide berth to chart his own policy by making clear that it is no longer seeking a "measured" pace of rate increases.
That means that Mr. Bernanke can start on Wednesday with his own agenda, but it also means that the uncertainties and risks of making mistakes are greater than in recent years.
Mr. Bernanke, a highly respected economist but almost unknown outside the circle of monetary economics, will be taking over the most powerful economic job in the world at a moment of both great strength and great uncertainty for the Fed.
Unemployment, at 5 percent, is back down to levels that most economists once considered "full employment." Inflation, despite high energy prices, is remarkably tame. Productivity is still climbing rapidly.
But Mr. Bernanke will also be inheriting big challenges, including a possible hangover from Mr. Greenspan's policy of flooding the economy with cheap money after 2001.
The United States' current account deficit, the gap between what it spends and what it produces, soared well past $700 billion in 2005 and requires about $2 billion a day in fresh foreign financing.
Energy prices, which declined during most of Mr. Greenspan's 18-year tenure, have climbed back to new records even as the United States' dependence on foreign oil has increased.
Wages of low-income and middle-income workers are barely keeping pace with inflation. Wage inequality appears to be widening between the top and bottom ranks of the work force, partly because of a relentless contraction in blue-collar factory jobs.
Both Mr. Greenspan and Mr. Bernanke appear to have been well-aware of the potential potholes that lie ahead.
In his last act as Fed chairman today, Mr. Greenspan came close to wrapping up his last major policy challenge before retiring: a nearly two-year effort to gradually reverse the cheap-money policies that he used to prop up the economy after 2001.
Mr. Bernanke will arrive at the Fed on Wednesday morning with considerable freedom to chart his own course.
For the first time in nearly three years, the Fed is no longer providing investors with an implicit promise about its coming decisions about interest rates in the months ahead.
But Mr. Bernanke's freedom to imprint his own ideas on policy also comes at a moment of precarious uncertainty. For the past three years, Mr. Greenspan and other Fed policymakers had unusual clarity about the priorities: first to shore up the economy with low interest rates after 2001 and then to re-establish a more normal or "neutral" policy once the economic recovery appeared to be self-sustaining.
The priorities now are more cloudy. Interest rates are back in line with historical norms, but the economy could be on the verge of a slowdown because of high energy prices and a weak housing market.
"The challenge is in making day-to-day policy at a time when mistakes are most likely to be made," said Laurence Meyer, a former Fed governor and now a top forecaster at Macroeconomic Advisors Inc.
"We are close in many ways to a soft landing," Mr. Meyer continued. "But that's really a razor's edge."