WASHINGTON, Dec 10 (Reuters) - The U.S. Federal Reserve"s experiment with running a "hot" economy has edged into historically uncharted territory, with an unemployment rate never reached without associated central bank rate increases and now levels of inflation that in the past also prompted a policy response. The Consumer Price Index for November posted the biggest annual increase in 39 years, data on Friday showed, amid signs that price pressures are broadening and likely leading policymakers at their meeting next week to significantly raise inflation projections that have been running behind actual outcomes. read moreThat may prompt a policy shift, with officials accelerating plans to end their bondbuying and, many analysts expect, signaling that rate increases may begin sooner than anticipated.The unemployment rate is also flashing red, at least by past Fed standards. The 4.2% rate reached in November has only been hit or exceeded about 20% of the time since the late 1940s, covering four periods of low joblessness, including the late 2010s, with the Fed raising rates during each. The central bank in 2020 concluded that inflation was now less of a risk and pledged to try to milk more jobs and a lower unemployment rate out of an economy it felt had changed in fundamental ways since the high inflation scares of the 1980s - a conclusion that"s now being tested in real time. "They are behind the curve and I have thought so for some time," said Glenn Hubbard, former chair of the Council of Economic Advisers under President George Bush and now a Columbia University economics professor. The Fed"s new approach hoped to drive an array of labor market indicators like the participation rate back to pre-pandemic levels, but Hubbard said "running the economy hot...is a risky bet" if it aims to offset structural economic forces like demographics that aren"t responsive, at least not quickly, to central bank policy.DECLINING REAL WAGES Fed officials still hope inflation will ease largely on its own, even as they prepare to shift policy in ways that would allow sooner and faster interest rate increases next year than had been anticipated. In the meantime, while Fed Chair Jerome Powell and other policymakers rebut comparisons between this era and the years in the 1980s when high inflation cut into living standards, recent price increases have posed a similar sort of political dilemma. On the surface wages are rising as employers struggle to fill open jobs in a pandemic era where the unemployed are reluctant to rejoin jobs for health or other reasons, and those who are in jobs have gained leverage to job-hop for higher pay. Yet once adjusted for inflation wages have fallen for nine of the past 11 months, with growth in "real" wages moving little beyond the pre-pandemic trend. That fact has hit home in the Oval Office, with President Joe Biden"s Democratic Party facing a potentially difficult mid-term election map next year and his approval ratings taking a hit in part because of rising prices. Biden in a statement Friday pitched the issue forward, arguing that key prices for gas and autos were already drifting lower, and said steps taken or proposed by his administration would help ease inflation"s pace. "Price increases continue to squeeze family budgets," Biden said. "We are making progress on pandemic-related challenges to our supply chain which make it more expensive to get goods on shelves, and I expect more progress on that in the weeks ahead." NEXT UP: THE FED The strong CPI data for November were expected, but still "only solidify the case for a faster tapering of asset purchases" when the Fed meets next week, said Rubeela Farooqi, chief U.S. economist for High Frequency Economics. "More important will be Chair Powell"s message on tightening of policy going forward." Central to Powell"s messaging will be a defense of why this time it"s different. The pandemic offers one rationale. The shock dealt to the American economy in 2020 was unrivaled in its speed and scope, and the reopening - far from the turgid recovery from the 2007 to 2009 recession - has been so fast it has caused problems of its own. Inflation is one aspect of that, with global supply chains trying to catch up with unprecedented consumer demand in the United States that was driven by another historic anomaly - personal incomes that rose, due to large government support programs, despite massive unemployment. But the Fed"s response is similarly unprecedented. The November unemployment rate is now close to the 4% level that policymakers consider sustainable over the long run. It is also edging towards what Fed officials have effectively penciled in as the lower limit on the unemployment rate of about 3.5%. Since policymakers began publishing quarterly economic projections in 2012 the median unemployment rate for any given year-end has slipped below 3.5% only once, and that just barely, at 3.45%. In data since January 1948, the unemployment rate has only fallen below 3.5% in 41 of 887 months - during a jobs boom of the early 1950s, again in the late 1960s, and never since. The central bank is counting on finding a sweet spot this time that has been elusive, a "soft landing" that brings inflation down from higher-than-desired levels while allowing the labor market to continue to heal. Spells of unemployment this low have not, so far, tended to end so well.