On Tuesday, Federal Reserve officials gathered to set the nation’s monetary policy. That probably won’t be the most interesting news to come out of the two-day, meeting, however.

On Wednesday afternoon, the leaders of the central bank will release their forecasts for  levels of economic growth, unemployment and inflation they expect to see over the coming three years. Those numbers, due out at 2 p.m., will offer a glimpse of how much juice they believe the recovery has in it. Lately, most economic data has looked stronger, even as federal budget cuts threaten to hold back growth as 2013 progresses.

The big question is whether Fed officials can get it right after years in which they have regularly predicted a stronger economy than the one that materialized. In January 2011, Fed officials predicted that GDP would grow around 3.7 percent that year. It clocked in at 2 percent. In January 2012, they anticipated growth of about 2.5 percent. We ended up with 1.6 percent.

Getting the forecasts right this time will be especially tricky: The economy came to a standstill at the end of last year, but job growth has picked up faster than expected. Lawmakers backed away from the fiscal cliff at the end of 2012 but couldn’t escape sequestration.

A lot is riding on the numbers swirling around in Fed crystal balls. Those forecasts are the foundation for critical decisions about how to support the economy. The Fed has often, both during the financial crisis and its aftermath, held their fire on monetary easing because they were overly optimistic about the economy.

To be fair, officials’ economic projections are not static. As time rolls on and data roll in, they have lowered their forecasts for growth, though they have always consistently predicted that better days are just around the corner. They have predicted that the U.S. economy would be back to a 4 percent rate of growth in 2012 … then 2013 … then 2014.

To be fair, part 2: Forecasting by committee is never easy. The central bank’s leadership is made up of seven governors and 12 reserve bank presidents. Each one crafts a forecast built on independent models, underlying assumptions and personal biases, resulting in slightly different views of where the economy is headed. (The numbers above are the midpoint of the “central tendency” of those projections.)

A much more rigorous analysis of Fed official’s forecasts was published in 2007 by researchers at the Fed itself and covered 20 years of historical predictions. It found that fall estimates for how the economy fared that year were off by about 0.6 percentage points. In other words, the Fed was imprecise in estimating how strong overall growth was even in a year that was mostly over. Forecasts for three years into the future missed the mark by about 1.5 percentage points.

Uncertainty surrounding the forecasts has only increased since that report was published. As Diane Swonk, chief economist at Mesirow Financial, put it: “It’s very hard to forecast into an abyss.”

Fed officials’ estimates have been higher than those of some private forecasters. Richard Moody, chief economist at Regions Bank, said his growth estimates are lower than the Fed’s because of a  fundamental  disagreement with Fed Chairman Ben S. Bernanke’s belief that the recession was driven by a dropoff in demand. “My premise from the start … is that it was never going to be a fast recovery because we were dealing with structural imbalances throughout the economy,” Moody said.  “That was always going to be kind of a painfully slow healing process.”

The financial crisis has opened new windows into the inner workings of the Fed. They don’t have access to a secret treasure trove of data. Their forecasts and monetary policy decisions are based on the same numbers that the public has access to. Their power lies in how they interpret that data  – and the consequences can be harsh if they get it wrong.