How much of a boost to the U.S. recovery could another trillion dollars or two buy?
That's a tricky question for the when it meets Tuesday to debate what would warrant pumping more money into the financial system.
To battle the financial crisis, the Fed bought $1.7 trillion of longer-term Treasury and mortgage-related bonds, supplementing its pledge to keep interest rates near zero for a long time.
All told, it helped stabilize a collapsing financial system and to avert what could have been a second Great Depression.
Now, faced with a 9.6 percent jobless rate and below-target inflation, Fed policymakers are trying to gauge how much they could achieve if they resume massive quantitative easing.
Few analysts expect the Fed to launch a new round of bond buying this week, and uncertainty over the impact of fresh moves may be a factor keeping the central bank on the sidelines.
"I think part of the hesitancy of the committee to use quantitative easing a second time around relates to views of its effectiveness," said Vince Reinhart, a former Fed staffer.
At the Fed's August meeting it decided to reinvest maturing mortgage-debt in Treasuries to keep its balance sheet steady, a move many analysts saw as a precursor to more easing.
Proponents of a relaunch of large-scale bond-buying say it will help prevent inflation expectations from falling and spur growth by further reducing borrowing costs for consumers and businesses.
Skeptics say the economic recovery has just hit a weak patch. They argue that more easing could be ineffective in helping the economy, potentially damaging Fed credibility.
An incremental drop in long-term yields may not be enough to force banks to stop hoarding safe-haven Treasuries and make loans to businesses instead, some analysts warn.
Some policymakers worry that more easing could fuel market imbalances or sow the seeds of sky-high inflation ahead.
There is also the risk that the Fed spooks investors.
"My own view is that any radical balance sheet program would be seen by many as an act of desperation which would dampen business sentiment and depress non-financial borrowing even more," said Wrightson ICAP Chief Economist Lou Crandall.
Hard to Measure Success
Fed bond purchases can have two effects. They can increase liquidity in strained markets and, by lowering yields, force investors to look for returns in riskier asset classes, helping to boost the supply of credit in the economy.
In addition, some officials believe bond buying helps solidify trust among investors that the Fed will keep policy easy for longer, further helping to lower borrowing costs.
The New York Federal Reserve Bank estimates that the $1.7 trillion of purchases lowered the yield on the 10-year Treasury note by between 30 and 100 basis points.
The estimate is based in part on the sharp drop in yields that occurred when the Fed first announced its large-scale bond-buying program.
But this "announcement effect" approach does not show how yields acted over the course of the program and may not appropriately capture the impact, analysts say.
It is tough to gauge how much of a move in yields can be tied to the Fed's actions after the fact, and it is also extremely difficult to predict the impact of another move.
When it comes to the benchmark overnight federal funds rate, "you can come up with rough orders of magnitude of the impact, but with quantitative easing there is so much uncertainty, you can't calculate it with any type of precision," said Dino Kos, former head of the New York Fed's markets group and a managing director at Portales Partners LLC.
The success of the first round of purchases may have been amplified by the stressed nature of markets at the time, as well as the fact that the purchases were focused on the smaller, less-liquid agency mortgage-backed securities market.
"If you show up and purchase assets when markets are stressed, you are not pushing back against much conviction so you can move prices more easily," said Reinhart, the former Fed staffer.
To get a significant effect in the Treasury market—where any new round of purchases would likely be centered—could be harder, says Mark Gertler, a professor at New York University.
"Evidence suggests it would take a huge purchase of long-term government bonds, maybe the whole market, to really have any effect, and the effect would be quite uncertain."
Rather than announcing such an eye-popping amount upfront, the Fed could decide to buy Treasuries in smaller steps, calibrated to the economic outlook at each meeting.
Forecasting firm Macroeconomic Advisors estimates each $100 billion in asset buys could lower the yield on the 10-year Treasury note by 0.03 percentage point.
That is a marginal move that could go unnoticed, though if Fed buying helped nudge up the inflation rate it could get a bit more of a bang for its buck on real rates.
Even a small amount of easing is not to be sneezed at, says Michael Feroli, chief U.S. economist at JPMorgan Chase.
"If you have a headache and only one aspirin left, do you decide not to take it because you wish you had two aspirins?"