To QE or not to QE? That is the question.

Federal Reserve Chairman Ben Bernanke is set to testify before Congress Thursday, and pretty much the only thing the market cares about is whether the central bank will deliver yet another round of stimulus.

After all, we’ve already been through two rounds of quantitative easing, Operation Twist is set to end this month and the market looks to be hooked on the Fed’s fiscal drugs. The recovery is weak and perhaps losing steam, unemployment remains stubbornly high, inflation still is nowhere to be found and the S&P 500 has fallen into a technical correction.

Keep in mind, however, that Bernanke might give no hints whatsoever Thursday, since the Fed’s next regular meeting is in just a couple of weeks. That’s probably a more likely time to pull another liquidity rabbit out the central bank’s hat. And the consensus is that Bernanke will almost certainly do … something.

Morgan Stanley economists figure there’s a better-than-50% chance the Fed will launch QE3 or some other funky monetary policy program, if not this month, then soon. Deutsche Bank and Goldman Sachs also are increasingly confident that more easing is on the way. Growth is lackluster, unemployment is high and prices are stable — a situation that screams for stimulus, the thinking goes.

“At a time when Fed officials are far short of their dual mandate of maximum employment and 2% inflation, financial conditions should be accommodative and GDP growth should be well above trend in order to re-employ displaced workers and avoid a gradual transformation of cyclical into structural unemployment,” writes Jon Hatzius, Goldman’s chief U.S. economist.

However, what more easing can achieve at this point is a huge question. If the purpose is to lower longer-term interest rates, well, the yield on the benchmark 10-year Treasury note is already near all-time lows.

And if the idea is to force investors out of low-interest bonds into stocks, that’s not working much either. Cash has flowed out of domestic stock mutual funds every month for a year. It’s going into foreign stock funds and bond funds.

That’s because risk aversion — also known as fear — is trumping punishingly low yields. If the eurozone touches off another full-blown credit crisis, banks and money markets could be a deadly place to have parked your cash. So investors are more than willing to accept 1.5% on a 10-year note — or a negative rate on the shortest-duration instruments — because they offer capital protection. It’s tired, but it’s true: The return of your principal is more important than return on your principal.

Yes, if history repeats itself, more QE should give a stocks a boost. But if the pattern of previous bouts of stimulus hold, the uptick will be less dramatic and more short-lived. It’s no secret that each of the two rounds of QE and then Operation Twist have successively produced diminishing returns for equity markets.

Meanwhile, another round of QE will give gold a lift, as well as other commodities. They’re highly sensitive to inflation and the whole reflation trade, for one thing. Heck, a subsequently weaker dollar should help everything priced in greenbacks. Jeffrey Kleintop, chief market strategist at LPL Financial, figures that a stronger dollar is responsible for about half the drop in gold prices from September 2011 until now. So QE will be great for the gold bugs.

But if yields do fall further, it might have nothing to do with the Fed throwing around the weight of its balance sheet. Crisis in the eurozone and the specter of recession and deflation could hammer yields far beyond the power of the central bank. Treasurys are low, but still plenty high when compared with sovereign debt of a bunch of other stalwart governments. The yield on 10-year German bonds is at 1.21%, while Japan’s 10-year debt stands at 0.86%. Comparable bonds from Switzerland, Hong Kong and Denmark yield less than 1%, too.

At this point, as much as the market wants more QE, the majority of its benefits look to be behind us. Yields are low. Fear is elevated. And monetary policy is no magic bullet.