The Federal Reserve’s experiment with a second round of quantitative easing is nearing an end. Did it achieve its goal of lowering interest rates and stimulating the economy?

Should we remember QE2 as a brilliant innovation, a central piece of the Fed’s future recession and deflation-fighting toolkit? Or is it the first step toward hyperinflation? When the Fed stops buying government bonds, will interest rates rise sharply because no one else is buying?

In fact, QE2 didn't stimulate the economy, as the left had hoped, nor will it lead to the inflationary or bond-market disaster feared by the right. QE2 did basically nothing. But that is a deep and unsettling lesson: The Fed is essentially helpless in the current situation.

The chart attached to the left shows how interest rates behaved through the QE2 episode.

The red dashed line represents total Fed holdings of Treasury notes and bills. You can see the sharp rise starting in November 2010. The Fed purchased $600 billion of long-term government bonds, giving banks $600 billion more reserves in return. (Bank reserves are accounts banks hold at the Fed.)

The vertical lines mark the two big Fed announcements. On Aug. 10, the central bank announced that it would reinvest maturing assets in Treasuries. On Nov. 3, it announced the actual QE2 program.

QE2 doesn't seem to have lowered any interest rates. Yes, five-year rates trended down between announcements, though no faster than before. The November QE2 announcement and subsequent purchases coincided with a sharp Treasury rate rise. The five-year yields where the Fed bought most heavily didn't decline relative to the other rates, as the Fed’s “segmented markets” theory predicts. The corporate and mortgage rates that matter for the rest of the economy rose throughout the episode.

How should we interpret this apparently abject failure? In March testimony before the Senate Banking Committee, Fed Chairman Ben Bernanke saw it as evidence of the central bank's great power:

“Yields on 5- to 10-year nominal Treasury securities initially declined markedly as markets priced in prospective Fed purchases; these yields subsequently rose, however, as investors became more optimistic about economic growth and as traders scaled back their expectations of future securities purchases.”

If yields go down, the Fed is successfully stimulating the economy with QE2. And if yields go up? Well, the Fed is successfully stimulating the economy with QE2. And Bernanke claimed almost miraculous additional effects:

“Equity prices have risen significantly, volatility in the equity market has fallen, corporate bond spreads have narrowed, and inflation compensation ...has risen to historically more normal levels.”

On the other hand, Philadelphia Fed President Charles Plosser warns that QE2 provides too much stimulus: The bank has "a trillion-plus excess reserves," he said, providing "the fuel for inflation."

Expected inflation could explain the sharp rise in long-term yields starting in November. But the rate for 10-year Treasury Inflation Protected Securities, or TIPS, rose in parallel, contradicting that interpretation. Simultaneously denying Bernanke, however, the five-year TIP rate didn't rise. An increase in that rate would have been a sign of a stronger economy in the next five years. The bond market is a tough critic.

Both sides ignore an inescapable conclusion: With near-zero short-term interest rates, and bank reserves paying interest, money is exactly the same thing as short-term government debt. A bank doesn't care whether it owns reserves or three-month Treasury bills that currently pay less than 0.1 percent.

This is what drove the Fed to QE2 in the first place. Conventional easing -- buying short-term Treasuries in exchange for reserves -– obviously has no effect now. Taking away your green M&Ms and giving you red M&Ms instead won't help your diet.

But if exchanging money for short-term debt has no effect, it follows inescapably that giving banks more money is exactly the same as giving them short-term debt. All QE2 does is to slightly restructure the maturity of U.S. government debt in private hands.

Now, of all the stories we've heard to explain our sluggish recovery, how plausible is this one: “Our big problem is the maturity structure of Treasury debt. If only those goofballs at Treasury had issued $600 billion more three-month bills instead of all these five-year notes, unemployment wouldn’t be so high. It’s a good thing the Fed can undo this tragic mistake.” That makes no sense.

For the same reason, when money is the same thing as debt, it doesn’t cause inflation.

Ineffective QE2 doesn't mean harmless QE2, however.

We are in danger of inflation for fiscal, not monetary reasons. If investors lose faith the U.S. will fix its long-run budget problems, they will try to sell government debt of all maturities. Rates will rise and stagflation will break out no matter what the Fed does.

Short-term debt dramatically increases this danger. If the U.S. were financed with long-term debt, bond prices would fall, but there would be time to fix the deficit and restore confidence in the debt. But the average Treasury maturity is less than a year. Every two years, the U.S. must find new borrowers to pay off most of our debt. If those investors depart, a stagflationary crisis must result. Our moment of low long-term rates is a golden opportunity to issue long-term debt, not to buy it back. QE2 was a small step in the wrong direction.

Moreover, QE2 distracts us from the real microeconomic, tax, and regulatory barriers to growth. Unemployment isn't high because the maturity structure of U.S. government debt is a bit too long, nor from any lack of “liquidity” in a banking system with $1.5 trillion extra reserves.

Mostly, it is dangerous for the Fed to claim immense power, and for us to trust that power, when it is basically helpless. If Bernanke had admitted to Congress, “there’s nothing the Fed can do. You’d better clean this mess up fast,” he might have had a much more salutary effect.

(John H. Cochrane is a professor of  finance at the University of Chicago Booth School of Business and a contributor to  Business Class.  The opinions expressed are his own.)