The Federal Reserve has ended its roughly $3.7 trillion program of bond buying, leaving in its wake a host of hard questions. Did it strengthen the economic recovery? If so, by how much? What are the long-run effects? Should it be used again? We don’t have good answers.

We need a dispassionate accounting of its successes and shortcomings, because the bond buying represents the most significant economic-policy innovation to emerge from the 2008-2009 financial crisis. Instead, the subject is defined by a patchwork of disconnected studies and much bewildering jargon. The bond buying itself is called both “quantitative easing” (known as QE) and “large-scale asset purchases” (LSAPs).

Let’s demystify.

Traditionally, the Fed influences the economy by changing short-term interest rates. It raises rates to quash inflation. It lowers them to stimulate expansion. But in late 2008, reeling from the financial crisis, the Fed effectively cut short-term rates to zero. So its main weapon was fully deployed and frozen. To avoid confessing helplessness, the Fed needed to do something else to revive the economy.

It decided to buy bonds — U.S. Treasury bonds and government-guaranteed mortgage securities, both with maturities of years, not days or weeks. The strategy was simple. The investors (individuals, pensions, bond funds) that sold to the Fed would receive mounds of cash which they’d invest in other bonds or stocks. Long-term interest rates would fall; stock prices would rise.

These changes would in turn bolster the “real economy” of production and jobs. Lower long-term interest rates would aid the credit-dependent housing and motor-vehicle sectors. A stronger stock market would make investors richer. They’d spend some of their gains — a phenomenon economists call the “wealth effect.” This added spending would raise output and employment.

So success occurs in two stages: first, favorable changes in financial markets; then higher spending. Is this what happened?

To evaluate changes in long-term interest rates, economists use “event studies.” These examine whether rates fall when the Fed announces more bond buying. For example, rates dropped roughly one percentage point when the Fed unveiled its first round, concluded a study by economists Arvind Krishnamurthy of Stanford University and Annette Vissing-Jorgensen of the University of California at Berkeley. That’s a huge change. Later announcements produced much smaller rate declines, the study said.

The next step is to feed lower interest rates into computer models that simulate the real economy. In the summer of 2012, then-Fed Chairman Ben Bernanke said that the Fed’s model found that the bond buying had created 2 million jobs and raised the economy’s output by 3 percent. These gains, too, are huge.

By this evidence, bond buying has been a roaring success. But there are grounds for skepticism. What’s unclear is whether these results are real — or just reflect optimistic assumptions.

Take the event studies. They observe interest rates only during the first hours or days after a Fed bond-buying announcement. Over longer periods, interest rates may reverse course. On his blog, economist James Hamilton of the University of California at San Diego, says that rates on 10-year Treasury bonds actually rose during periods of Fed bond buying — the opposite of the goal. Whatever the Fed’s influence, he writes, it was overwhelmed by “developments beyond [its] control.”

Likewise, economic models may exaggerate the tendency of lower interest rates and higher stock prices to increase spending. Maybe the financial crisis has made people more cautious. The models may be outdated.

Not surprisingly, Bernanke’s upbeat assessment of the Fed’s impact isn’t universally shared. A study by Jing Cynthia Wu of the University of Chicago and Fan Dora Zia of the University of California at San Diego, contended that the Fed achieved only modest gains. Without the Fed’s moves, the unemployment rate in December 2013 would have been 6.83 percent instead of 6.7 percent, the study estimated, and the index of industrial production would have been 101 instead of 101.8. Slight improvements.

Through its brief life, the Fed’s bond buying has been enormously controversial. Many critics warned that, by pumping out so much money, it would ignite uncontrolled inflation. This hasn’t yet happened.

But supporters of the bond buying may also have overstated their case. Although the nearly $4 trillion the Fed spent is a lot, it’s small compared with the size of U.S. credit markets — all the outstanding bonds and loans. At the end of 2013, that was $57 trillion. Similarly, the value of U.S. stocks was $34 trillion. These huge amounts may have blunted bond buying’s impact on rates and stocks. Foreign experience is also mixed; Japan’s aggressive quantitative easing seems only partially successful.

We desperately need more rigorous research by the Fed and private economists. Used once, bond buying is bound to be proposed again. When that happens, we ought to know how well it did.

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