But when normal interest rates are closer to 3 percent, the Fed can cut rates only a few times, because rates can only go so low — perhaps as low as zero, maybe a tad lower. This means that in even a typical downturn, the Fed may be unable to cut rates as much as it would like.

Even worse, this limit is a far bigger problem when an economic downturn follows closely on the heels of a previous recession. Right now, for instance, the central bank’s main short-term rate, the federal funds rate, is still only three-quarters of a percent to 1 percent, because the Fed wants to continue stimulating the recovery. This leaves the central bank with very little room to respond if the economy falters. Even a minor slowdown now could require a larger rate cut than is feasible, once again leaving policy makers wishing they could do more.

This dynamic can feed on itself. The less ammunition the Fed has to blast the economy out of its malaise, the weaker and slower will be the recovery, making it more likely that the next bad shock will require the Fed to cut rates more than is feasible.

To assess these problems, two senior Federal Reserve economists, Michael T. Kiley and John M. Roberts, ran hundreds of simulations in the Fed’s large-scale macroeconomic model, evaluating how the United States would perform in response to the sorts of shocks that have historically buffeted the economy.

In one set of simulations that you might call the good old days, they set the normal interest rate at 6 percent, and then let the Fed adjust rates as economic conditions evolved. In that environment, interest rates hit zero only around 2 percent of the time. This accords with the reality that the lower limit on interest rates simply was not a problem until recently.

But times have changed. When the economists set the normal interest rate at 3 percent and let the Fed adjust interest rates as conditions warranted, rates moved down to zero percent and could not move any lower roughly a third of the time. In some of these cases, the economy didn’t need much extra punch, and so this slowed the recovery only a little. In others, it was a more telling constraint, and it took years for the economy to return to normal.

Their research paper, “Monetary Policy in a Low Interest Rate World,” which was presented at a recent meeting of the Brookings Papers on Economic Activity, explains why this is so worrisome.