To make the procedure work, the Fed holds lots of bonds, which in turn creates excess reserves in the banking sector. But as the central bank pared back its balance sheet, nobody knew for sure just how many reserves needed to stay in the system to make it work.

Last week, markets handed the Fed an answer.

Evidence of trouble first appeared on Sept. 16, when a dollar shortage reared its head in the market for overnight repurchase agreements, or repos — basically short-term loans that hedge funds and banks tap for funds. The cash crunch occurred as corporate taxes came due and government bond issuance sopped up liquid cash.

Usually, banks would have swooped in to supply fresh liquidity before conditions got out of line, attracted by the climbing repo rates. But this time, they hoarded their reserves. The Fed seems to have shrunk its balance sheet to a place where reserves no longer come to the rescue during times of market pressure, rates strategists and economists said.

The central bank had hoped to stop the drawdown before reserves grew so thin that market conditions got messy, based on officials’ public comments over the years and interviews with people familiar with the process. While officials had entertained the possibility of occasionally intervening in markets again, doing so regularly was not the plan.

But last week’s shortage forced the Fed to jump into the market to supply cash for the first time since the financial crisis. The New York Fed has announced that it will continue to carry out similar operations until Oct. 10.