The Federal Reserve says it will keep buying bonds until the labor market has “improved substantially,” without defining the phrase. Officials may have adopted a threshold nevertheless, say two former Fed economists.

Chairman Ben S. Bernanke needs to see four months of job growth averaging at least 200,000 to justify reducing the pace of asset purchases, according to Vincent Reinhart, a former director of the Fed’s Division of Monetary Affairs. Roberto Perli, a former researcher in the division, said the central bank would need to see that pace “through the summer.”

“They would see that as confirmation that the economy is on a self-sustaining trajectory and they would thus be confident that they could reduce the pace” of quantitative easing, said Perli, a partner at Cornerstone Macro LP in Washington.

The figure helps provide clarity as investors seek to determine when the Fed will start to pare back the $85 billion in monthly bond purchases that kept borrowing costs low and fueled a stock-market rally. Yields on 10-year Treasury notes are close to a one-year high on speculation tapering is imminent.

The May payrolls increase fell short of 200,000. The Labor Department said today that payrolls rose 175,000 last month, after a revised 149,000 gain in April. The unemployment rate rose to 7.6 percent from 7.5 percent. The report will provide an important clue to the outlook for monetary policy.

Boston Fed president Eric Rosengren and Chicago’s Charles Evans, both voting members of the Federal Open Market Committee this year who have consistently supported increased stimulus, have cited job growth of 200,000 as a benchmark for labor-market improvement.

Rule of Thumb

Reinhart, chief U.S. economist at Morgan Stanley in New York, says investors should pay attention to the 200,000 figure, calling it “a good rule of thumb.” Fed officials “probably need four months of that on average to justify tapering balance- sheet expansion,” he said June 3 in a Bloomberg Television interview with Tom Keene.

Reinhart wrote in a May 28 note to clients he doesn’t expect the Fed to reach that hurdle until December because the economy is likely to encounter a “soft patch.”

“Historically, 200-plus was typically the kind of pace you would see in a more normal recovery,” said Michael Hanson, senior U.S. economist for Bank of America Corp. in New York and a former Fed economist. “It’s a quantifiable metric that we’ve turned the corner in the labor market. It looks much more like recovery.”