But if international conditions then are anything like they are now, and inflation still doesn’t pose much of a threat, Mr. Summers said, “it will be just as significant an error to move in December as it would have been to move in September.”

To some observers, the delay by the Fed will help give emerging markets more time to prepare and also recover from China-induced volatility. But Frederic S. Mishkin, a Fed board member from 2006 to 2008, said it could actually complicate the situation.

“This exacerbates the risks and makes the communication even more difficult going forward,” said Mr. Mishkin, now a professor at Columbia Business School. “When will global conditions be strong enough to raise rates? This will create even more confusion.”

Elsewhere in the world, it is no so much the initial increase itself, which is expected to be limited to a modest quarter of a percentage point, that worries experts as the prospect of further aftershocks as the Fed shifts from an easy money stance to a gradually tightening posture.

Mr. Rogoff, who wrote the 2009 book “This Time Is Different: Eight Centuries of Financial Folly” (Princeton University Press), with Carmen Reinhart, said it was “remarkable how focused the world is on the Fed, and there’s no question emerging markets are very vulnerable right now.”