By James Ramage And Min Zeng 

In the race to predict the timing of the Federal Reserve's anticipated interest-rate rise, traders are digging ever deeper into the slew of economic data points released each day.

On Friday, it was the turn of an often-overlooked report on wage growth to hit center stage. The Labor Department on Friday released data showing wage growth in the second quarter was the lowest since records began in 1982.

The report, which is often watched by the Fed as a sign of inflationary pressure in the economy, fueled doubts among some investors and traders that the Fed will increase the short-term benchmark interest rate in September as many economists predict. Some traders speculated that December, and possibly even early 2016, is increasingly becoming a more likely moment for the Fed to move.

Both bond yields and the dollar fell sharply on the report, illustrating investors' intense preoccupation with the timing of the first rate increase in nearly a decade. Friday's moves also foreshadow the heightened volatility that many traders anticipate as the September meeting nears.

Friday's rally in Treasurys pushed the yield on the 10-year Treasury note to its biggest monthly decline since January. The yield on the two-year note, among the most sensitive to changes in the outlook for Fed policy, also tumbled. Bond yields fall when prices rise.

Many market watchers agree that when the Fed does raise rates from near-zero levels, it will move slowly, which should cap moves across stock, bond and currency markets. But big prices swings are still likely, analysts say, as investors track economic data to position themselves for a September, December or even 2016 rate increase.

"The markets are justifiably sensitive right now, especially when relevant economic data come in at extreme levels, and the market is already 50-50 on the Fed hiking interest rates in September," said Shahab Jalinoos, currency research analyst at Credit Suisse.

The Fed has been monitoring the employment market closely. After its most recent two-day policy meeting that ended Wednesday, the central bank acknowledged that it is still on track to raise rates this year due to gains in the U.S. labor market.

The U.S. employment-cost index, a measure of workers' wages and benefits also known as ECI, rose a seasonally adjusted 0.2% in the second quarter from the first quarter. That fell below Wall Street expectations for a 0.6% increase.

Steven Englander, head of developed-market currencies strategy at Citigroup said the ECI was a "huge shock." He added: "People are now thinking this number will give the Fed pause."

In the moments immediately after the report's release, the dollar sank as much as 1.7% against the euro before paring most of the losses later in the day. In late New York trading on Friday, one euro bought $1.0984, compared with $1.0933 late Thursday.

Despite Friday's selloff, the dollar rose 1.4% against the euro for the month of July.

While the U.S. economy picked up speed in the second quarter after a soft patch, Fed officials and investors are grappling with how to interpret sluggish global economic growth and subdued inflation. Commodities in recent days have resumed falling. And Chinese stocks in July posted their biggest monthly selloff in six years, heightening concerns over the slowdown of the world's second-largest economy.

The prospect of higher rates has lured fund managers to the dollar, sparking a rally in the greenback last year that sputtered early in 2015 amid a soft patch in the U.S. economy. Since then, the dollar has gyrated on economic indicators and remarks by Fed officials.

The yield on the benchmark 10-year Treasury note on Friday fell to a three-week low of 2.207% from 2.268% Thursday. The yield on the two-year note slid to 0.676% from a one-month peak of 0.731% on Thursday.

The labor cost report "is a red light for the Fed," said Jonathan Lewis, chief investment officer at Samson Capital Advisors LLC, which has $7.4 billion in assets under management. "This economic recovery is not strong enough to generate consistently positive economic data, let alone consistent upward pressure on wages."

Mr. Lewis said he is skeptical the Fed can raise rates in September and added that Friday's report is "a green light for investors to move out of cash and into bonds."

The odds of a rate increase by the Fed at the September policy meeting were 38% Friday, compared with 48% Thursday and 40.5% a week ago, according to traders. The odds for a rate increase at the December meeting were 68.4 % Friday, compared with 80.5% Thursday and 71.7% a week ago.

The calculations are based on implied yields from fed-funds futures which are used by investors and traders to place bets on central-bank policy.

Federal Reserve Bank of St. Louis President James Bullard played down the ECI report, saying that the Fed is in "good shape" for increasing the rate target at the Sept. 16-17 meeting. Mr. Bullard doesn't currently hold a vote on the Fed's policy-making committee.

The Dow Jones Industrial Average shed 56.12 points, or 0.3%, to 17689.86, on Friday, dragged down by a decline in shares of big oil companies that reported weak earnings. The move lower was muted by Friday's wage report and the prospect of ultralow rates for longer.

The nonfarm payrolls report due next Friday is expected to show 215,000 new jobs were added in July, in line with the recent trend of strong employment growth. Some traders played down the importance of the wage report, saying that the two job reports ahead of the September Fed meeting will weigh more heavily.

Daniel Mulholland, senior U.S. Treasury trader at Crédit Agricole in New York, said the door remains open for the Fed to raise rates in September amid solid jobs growth. Fed Chairwoman Janet Yellen "has previously told us that wage growth is not a pre-condition for rate hikes," said Mr. Mulholland. "The Fed has told us they will be data dependent and there are two more payroll reports prior to" the Fed's next policy meeting in September, he said.

"Data dependency is a nice option for the Fed, but it makes the market more prone to overshooting in either direction after each major data release," said Zhiwei Ren, managing director and portfolio manager at Penn Mutual Asset Management Inc., which has $20 billion assets under management.