* Graphic: World FX rates in 2019 http://tmsnrt.rs/2egbfVh
* Stocks gain broadly after Fed's policy caution
* Fed slams brakes on rate hikes, Treasury yields skid
* Facebook (NASDAQ:FB) soars after better than expected results
By Herbert Lash
NEW YORK, Jan 31 (Reuters) - Global equity markets mostly rose on Thursday, propelled by Facebook's stellar earnings and the Federal Reserve's pledge to be patient in raising borrowing costs further, while U.S. bond yields fell on indications of weaker than expected inflation.
Oil prices rose for a third day, extending a rally this month as an output cut by the Organization of the Petroleum Exporting Countries, Russia and others took effect. The dollar was mixed after the Fed's policy statement on Wednesday.
MSCI's gauge of global stock performance and an emerging markets index rose, as did the Nasdaq and S&P 500 on Wall Street, propelled by a 13 percent gain by Facebook after its quarterly results topped analysts' estimates. shares edged lower and the Dow fell on downbeat reports by DowDuPont Inc DWDP.N , among others, as investors awaited news about the U.S.-China trade talks in Washington.
But broadly speaking, U.S. stocks rose.
"We have positive earnings, positive economy and a positive Fed," said Andre Bakhos, managing director at New Vines Capital LLC in Bernardsville, New Jersey, adding that trade was the missing piece of the puzzle for investors.
"It seems as if most of the fears have been taken away except for trade," Bakhos said.
The two-day talks, which began on Wednesday, are expected to be tense, with little indication so far that Beijing is willing to address core U.S. demands to budge on trade practices and fully protect American intellectual property rights.
If a deal is not reached soon, Washington has threatened to more than double tariffs on Chinese goods on March 2.
E-commerce behemoth Amazon AMZN.O was the other big focus, with it set to report results after the closing bell.
MSCI's gauge of stocks across the globe .MIWD00000PUS rose 0.76 percent, on track to its best January on record, and its emerging market index .MSCIEF gained 1.46 percent. The pan-European STOXX 600 index .STOXX lost 0.20 percent and FTSEurofirst 300 .FTEU3 slid 0.12 percent.
The dollar dropped to a two-week low versus the yen, pressured by the Fed's cautious U.S. economic outlook, and it was lower against the Canadian dollar and Mexican peso.
The dollar index .DXY rose 0.09 percent, with the euro EUR= down 0.11 percent to $1.1464.
The Japanese yen strengthened 0.21 percent versus the greenback at 108.83 per dollar.
The Employment Cost Index, the broadest measure of labor costs, rose 0.7 percent in the fourth quarter after an unrevised 0.8 percent gain the previous quarter, the Labor Department said.
The data continued a pattern of low inflation. yields US2YT=RR , which reflect expectations of rate hikes, fell to a nearly four-week low of 2.49 percent.
"What you've seen the last couple days with the market is the Street's reaction to recognition that cheap money is going to continue for the foreseeable future," said Brian Ward, chief executive of Trimont Real Estate Advisors in Atlanta.
The 10-year U.S. Treasury note US10YT=RR rose 14/32 in price to push its yield down to 2.6453 percent.
U.S. West Texas Intermediate (WTI) crude futures CLc1 were up 85 cents at $55.08 per barrel. Brent crude oil futures LCOc1 rose 49 cents to $62.14.
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