(Adds U.S. market open, byline, dateline; previous LONDON)
* U.S., German yields hover at multi-year highs after Fed
* Oil rises as OPEC compliance eclipses U.S. output boom
* Dollar pares gains against yen; euro strengthens
NEW YORK, Feb 1 (Reuters) - The dollar eased and global equity markets edged higher on Thursday as a note of caution over rising interest rates and high stock valuations dampened investors' appetite for risk assets after a euphoric January in markets.
A fresh slide in drugmakers and a plunge in PayPal shares offset gains in Facebook, AT&T and eBay, which shot up almost 15 percent.
European shares, as marked by the pan-regional STOXX 600 index, fell for a fourth day, led lower by Danish drugmaker Novo Nordisk after its operating profit fell short of expectations.
"At currently high valuations for developed market equities, investors should tread cautiously in what remains a top-of-cycle environment, even if rising bond yields are more likely a headwind than a precursor to a crisis," said Alastair George, chief strategist at Edison Investment Research.
MSCI's gauge of stocks across the globe shed 0.04 percent while stocks on Wall Street rose after spending much of the early session trading little changed.
The Dow Jones Industrial Average rose 105.95 points, or 0.41 percent, to 26,255.34. he S&P 500 gained 8.55 points, or 0.30 percent, to 2,832.36 and the Nasdaq Composite added 12.60 points, or 0.17 percent, to 7,424.08.
In Europe, the STOXX 600 fell 0.59 percent and the pan-regional FTSEurofirst 300 index lost 0.70 percent.
Stretched valuations, a long overdue pullback in stocks, and uncertainty over a potential shutdown of the U.S. federal government are driving a sense of caution in the market, said Peter Kenny, senior market strategist at Global Markets Advisory Group in New York.
"Rising interest rates don't necessary mean a hard stop for equity prices moving higher but they do add a degree of moderation to the enthusiasm," Kenny said.
The dollar, which fell 3.25 percent in January to mark its worst monthly performance since March 2016, pared gains against the yen as stocks fell in Europe and treaded water on Wall Street.
The dollar struggled in January as expected monetary policy-tightening elsewhere in the world, along with stronger global economic growth, encouraged investors to go abroad, particularly the euro zone.
The dollar index fell 0.35 percent, with the euro up 0.45 percent to $1.2476. The Japanese yen weakened 0.30 percent versus the greenback at 109.53 per dollar.
German 10-year bond yields hit two-year highs as yields firmed across the euro zone after Federal Reserve policy-makers on Wednesday flagged a potential uptick in inflation.
Germany's 10-year government bond yield, the benchmark for the euro zone, hit a two-year high of 0.738 percent..
U.S. Treasury yields climbed further as a private report on domestic factory activity in January showed prices manufacturers paid rose to their highest level in nearly seven years, suggesting inflation is gaining traction.
Benchmark 10-year notes last fell 8/32 in price to yield 2.7482 percent, up from 2.72 percent late on Wednesday.
Oil rose after a survey showed the Organization of the Petroleum Exporting Countries' commitment to its supply cuts remains in place, even as U.S. production topped 10 million barrels per day for the first time since 1970.
U.S. crude rose 0.9 percent to $65.31 per barrel and Brent was last at $69.15, up 0.38 percent on the day.
(Reporting by Herbert Lash; Editing by Nick Zieminski)