* Dollar index drops after big gain to open 2017
* Euro gains on strong European data
* Mexican peso hits record high (Recasts with U.S. open, adds quote, changes dateline; previous LONDON)
By Dion Rabouin
NEW YORK, Jan 4 (Reuters) - The dollar fell against the euro and yen on Wednesday, backing off a 14-year high against a basket of currencies with investors cautious about increasing bets on the greenback without fresh clues on the U.S. economy and the timing of interest rate increases.
The dollar surged to its highest levels since late 2002 on Tuesday - the first day of trading in 2017 for most financial centers - after U.S. manufacturing data beat expectations.
Analysts said low volume in markets this week may have exaggerated Tuesday's moves, pushing the dollar higher in the absence of some larger market participants.
The strong move triggered some profit-taking on Wednesday, said Kathy Lien, managing director at BK Asset Management, but she noted its impact should not be overestimated.
"At the start of North American session there's just a little bit of excitement of continuation," Lien said. "Slowly, you're getting more of a return to normal trading conditions and when that happens you tend to have a bit more two-way action."
The euro climbed 0.7 percent to $1.0475, boosted by data showing euro zone prices rose more quickly than expected in December and surveys suggesting business growth reached its highest in more than five years.
The dollar fell 0.5 percent against the yen to 117.23 yen.
German 10-year Bunds touched their highest level in nearly three weeks on Tuesday and extended those gains on Wednesday.
The push higher in euro zone bond yields helped the euro rise to more than one cent above its Tuesday trough of $1.0340, the lowest in 14 years. However, the currency was still well below a three-week high of $1.07 touched last week and more than 6 percent lower than two months ago.
"Before it's all over I think euro is going back to its historic lows, but I think that we've had a big move in (the fourth quarter of 2016) and we're vulnerable to a little bit of position adjustments," said Marc Chandler, chief global currency strategist at Brown Brothers Harriman & Co.
The dollar has climbed almost 6 percent since Donald Trump was elected U.S. president eight weeks ago, on expectations that his administration will introduce reflationary measures backed by large fiscal spending and prompt the Federal Reserve to follow through with a series of interest rate hikes.
The Mexican peso hit its lowest level on record against the greenback, falling to 21.404 pesos per dollar. (Reporting by Dion Rabouin; Editing by Dan Grebler)