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* Fed's Dudley: bank may shrink balance sheet this year
* U.S. annual inflation rose most in five years
* Chicago PMI was stronger-than-expected (Recasts, adds comment, byline, details, data, table updates prices)
By Gertrude Chavez-Dreyfuss
NEW YORK, March 31 (Reuters) - U.S. Treasury debt yields were mostly lower on Friday after New York Federal Reserve Bank President William Dudley said the central bank was not in a huge rush to tighten monetary policy since the economy is not overheating. Yields on U.S. 30-year bonds were higher, however, because of rebalancing of portfolios by pension funds for month-end purposes, analysts said.
Investors have currently priced in two more interest rate increases in 2017 after the Fed hiked at its last policy meeting.
In an interview with Bloomberg TV, Dudley, a voter on the Federal Open Market Committee and a known supporter of low interest rates, said a couple more rate increases in 2017 seem reasonable but that there is no great urgency.
He also said the Fed could begin shrinking its $4.5 trillion balance sheet as soon as this year, earlier than what most Wall Street economists expect.
"What you saw in the short-term interest rate market initially was a bit of a dovish perception in response to Dudley's comments," said Guy LeBas, chief fixed income strategist at Janney Montgomery Scott in Philadelphia.
However, Dudley's comments on shrinking the balance sheet, which the Fed official said was tantamount to raising rates, did steepen the yield curve, after a flattening trend the last two weeks.
The gap between the yields of shorter-dated and longer-dated Treasuries increased on Friday, with the spread between the two-year and 10-year rising to as much as 114.60 basis points, the steepest in a week.
The curve steepened because Dudley's comments suggested that by reducing its balance sheet, the Fed would sell some bonds or pause buying them, which should push rates on the long end of the curve higher, analysts said.
Friday's U.S. economic data was a mixed bag, with a report showing the largest annual increase in U.S. inflation in nearly five years. The personal consumption expenditures (PCE) price index rose 2.1 percent year-on-year, the biggest such gain since 2012.
Factory activity in the U.S. Midwest for March, on the other hand, was more robust than expected, but consumer sentiment as measured by the University of Michigan eased this month. .
The net effect on Treasuries was still lower yields, except on U.S. 30-year bonds.
In mid-morning trading, 10-year notes were up 2/32 in price to yield 2.410 percent, compared with 2.418 percent on Thursday.
U.S. two-year note yields were at 1.265 percent, down from 1.286 percent late on Thursday.
The U.S. 30-year bond, meanwhile, was down 7/32 in price, yielding 3.038 percent, up from Thursday's 3.026 percent. (Reporting by Gertrude Chavez-Dreyfuss)