NEW YORK, Oct 14 (Reuters) - The benchmark U.S. 10-year Treasury yield fell on Thursday after data on the labor market and inflation eased worries that the Federal Reserve may need to take action earlier than expected to combat rising prices. Weekly initial claims for state unemployment benefits dropped 36,000 to a seasonally adjusted 293,000 versus expectations of 316,000. Other data showed the producer price index for final demand increased 0.5% in September after advancing 0.7% in August and was just shy of the 0.6% estimate. Shorter-term yields have risen over the past two days while longer dated yields have dipped, which has served to flatten the yield curve, indicating the market is anticipating a rate hike by the Fed. The gap between yields on two- and 10-year Treasury notes , seen as an indicator of economic expectations, touched a two-week low on Wednesday after data showed consumer prices increased solidly in September and were likely to keep moving higher. "Today makes more sense, there was a fear that CPI was going to print way worse than consensus," said Jay Hatfield, founder and CEO of Infrastructure Capital Management in New York. "The CPI data yesterday wasn"t worthy of the move. It"s a little bit of a relief rally." The yield on 10-year Treasury notes was down 2.3 basis points to 1.526%. Still, the yield gap on two- and 10-year Treasury notes flattened for a third straight day and was at 117.1 basis points after falling to 116.4, its lowest level since Sept. 24. St. Louis Fed President James Bullard said the current high levels of inflation may not abate as soon as many Federal Reserve policymakers expect, and again urged the central bank to pursue a faster taper of its bond-buying program. San Francisco Federal Reserve Bank President Mary Daly on Thursday said inflation and employment have made enough progress for the U.S. central bank to begin scaling back its monthly bond buying, but is far from ready for interest rate hikes. The yield on the 30-year Treasury bond was down 0.7 basis points to 2.034%. The two-year U.S. Treasury yield, which typically moves in step with interest rate expectations, was down 1.4 basis points at 0.354%. October 14 Thursday 10:32AM New York / 1432 GMT Price US T BONDS DEC1 159-30/32 0-9/32 10YR TNotes DEC1 131-112/256 0-56/256 Price Current Net Yield % Change (bps) Three-month bills 0.045 0.0456 -0.005 Six-month bills 0.0575 0.0583 0.000 Two-year note 99-204/256 0.3541 -0.014 Three-year note 99-248/256 0.6355 -0.026 Five-year note 99-30/256 1.0582 -0.029 Seven-year note 99-84/256 1.3515 -0.025 10-year note 97-124/256 1.5264 -0.023 30-year bond 99-64/256 2.0336 -0.007 DOLLAR SWAP SPREADS Last (bps) Net Change (bps) U.S. 2-year dollar swap 13.75 0.75 spread U.S. 3-year dollar swap 14.25 0.75 spread U.S. 5-year dollar swap 7.50 0.25 spread U.S. 10-year dollar swap 1.00 0.00 spread U.S. 30-year dollar swap -24.50 -1.00 spread (Reporting by Chuck Mikolajczak; Editing by Will Dunham)