NEW YORK, Dec 31 (Reuters) - U.S. Treasury yields were lower on the last trading day of the year, pulling the yield curve flatter, as thin volume exaggerated market moves. Long-dated Treasury yields fell on Thursday morning, flattening the yield curve, despite an unexpected drop in unemployment claims for the second straight week. Initial claims for state unemployment benefits slid to a seasonally adjusted 787,000 for the week ended Dec. 26, from 806,000 in the prior week, the Labor Department said on Thursday. But they remain elevated more than nine months into the health and economic crisis triggered by the coronavirus pandemic, signaling a long recovery for the U.S. job market. The benchmark 10-year yield fell 1 basis point to 0.917%, pulling one measure of the yield curve - the spread between the two- and 10-year yields - down to 79 basis points, the lowest in a week. The yield on the 30-year bond was last down 1.3 basis points at 1.649%. Though the drop in jobless claims is a positive sign for the U.S. labor economy, thin trading volume skewed the Treasury market’s response to the data. With few people in the office, an early shutter of the Treasury market today, and some international markets already closed ahead of the holiday on Friday, yields were being directed by one-off trades rather than broader trends. “Overnight Treasury volume was about 35% of average with some key markets shut,” said Bill O’Donnell, rates strategist at Citigroup. The S&P 500 index was up modestly on Thursday morning, while the Nasdaq and Dow were roughly flat, indicating there was no broader risk-off move. The move lower in yields on Thursday morning may be attributable to a broader trend that could persist in the new year, said analysts at Action Economics. While the Treasury is expected to auction nearly $2 trillion worth of new supply in 2021, the Federal Reserve is expected at some point to increase its purchases at the long end of the curve. “Yields have pared recent gains amid the prospects for a shift in QE buying to longer dated maturities and dip buying as the 10-year approaches the 1% level.” (Reporting by Kate Duguid Editing by Nick Zieminski)