TREASURIES-US yields hold declines on hopes for Iran deal

(Updates with latest yields, adds Chicago PMI in paragraphs 1 and 6-11)

WASHINGTON, May 29 (Reuters) - U.S. Treasury yields edged lower a fourth straight day on Friday, closing out a week in which reported progress in efforts to secure a truce between the United States and Iran had spurred some optimism on markets.

In a speech, Michelle Bowman, the Fed's vice chair for supervision, said it was still early to gauge the Middle East war's impact on the economy but that a prolonged energy shock could require the central bank to change its stance on monetary policy. The Fed's preferred inflation gauge last month hit its highest level in three years, according to Commerce Department data released on Thursday. That came among a batch of economic figures that analysts said held warning signs for stagflation.

Lou Brien, market strategist at DRW Trading, said the fragile pause in hostilities since last month was easing the upward pressure on crude oil prices and inflation expectations, helping move Treasury yields lower.

"We're probably not done with high oil prices just simply because we've possibly come to an agreement. We've been here before," he said. "The price has come down and that's given the bonds a chance to take a breath." Elsewhere on Friday, the Commerce Department reported slightly better-than-expected figures for the U.S. trade balance. And in a bright spot, the MNI Chicago Business Barometer, a weighted index measuring business activity in the Chicago area, surged past expectations to its highest level in more than four years.

The yield on the benchmark U.S. 10-year Treasury note was last down 1.6 basis points (bps) to 4.439%, putting it on pace for a decline of 12.5 bps for the week, marking the biggest drop since early February. For the month, the yield was up 5.9 bps on track for a third straight monthly rise.

The yield on the 30-year bond fell 0.2 bps to 4.983%, leaving it on pace for an 8.9-bps fall, the largest decline since late February. It was likewise up marginally for the month, also the third straight month of gains.

A closely watched part of the U.S. Treasury yield curve measuring the gap between yields on two- and 10-year Treasury notes, seen as an indicator of economic expectations, was at a positive 43.7 bps.

The two-year U.S. Treasury yield, which typically moves in step with interest rate expectations for the Fed, fell 2.5 basis points to 4%, leaving it on pace for a fall of 11.3 bps for the week. However, it still recorded a rise of 12.9 bps for the month, its third straight monthly increase.

The breakeven rate on five-year U.S. Treasury Inflation-Protected Securities (TIPS) was last at 2.527% after closing at 2.559% on May 28.

The 10-year TIPS breakeven rate was last at 2.39%, indicating the market sees inflation averaging about 2.4% a year for the next decade. (Reporting by Douglas Gillison in Washington; Editing by Sharon Singleton and Nick Zieminski)