(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.