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By Ann Saphir

Aug 13 (Reuters) - Chicago Federal Reserve Bank President Austan Goolsbee said on Thursday that the latest U.S. inflation data has been a "little better," and he is hopeful that as the effects of tariffs and higher oil prices from the Iran war fade, inflation can continue to improve.

"If we can get some of this stuff into the rearview mirror then I think we get back on what I was calling the golden path, which is inflation heading back to 2%," Goolsbee said in an interview with Fox News Channel's Special Report with Bret Baier. "The overall level being in the 3%, that's too high; that's not great. The good news is the new information that's been coming in has been a little better."

The Fed last month held the short-term policy rate in the 3.50%-3.75% range, though at least five of the central bank's 19 policymakers wanted to raise rates instead, based on votes cast at the time and public remarks made since.

The Fed targets 2% inflation by the 12-month change in the personal consumption expenditures price index; in June, PCE inflation was 3.7%, down from its recent 4.1% peak in May.

As recently as last week traders had been pricing in a Fed rate hike as soon as September, but back-to-back reports this week of milder-than-expected consumer and producer price inflation in July, following last Friday's weak jobs report, have mostly erased the expectation of any near-term Fed move. 

"Inflation has been too high and our progress stalled out a little bit and was going the wrong way," Goolsbee said on Thursday.

"But now, for a couple of months, we've been getting a little bit better readings and hopefully that will continue. But we're in that delicate space where the overall economy feels fairly stable and we're mostly watching the inflation component," he said.