According to Paul Krugman, a cooling in the cost of rent is a sign that US inflation is flattening.

The Federal Reserve may be able to change its approach to interest rate hikes if rents are slowed.

He said that apartment rent prices are more important than people think.

Rents are a key driver of core inflation.

Rents fell by over 1% in Nashville and Austin, according to a report by Apartments.com.

The consumer price index for August is due on Tuesday. August's headline inflation is expected to rise to 8.1% from July's 8.5%.

At its September meeting, the Fed could take a softer stance on interest rate hikes if it sees signs that the rate is decreasing.

Core inflation, which drives Fed policy, is on course to flatten as a result of a decline in rents.

Krugman believes that the market's inflation expectations are not out of whack. The Fed can raise interest rates gradually and reduce the risk that it will crush economic growth or cause unemployment to go up.

He said last week that we could have a soft landing. I want gradual rate hikes until there are clear signs of slowing inflation.

Paul Volcker, who hiked interest rates to 20% in the 1980s to bring soaring prices under control, was Krugman's reference. The US experienced a recession after inflation fell to 3.4% from 9.8%.

Next week is when key inflation data will be released. Analysts don't think the Fed will pivot at its upcoming meeting if the consumer price index falls.