June's inflation report came in lighter than expected, sparking a rally in equity markets, particularly small-cap stocks tracked by the iShares Russell 2000 ETF ( IWM ) , which are more interest-rate sensitive than larger corporations.

Blu Putnam, the former chief economist at CME Group, shed some doubt on the idea the Federal Reserve will cut interest rates based on the lighter inflation numbers during his Thursday appearance on Benzinga's PreMarket Prep. 

The Numbers: June's CPI came in at -0.1%, which was below the street's expectations of a positive 0.1%. The year-over-year Consumcer Price Index (CPI) dropped to 3% from 3.2% in May.

While many experts see the lighter-than-expected inflation numbers as a signal that the Fed will be able to cut interest rates, Putnam was not as convinced.

Read Also: Inflation Slows More Expected To 3% In June, Heightens Expectations For Rate Cuts: Treasury Yields Tumble

"Well they're good numbers, it's further progress, it's not enough progress in my view to convince J Powell and the FOMC that it's time to cut rates," Putnam said.

"They've been talking about their lack of confidence pretty regularly, but this is a good number and it's in the right direction. It's all positive, but it may not be positive enough, certainly not for July, maybe for September, we'll get some more information before then."

Putnam also argued that even though inflation has been dropping, it could get “sticky” around 3%, which is still a full percentage point higher than the Fed's inflation target of 2%. Because inflation is still higher than the Fed's target rate, the central bank may not be inclined to cut rates unless there is another reason to — such as continued weakening of the labor market or other recession indicators.

Putnam said that to get to the Fed's target rate, the economy may need to endure some pain.

"Well we can [get back to 2%], but not the way we want to," Putnam said.

"We were at 2% from 1994 to 2000 because of a lot of context. Globalization was in play, China was growing fast and producing cheap goods, supply chains were working well and optimized for the lowest cost,” Putnam said.”There were a lot of good supporting factors for subdued inflation that had nothing to do with Federal Reserve policy.”

But now there are geopolitical tensions, supply chains are being rearranged, globalization is not moving forward, tariffs are in the news, Putnam noted.

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