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GDP won't accelerate, so why hike rates: Former Fed gov

The Federal Reserve may have missed its window for an interest rate hike, former Fed Gov. Larry Lindsey said Monday, a month before the central bank's crucial September monetary policy meeting.

"Looking at the Fed's own behavior, I'd bet they're going to take a pass in September," predicted Lindsey, who also served as director of the National Economic Council for President George W. Bush.

"I think [the Fed] could have done it painlessly. There's no cause and effect here," he said. "I think they're running the risk of raising and then being embarrassed by a slowdown."

Lindsey said he's dubious of the widely held notion of an economic pop in the second half of the year. "We are not going to have an acceleration in the second half. I think if anything we're going to have a deceleration. I think ... 1.9 [percent] is probably about right for the the year."

In the Fed's June economic projections, excluding the three highest and three lowest forecasts, policymakers saw economic growth in 2015 of between 1.8 and 2 percent.

That's down from in March, when the central bank forecast a GDP advance of between 2.3 and 2.7 percent for this year.

"The Fed is constantly drawing down its estimates for growth this year," the CEO of economic advisor The Lindsey Group told CNBC's "Squawk Box" in an interview. "If they've cut their growth forecasts ... it doesn't seem like a more likely environment in which to lift off from zero. It seems less likely."

The debate on Wall Street centers on whether the Fed may choose to hike rates for the first time in nine years at its September or December meeting.

Bets on next month's gathering had seemed to come back into favor after the solid July employment report released earlier this month. But with the Chinese yuan under pressure after last week's devaluation, expectations appear to be tilting for an initial Fed move in December.

The CME FedWatch tool—which tracks daily market reaction on potential changes to the fed funds target rate—puts the probability of a hike at 41 percent in September and 68 percent in December.

"I think they should have hiked [already]," Lindsey said, but acknowledged, "We are in a very difficult endgame right now."

On Friday, former Dallas Fed President Richard Fisher told CNBC that China's currency devaluation should not be used as an excuse by the U.S. central bank to delay raising rates.

Read MoreChina puts Fed in 'awkward' spot: Ex-Fed's Fisher

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