Strong GDP growth isn't a sign the US has escaped a recession, and interest rates are a big headwind to economic activity, top economist Mohamed El-Erian says

• The strong GDP report isn't a sign the US has dodged a recession, Mohamed El-Erian said. 
• High interest rates still pose a big threat to households, business, and the US government.
• That poses a "significant headwind to economic activity," and the outlook for 2024 is uncertain. 

This quarter's US GDP numbers came in hot, but that doesn't mean the US economy is out of the woods. 

The annualized gross domestic product, a measure of all goods produced in the economy, clocked in at 4.9% last quarter — the fastest pace of growth in almost two years. And while that is a sign of a strengthening economy, according to economist Mohamed El-Erian, it's not time to let go of recession angst.

"What we should not do is take this as a signal of the all clear for 2024," El-Erian said on CNBC's Squawk Box on Thursday. "As you know, I've always pushed back on the notion that we would have a recession in 2023, I'm a little worried about 2024."

Boosting concerns are the rising US deficit and a rising number of bankruptcies, as well as an economy that is seeing inflation hugging 4%. But strong retail sales numbers and a blowout September jobs report have led many investors to flip to the no-recession camp.

While the GDP numbers underscore US "exceptionalism," El-Erian said, high interest rates are impacting all corners of the economy, and that's something to watch out for. 

"We have, first, the rundown in savings, that's a big issue," he said. "Secondly, what's been happening in the interest rate market is really problematic. It's problematic for businesses, it's problematic for governments, for the Fed. It's problematic for households. And that is a significant headwind to economic activity."

For over a decade following the 208 crisis, borrowing costs were at near-zero levels, driving economic activity by encouraging lending and keeping markets awash in liquidity, which helped push asset prices up.

Now, the Fed's rate hikes have spiked the cost of credit throughout the economy, and markets are already reacting to the change. Mortgage rates have punched through multidecade highs, the commercial real estate market is trembling, and the government is going to have to pay a lot more interest to service its massive pile of debt.

Also reacting to the Fed rate hikes right now is a crashing bond market that El-Erian describes as "unanchored." Expecting interest rates to remain higher for the foreseeable future, the bond market has witnessed a historic sell-off in recent months. This week, the 10-year Treasury breached 5% for the first time since 2007.

"There's two things that are here and going to stay here," El-Erian said about the bond market. "That the Fed being a net seller, and the government issuing more debt. The question mark, and you saw that in the auctions yesterday, is who is going to buy? And that question about buyers isn't going to go away any time soon," referring to Wednesday's auction of five-year Treasury bonds, which was greeted by tepid demand from investors.