Republican presidential candidate Fred Thompson made a crisp debut in his first 2008 debate appearance on Tuesday, and rivals Rudy Giuliani and Mitt Romney battled over their records on taxes and spending.

Thompson, who did not participate in two debates held since he formally entered the race last month, said the U.S. economy was not headed for a recession and warned against strict trade restrictions on China during the debate with his eight Republican rivals.

But he was a bystander in an early confrontation between Giuliani, former mayor of New York, and Romney, the former Massachusetts governor, who continued their running campaign-trail battle over tax and spending policies while in office.

Giuliani, who leads Republicans in national opinion polls in the November 2008 presidential race, said he brought taxes down 17 percent in New York while Romney let them increase by 11 percent in Massachusetts.

"The point is, you've got to control taxes. But I did it. He didn't," Giuliani said.

Romney shot back: "It's baloney. Mayor, you've got to check your facts. I did not increase taxes in Massachusetts. I lowered taxes."

Thompson and the other Republicans criticized the explosion of federal spending in recent years and said rising budgets and deficits under President George W. Bush had to be tamed. Arizona Sen. John McCain pointed to his own Republican Party as the culprit.