In 2004, when fewer people paid attention to him, Donald J. Trump gave CNN a bottom-line assessment of political parties: “It just seems that the economy does better under the Democrats.”

If that sounds awkward now for Mr. Trump, who leads opinion polls for the Republican presidential nomination, it may be even more awkward for his party next year, because its ability to claim superior economic know-how over Democrats has grown weaker ever since he made that assertion.

Like his rivals, Mr. Trump offers the familiar Republican recipe of tax cuts to spur growth and create jobs. But on the economy, Republicans have a data problem.

The party still likes to invoke its success under President Ronald Reagan, who cut taxes after defeating Jimmy Carter in 1980. By the mid-1980s, stagflation had turned into an economic boom.