You can't say it's not ambitious. Speaking at the Detroit Economic Club Wednesday, Jeb Bush laid out the foundation of a presumptive presidential run, and one of the principles is growth.

"I don’t think the U.S. should settle for anything less than 4 percent growth a year—which is about twice our current average. At that rate, the middle class will thrive again," Bush said. "And in the coming months, I intend to detail how we can get there, with a mix of smart policies and reforms to tap our resources and capacity to innovate, whether in energy, manufacturing, healthcare or technology."

That seems both unrealistic and politically curious. Let's start with the number. That's not quite as aggressive as the 5 percent goal Tim Pawlenty set (and was mocked for) during the 2012 Republican primary, but it's still pretty high. In a July 2014 paper, Alan Blinder and Mark Watson considered growth rates by presidential administration. Here are the basic numbers:

Percentage GDP Growth by Presidential Administration

One thing that jumps out is that the growth rate under Obama is fairly anemic, as Bush implied. (The economic collapse likely accounts for much of the poor showing in Obama's first term and George W. Bush's second.) The other thing that jumps out is how few presidents have achieved average annual growth of 4 percent or more. Harry S Truman benefited from the post-war peace dividend. John F. Kennedy and Lyndon Johnson enjoyed a booming economy; Richard Nixon and Gerald Ford faced stagflation and its aftereffects. In his second term, as the economy boomed and the tech bubble inflated, Bill Clinton nosed barely above 4 percent.

Blinder and Watson set out to examine whether partisanship had much to do with these results. They found that Democratic presidents had a significantly better track record, but it wasn't because progressive policies are way better.

"Democrats would no doubt like to attribute the large D-R growth gap to macroeconomic policy choices, but the data do not support such a claim," they wrote. "It seems we must look instead to several variables that are mostly 'good luck,' with perhaps a touch of 'good policy.' Specifically, Democratic presidents have experienced, on average, better oil shocks than Republicans (some of which may have been induced by foreign policy), a better legacy of productivity shocks, more favorable international conditions, and perhaps more optimistic consumer expectations."

That could cut either way for a (third) President Bush—maybe he'd get lucky, he wouldn't face any oil shocks, and Obama would have borne the brunt of the recovery, paving the way for a boom period after he leaves office, just like Truman did. But CBO projections don't suggest growth that high. Looking at growth rates around the world shows that few developed countries are above the 4 percent rate now. The same held true in the 1990s.

Bush, the former Florida governor, wants voters to believe that an innovative slate of policies, involving less regulatory red tape, more business competition, better schools, and rewritten laws can counteract that. And if they're truly unprecedented, perhaps they can—that's what's interesting about things that have never been tried. What the Blinder and Watson paper counsels is to be skeptical of any leader's claim that she can exert much effect on GDP.

GDP growth is a somewhat strange vessel for Bush's message anyway. In line with other Republicans, Bush has started talking about inequality recently. "Far too many Americans live on the edge of economic ruin," he said Tuesday. "Something is holding them back. Not a lack of ambition. Not a lack of hope. Not because they are lazy or see themselves as victims." He bemoaned diminished economic mobility. But GDP is an awfully abstract notion to use as a political tool. While there's a strong relationship between economic growth and presidential elections, it's hard to imagine many voters choosing their candidate based on GDP projections—just ask President bank lobbyist Tim Pawlenty.

More to the point, it cuts against Bush's own focus on inequality. After all, one of the chief lessons of the current recovery is that even as economic growth recovers, many Americans are being left behind. That's one reason politicians are talking more about the middle class or inequality than they are about the overall economy. While stronger growth is obviously preferable to weaker, there's no guarantee that the citizens Bush is worried about—including those in Detroit—will have much to show for it.