President Trump wants to turbocharge the economy.

Trump has set a goal of 4% annual economic growth, double the average under President Obama. President George W. Bush's top economist says it's entirely possible for Trump to do that, but he must stay focused on tax cuts and scaling back regulations.

"The earlier the better on tax reform," says Glenn Hubbard, the head of the Council of Economic Advisors under Bush and the current dean of Columbia Business School. He was also Mitt Romney's top economic adviser during the 2012 presidential race.

Several White House officials have said they want a massive overhaul of the U.S. tax code by August. Hubbard calls that a "good time frame." Bush was able to get a tax cut through Congress by May 2001, but Hubbard says that team came with a detailed plan, something Trump hasn't done yet.

"Four percent growth is difficult in the longer term, but in the short-term with good policy, the economy can definitely pop," Hubbard told CNNMoney. The Bush administration manged to get growth above 4% for several quarters in Bush's first term, but not for an entire year.

But Hubbard has a word of caution for the Trump team: Don't spoil the pro-growth agenda by putting up barriers to trade. He's also skeptical of the controversial border tax adjustment plan that some Republicans in Congress are pushing.

Related: How much credit should Trump get for jobs?

Hubbard to be next Fed chair?

Hubbard's views are being watched closely. There's chatter in Washington that Hubbard may be on the short list for Trump to appoint as Federal Reserve chair when Janet Yellen's term ends in February 2018. Hubbard declined to comment on a possible post.

"My hope would be that the [Trump administration] focuses on tax reform and regulatory reform and then turns to whatever it is they want to do on trade," Hubbard says.

That's certainly what Wall Street wants. America's top investors and banks see Trump's desire to crack down on trade with China, Mexico and other countries as the No. 1 threat to the U.S. economy.

"To me the answer is not to turn back the clock on trade, but to help people impacted," says Hubbard, who is advocating for more tax credits and funds to help displaced workers get new jobs. The U.S. has lost 5 million manufacturing jobs since 2000.

Hubbard believes that Trump deserves some credit for the 235,000 jobs the economy added in February and that the Fed should raise interest rates this week. Many liberal economists argue that Trump just benefited from the healthy economy Obama handed him.

"Animal spirits have been unleashed. Trump has successfully pivoted expectations toward faster growth," he says, although he warns optimism can only take the economy so far.

Related: What worries investing guru Jack Bogle right now

Trump should be 'very careful' on border tax idea

Trump has not appointed anyone to head the Council of Economic Advisers, Hubbard's old position. Instead, Trump demoted the CEA director role. It will not be part of his Cabinet.

"Economists offer a perspective in policy debates. Presidents won't always agree with it, but you need to hear what economists have to say," Hubbard says in defense of the CEA.

A key area where Hubbard thinks some economic reason is needed is on the border tax adjustment plan. Some Republicans in Congress want it as part of tax reform. The White House hasn't said whether it's for or against the policy.

Related: Border adjustment tax: What you need to know

A border tax adjustment would give tax breaks to American companies that ship products to other countries, and it would strip away tax breaks from American companies that import goods from other countries.

"I would be very careful about making a change that large," Hubbard says. The problem, Hubbard says, is that it looks good on paper, but the only countries that have tried anything like this are very small and far less complex than the U.S.

Some Republicans want to crack down on companies that import from overseas, especially from China and Mexico. They see the border tax adjustment as a way to punish companies that import a lot, but Hubbard says that's the "incorrect reason" to do it and could backfire by causing Americans to pay a lot more at stores.

Major retailers like Walmart are coming out strongly against the idea.

"The problem is it's a very large change in the largest economy in the world," Hubbard says.