Hillary Clinton said again last week that she would not "add a penny to the national debt," repeating a claim she made during her first debate with her Republican rival.

This claim is, at best, an exaggeration. Under Clinton's policies, the national debt held by the public would increase from roughly $14 trillion today to more than $23 trillion in a decade, according to an analysis from the Committee for a Responsible Federal Budget. That's an increase of $9 trillion.

Clinton could offer several compelling arguments about the national debt without resorting to hyperbole.

While $9 trillion might sound like a colossal amount of money, it is less significant in the context of America's already sizable national debt and continually expanding economy. Some economists, including former Treasury Secretary Larry Summers, have even argued that an increase in the national debt could be beneficial.

In any case, as Clinton correctly noted, Donald Trump's plans could increase the national debt above $28 trillion, according to the analysis. He has proposed both ambitious new federal expenditures along with historic reductions in taxes, which would force the government to borrow.

Here's how the candidates' policies would affect the national debt.

Measuring the debt

Talking about the size of the national debt in terms of trillions of dollars can be misleading. For a smaller country, $14 trillion in debt could be an overwhelming burden, but the U.S. economy is vast and still expanding.

For these reasons, economists usually talk about the national debt as a percentage of the broader economy. Under Clinton's proposals, the debt would increase from about 77 percent of the gross domestic product today to 86 percent in a decade.

Clinton's defenders might argue that this increase is not noticeably different from current projections. Clinton has proposed new spending, but she has also proposed new taxes to pay for almost all of her programs. She would not increase the national debt by much more than it is increasing already.

“Clinton is referring to the overall impact of the plans she has put forward,” said Julie Wood, a campaign spokeswoman, in a statement. “The specific proposals she has offered to pay for them means they would not add to the debt.”

The national debt is indeed increasing, though, and Clinton's policies would not mitigate this increase.

Since the debt is already at elevated levels relative to the past several decades, some economists would likely argue that her policies are imprudent -- and that is her responsibility as a presidential candidate to find ways of keeping the national debt in check.

"You wouldn’t know that we have an unsustainable fiscal path from the debate we’re having right now," Rudolph Penner, a former director of the Congressional Budget Office, told the Wall Street Journal last year.

On the other hand, some economists argue for an increase in debt. "Markets are sending a clear signal that they want more, not less, government debt," Summers wrote earlier this year.

He argues that by borrowing money to invest in useful projects, the government could make the economy more efficient and productive, while stimulating demand for goods and services by putting more money in the pockets of its employees, contractors and taxpayers.

It is worth debating whether the national debt should increase or decrease, and by how much. Yet Clinton's claim she would not increase the debt as president is misleading, however the debt is measured.

Borrowing trillions

Meanwhile, Trump has laid out policies that would increase the national debt to 105 percent of gross domestic product after a decade -- a level not seen since the end of the Second World War, when the federal government borrowed heavily to finance the war effort.

Trump has claimed that his policies would be "deficit neutral," meaning that they would not require the government to borrow more relative to current projections. Since Trump has called for reducing taxes substantially, he would also have to reduce federal spending in order for the government to avoid borrowing more.

Yet Trump has also said he will not reduce spending on entitlements or the military, which together account for the bulk of the federal budget. Meanwhile, he has also called for major new expenditures on infrastructure and a wall on the Mexican border. Independent analysts are skeptical that Trump will be able to avoid adding trillions to the national debt.

One of Trump's economic advisers conceded this point last month, making the argument that a major increase in the debt would be good for the country.

A majority of Americans believe that Trump would handle the federal budget deficit better than Clinton, according to polling by Gallup. Aside from those professional economists who do want the deficit increased, the public is probably mistaken. The federal government would likely borrow trillions more under Trump than Clinton.

Correction: The national debt held by the public currently is about$14 trillion. An earlier version of this story misstated that number.

This post has been updated with a response from the Clinton campaign.