Fact-checking Tuesday's vice-presidential debate

At Tuesday night's debate at Longwood University in Virginia, Gov. Mike Pence of Indiana, the Republican nominee for vice president, and Sen. Tim Kaine of Virginia, the Democratic nominee, spent much of their time attacking the pasts and policies of the presidential candidates. Sometimes they stuck to facts, and sometimes they strayed:

Kaine said Donald Trump paid few taxes and lost $1 billion a year.

An overstatement.

What we know is that Donald Trump declared a $916 million loss on 1995 tax returns obtained by The New York Times. That could have allowed him to avoid legally paying taxes for up to 18 years.

But because Trump has refused to release his full returns for any year, we don't know the truth about what he has or has not paid in taxes, or about any losses he might have claimed in other years.

— Megan Twohey

Pence said Trump would "lower taxes across the board for working families."

Not quite.

Trump's plan would reduce the average tax burden for low-, middle- and upper-income households, but would not cut everyone's taxes. One new analysis finds that roughly 7.8 million families with children would pay higher taxes under Trump's plan. That includes roughly half of all single-parent households.

Lily Batchelder, a New York University professor and former aide to President Barack Obama who did the analysis, estimates that 20 percent of families with children would see tax increases. The conservative Tax Foundation has reviewed her findings and says that it agrees.

— Binyamin Appelbaum

[Analysis: Winners and losers from the vice-presidential debate]

Pence said that Trump had promised not to change Medicare.

He made the promise.

Trump has broken with the Republican leadership in Congress and the Republican Party platform with his promise to leave the government Medicare program unchanged. House Speaker Paul D. Ryan has long been identified with a plan to partly privatize the health care program for seniors, and Medicare reform was a centerpiece of Mitt Romney's 2012 presidential campaign.

But Trump has consistently said that he would not touch the program.

— Margot Sanger-Katz

"There are millions more people living in poverty today than the day President Obama" took office, Pence said.

Probably not.

Poverty data is reported annually, not by month, so it's hard to isolate precisely whether the number of people in poverty is higher or lower than when Obama took office in January 2009 — particularly given that the economy was in collapse at the time of his inauguration.

There were 426,000 fewer Americans living in poverty in 2015 than in 2009, the year Obama took office, according to census data. But if you compare the 2015 level to 2008, when Obama was elected (and when the Great Recession began), the number has indeed risen by 3.3 million.

— Neil Irwin

Kaine said the Bush tax cuts were a cause of the Great Recession.

Just not true.

The Bush tax cuts were a primary cause of the explosion of federal debt during the first decade of the 21st century. But they were not a direct cause of the Great Recession that began in 2008 — and it's hard to make the case that they were a significant contributing factor.

The recession was triggered by a housing bubble that undermined a highly leveraged financial system. The resulting crisis of confidence sent economic activity into a tailspin. The result was the worst economic crisis since the Great Depression.

— Binyamin Appelbaum

Kaine said Hillary Clinton eliminated the Iran nuclear weapons program.

A stretch.

Kaine's assessment gives Clinton more credit than she or the Obama administration deserves.

It is true that the nuclear agreement sharply cuts back the number of centrifuges and nuclear material Iran can have, prolonging the period of time Iran would need to manufacture a weapon. But it does not eliminate Iran's nuclear infrastructure, and the deal has a sunset clause, meaning Iran will be able to resume its work after the deal expires in 15 years.

— Mark Landler

Kaine said that Pence "was the chief cheerleader for the privatization of Social Security."

Mostly right.

As a member of House of Representatives, Pence supported President George W. Bush's plan to revamp Social Security, with an option for individual private accounts. And Pence would have gone even further in some respects.

Bush wanted to allow workers to set aside up to 4 percent of their earnings for individual accounts, instead of having that money go into the Social Security system.

As chairman of the conservative House Republican Study Committee, Pence wanted to let workers set aside up to 6 percent.

— Robert Pear

Pence maintained that the Obama administration had doubled the federal debt.

Not so fast.

The debt held by the public has nearly doubled since the 2009 fiscal year — from $7.5 trillion to an estimated $14.1 trillion for the fiscal year that ended Friday, according to the Office of Management and Budget. But much of that cannot be attributed to Obama's policies.

The increased debt partly reflects costs incurred during the recession he inherited, in lost revenues and automatic safety-net assistance like jobless payments. Much more reflects spending on Medicare, Social Security and Medicaid that is rising as the population ages, regardless of who is president.

— Jackie Calmes

Kaine said President Nixon had released his tax returns while under audit.

Yes, but after the election.

One reason Trump said he has not released his income taxes is that they are under audit. Kaine asserted that President Richard M. Nixon had released his taxes while under audit.

The statement, though true, was somewhat misleading. Nixon released his taxes while under audit — but it was not until a year after his 1972 re-election.

— Steve Eder