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President Barack Obama and Republican nominee Mitt Romney made a number of assertions in their debate in Denver. How did they square with the facts?

Romney's Tax Plan

The Claim • Romney's tax plan can't add up, Obama said during tonight's debate. "It's math," he said. "It's arithmetic."

The Background • Romney has proposed reducing income tax rates by 20 percent and eliminating the estate tax and the alternative minimum tax. He says his plan would boost growth, while avoiding an expansion of the federal budget deficit because he would curtail deductions, exemptions and credits. He also says there are enough tax breaks for top earners that he would eliminate to avoid shifting the burden to the middle class.

The Facts • Romney's tax plan can't add up under congressional budget-scoring rules that don't let him assume that economic growth will generate higher tax revenue.

Obama's argument rests on an August analysis by the nonpartisan Tax Policy Center in Washington. That group sought to see if it was simultaneously possible to meet all of Romney's principles: Cut tax rates, avoid shifting the tax burden to the middle class, don't increase the budget deficit, and keep tax benefits for savings and investment.

The study found that, in 2015, $86 billion of the tax burden would be shifted to the middle class to keep the plan from increasing the deficit.

Romney's advisers contested that analysis. They maintain they would consider some changes that the Tax Policy Center kept off the table, such as the tax exemption for municipal bonds. Those changes make the plan more arithmetically possible, though still politically difficult. Romney's campaign hasn't provided enough detail about what he's proposing for deductions and exemptions to be able to analyze it completely.

Romney said in the debate that his plan wouldn't cut enough tax breaks to offset all of his tax cuts. Economic growth, he said, would be generated by his tax plan would make up the difference. He hasn't specified how much.

Congressional budget-scoring rules are conservative about anticipated growth from tax cuts because economists disagree over how much they spur the economy. If Romney's plan goes to Congress, he wouldn't be allowed to assume higher revenue from growth and, in that sense, it wouldn't add up.

Taxes for the wealthy

Claim • Romney says he wouldn't cut taxes on the wealthy.

Facts • Romney wants to cut personal taxes by 20 percent for everyone, including the wealthy. He also wants to cut taxes on interest, dividends and capital gains for Americans with adjusted gross income below $200,000. Obama, however, wants to return taxes to Clinton-era rates for individuals who make more than $200,000 in annual taxable income and families who make more than $250,000 in taxable income. So Romney wants to maintain tax cuts for the wealthy that Obama would eliminate.

Health-Care Cost Increases

The Claim • Romney said, "Health-care costs have gone up by $2,500 a family" under Obama.

The Background • During the legislative debate over the president's health-care overhaul law, critics charged the measure wouldn't do enough to control medical costs. Since enactment, insurance industry spokesmen and others have warned the law's new requirements to, among other things, cover people with pre-existing medical conditions and allow young adults to stay on their parents' policies will drive up insurance premiums. The $2,500 figure plays into these themes. The number appears to come from a recent Kaiser Family Foundation survey that shows average premiums for a four-person family rose $2,370 between 2009 and 2012.

The Facts • The number Romney cited is in the ballpark. The fact he didn't mention is that the rate of increase has slowed under Obama. Kaiser calculated insurance rates over the past 10 years. They rose at an average annual rate of eight percent from 2002 through 2008, the year Obama was elected. Since he came to office, Kaiser said, the average annual rate has been 4.3 percent.

Medicare cuts

Claim • Romney said Obama's health care law cuts $716 billion from Medicare which will hurt current beneficiaries.

Facts • This has been one of Romney's favorite lines of attack, but his claim that Obama's health care law cuts $716 billion in benefits for current Medicare beneficiaries is not true. The health care law will limit payments to health care providers and insurers — not senior citizens' benefits — as part of an effort to rein in costs over the course of the next decade. Romney and other opponents of the law, however, contend that the payment cuts would affect seniors' benefits as an unintended consequence because they assert doctors will stop accepting Medicare patients and it could force some health care facilities to close.The law has not yet been fully implemented, so the cuts affects on beneficiaries are uncertain. But the law as written does not cut benefits for senior citizens. It is also worth noting that Romney's running mate, Rep. Paul Ryan, R-Wis., included the same spending cuts in his own 2012 budget blueprint that House Republicans supported with near unanimity.

Private-sector job gains

The claim • Obama said the U.S. economy has created 5 million private-sector jobs the past 30 months.

The facts • After the economy plummeted in late 2007 and throughout 2009, the United States has gained 4.6 million private-sector jobs since the labor market bottomed in February 2010 — or 5.1 million under preliminary revisions released last week that are not part of the official tally by the Bureau of Labor Statistics.

Still, that's weak by historical standards. Under President George W. Bush, the private sector also added 5 million jobs in the 30 months after employment hit bottom following the 2001 downturn, and the pace of private-sector gains in the previous two recoveries was far stronger.

The middle class

Claim • Romney said middle-class families' income is down $4,300 since Obama took office.

Facts • According to a March analysis by Maryland-based economic consulting firm Sentier Research, Romney was correct. According to their analysis, based on February's Current Population Data compiled by the U.S. Census Bureau, the median household income was $50,065 in February, compared with $54,481 in December 2007 — right as the recession was starting — and about 11 months before Obama was elected. The current median household income is $50,678.

What Romney didn't say is that the decline in real median household income has been occurring over the course of the past decade, well before Obama took office. The trend has continued under the Obama administration, but it did not start there.

Energy independence

Claim • North America can become energy independent under Romney's plan, creating 4 million jobs.

Facts • This is likely to happen anyway, possibly as soon as the end of the decade, Citigroup said in a book-length report earlier this year. The key factor is not changes in policy, but changes in drilling technology that have let America increase oil production faster than any other nation in the world in the past four years, Citigroup said. Declining crude oil imports, and more exports of natural gas and refined oil products, could reduce the trade deficit by as much as 40 percent, adding 1percent a year to economic growth, Moody's Analytics estimates. Citgroup estimated that the emergence of the United States and Canada as a "new Middle East" could add 3.6 million jobs.