Rick Wilking/Reuters
President Barack Obama (l.) listens as Republican presidential nominee Mitt Romney answers a question during the second presidential debate in Hempstead, New York, October 16.

Presidential debate 101: Does Romney’s tax math add up?

Here’s a closer look at the tax reform proposals that Mitt Romney discussed during Tuesday night's debate. Do President Obama and others have a point in challenging the math?

When Republican candidate Mitt Romney floated some fresh details about his tax reform plan during Tuesday night’s debate, moderator Candy Crowley pressed a question that's on many voters' minds: What if Mr. Romney's numbers don't add up?

"Well of course they add up," was his quick reply.

He didn't elaborate much beyond that. So let's just say that the debate over Romney's tax math – with President Obama not the only one calling his rival's plan "sketchy" – hasn't been settled.

Here’s a closer look at the changing terrain of the tax reform tussle.

Romney affirmed Tuesday night some of the same points he made in Debate No. 1: that his plan doesn't involve tax cuts for the rich, that middle-class families will get some tax relief, and that his plan for a 20 percent reduction in income tax rates could be paid for by limiting tax breaks.

But he appeared to give new detail on how a cap for deductions might work.

"In terms of bringing down deductions, one way of doing that would be ... say everybody gets – I'll pick a number – $25,000 of deductions and credits, and you can decide which ones to use," Romney said in response to a voter question in the town-hall style debate. He specified, "Your home mortgage interest deduction, charity, child tax credit, and so forth, you can use those as part of filling that bucket, if you will, of deductions."

In answering the tax question, Romney also noted, "The top 5 percent of taxpayers will continue to pay 60 percent of the income tax the nation collects. So that'll stay the same."

But by referring to the "top 5 percent," Romney may have changed his definition of the middle class. If he now means that his relief for taxpayers in the middle ends at the top 5 percent, that means in effect that the middle class ends somewhere below $200,000 in adjusted gross income.

In September, by contrast, Romney said, "Middle income is $200,000 to $250,000 and less."

Roughly the top 3 percent of US households have incomes of $200,000 and higher. Romney's other 2 percent would come from the top end of the next group tracked by the Internal Revenue Service, the roughly 10 percent of tax filers with adjusted gross incomes of between $100,000 and $200,000.

So after Tuesday night, where are we in the debate over Romney's tax plan?

Here are some important parts of the answer:

Skeptics of Romney's tax math still abound. Among them is Mr. Obama. Here's an excerpt of what the president said Tuesday night:

"Look, the cost of lowering rates for everybody across the board, 20 percent, along with what he also wants to do in terms of eliminating the estate tax, along with what he wants to do in terms of corporates, changes in the tax code, it costs about $5 trillion.”

Obama continued, “Governor Romney then also wants to spend $2 trillion on additional military programs, even though the military's not asking for them. That's $7 trillion. He also wants to continue the Bush tax cuts for the wealthiest Americans. That's another trillion dollars: That's $8 trillion....  $8 trillion before we even get to the deficit we already have."

According to the nonpartisan Tax Policy Center, Obama is correct about the $5 trillion figure, which refers to a 10-year period. But the other $3 trillion may be unfair to lump in. After all, continuation of the Bush tax cuts is often assumed to occur, when budget experts create "base lines" for forecasting.

That is, the Bush rates are "current policy," even though they are scheduled to expire. Obama's own budget counts eliminating Bush rates for the rich as an action that reduces the deficit.

On the military spending, that's a legitimate fiscal issue for Obama to raise, but it's on the spending side of the ledger. If Romney's stated goal is to be deficit-neutral on the tax revenue front, then his defense spending isn't part of the equation. (The real question is whether, on the spending side, Romney can achieve his called-for deficit reduction while keeping military spending so high.)

That still leaves $5 trillion in lost tax revenue to pay for. Independent tax experts say it's very hard to fully offset that by reducing tax breaks – especially if the middle class needs to come out with a net tax cut.

Romney's defenders have argued that, depending on how aggressively the plan chops tax breaks, the math can work out. The size of all "tax expenditures" (things like deductions and credits) in the individual income tax is huge – an estimated $1.1 trillion in 2014, for example. And a large share of them go to wealthy taxpayers.

Romney's allies also argue that his critics don't give enough allowance for the plan's positive impacts on economic growth, which could result in added tax revenue that's missed in traditional forecasting.

But his critics say it's politically very hard to have the elimination or reduction of various tax breaks add up to $5 trillion – all while having the rich pay the same share of overall US taxes that they do now. Critics also note that when you reduce tax rates, the value of "tax expenditures" goes down. So it's wrong to think of that $1.1 trillion, for example, as a pool of money that can all be tapped to pay for tax rate reductions.

Some final points:

• The $25,000 figure may not be etched in stone. Romney's "I'll pick a number" phrasing could be understood to mean the number is notional for now. But the fact that he mentioned the figure at all, in front of millions of TV viewers, says something.

• Relatively few households have deductions that total more than $25,000. The average deduction for tax filers with incomes in the $60,000 to $100,000 range, for example, is $20,169, according to research by the Tax Foundation.

• A deduction cap would create winners and losers. For example, even if Romney plan delivered a net tax break to the average middle-class family, some households might end up paying more because of the deduction limit.

• The economic-growth side of tax reform is important. If reform is revenue-neutral, the big rationale for doing it has to do with job creation. Romney emphasized this point during the debate.

"Why do I want to bring rates down and at the same time lower exemptions and deductions, particularly for people at the high end? Because if you bring rates down, it makes it easier for small business to keep more of their capital and hire people," Romney said. "And for me, this is about jobs."

It's a matter of debate among economists whether the impacts would be large or modest, but even Obama has embraced the general idea of "lower rates, broaden the base," which in his case is to blend growth and deficit reduction.

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