During a campaign stop in Stamford, Connecticut, on Tuesday morning, President Obama said Mitt Romney’s tax plan amounts to another big tax cut for the rich financed by tax hikes for less-wealthy Americans: “It’s like Robin Hood in reverse,” he said. “It’s Romney Hood.” It’s a good line, but what’s the truth of it? In my last post, I remarked that the Obama campaign was intent on fanning fears that Romney was planning a covert tax hike on middle-class Americans. Following Obama’s remarks, the Romney campaign quickly fired back, saying, “There’s only one candidate in this race who’s going to raise taxes on the American people—and that’s Barack Obama.”

The President wasn’t talking off the top of his head, though. In attacking Romney’s proposal to cut tax rates across the board and scale back some popular tax breaks, he and his campaign are citing a new study I also mentioned yesterday, from the Tax Policy Center, a non-partisan Washington research institute. The study clearly says that Romney’s plan would leave wealthy Americans considerably better off. According to the three economists who authored the report, those lucky folks earning a million dollars a year would end up taking home an extra eighty-seven thousand dollars in income. By contrast, taxpayers earning under two hundred thousand dollars a year would be hit with a tax increase of five hundred dollars. And those figures are calculated on the assumption that a Romney administration would eliminate many of the tax loopholes enjoyed by the rich. If that didn’t happen, the report says, a Romney Administration would have to take even more money from ordinary Americans.

As you might expect, the Romney camp has dismissed the study as a partisan attack, calling it “another biased study from a former Obama staffer that ignores critical parts of Governor Romney’s tax reform program, which will help the middle class and promote faster economic growth.” The former Obama staffer is Adam Looney, who worked on tax issues at the Council of Economic Advisers, and who previously worked at the Federal Reserve Board. In addition to contributing to Tax Policy Center studies, he is currently the policy director for the Hamilton Project, a research institute established by Robert Rubin. That marks him out as a fiscally conservative Democrat, I suppose, but it hardly invalidates the study. Another of its other authors, William Gale, once worked at the White House for a Republican President: George H. W. Bush. The third author, Samuel Brown, is another veteran of the Federal Reserve. All three are acknowledged experts on the tax system.

The Tax Policy Center report stands on its own merits, which are considerable. Perhaps the most notable thing about the criticisms from the Romney campaign is that they don’t contain any refutations of any individual figures. Conceivably, that is because Romney’s advisers don’t want to get bogged down in a debate about fairness and equity. Much more likely, it is because they couldn’t find anything in the report that can be easily refuted. It’s yet another example of the Romney campaign paying a political price for its pandering and opaqueness. Romney only proposed such huge and irresponsible tax cuts in response to criticisms from his rivals in the G.O.P. primary. Since then, he’s refused to say in any detail how he’ll pay for them, which invites others to speculate about their distributional consequences.

Essentially, the report is an accounting exercise. It takes all of the economic pledges that Romney has made and examines what he would have to do in order to meet them. For those of you who have forgotten, here’s what the Mittster has promised: An indefinite extension of the 2001-2003 Bush tax cuts; a further twenty per cent cut in income-tax rates across the board; the elimination of all taxes on investment income for families earning less than two hundred thousand dollars a year; repeal of the alternative minimum tax (A.M.T.); elimination of the estate tax; a big reduction in the corporate-tax rate; and a repeal of the tax increases included in the 2010 health-reform bill.

That’s quite a list. But Romney has also insisted that his tax reforms would be revenue neutral. In order to pay for them, he says he would scale back some popular tax deductions, such as the mortgage-interest deduction and the deduction for employer-provided health care. That’s where things get sticky. According to the Tax Policy Center study, in 2015 the proposed tax cuts would reduce federal revenues by four hundred and fifty-six billion dollars, or about an eighth of the total. In order to make up a gap that large, a Romney Administration would have to eliminate a heck of a lot of loopholes.

Despite calls from many quarters, Romney hasn’t specified which tax breaks and loopholes—for some mystifying reason, they are sometimes called “tax expenditures”—he would tackle: the details of his plan would be up for discussion with Congress, he says. Two things he has stated are that he favors a progressive tax system and that he would mainly target loopholes enjoyed by the rich. But here he runs into some internal contradictions. As his own finances demonstrate, some of the biggest tax benefits enjoyed by the rich come in the form of ultra-low tax rates on investment income—capital gains and dividends—and tax-favored savings accounts: I.R.A.s, Keogh accounts, 401(k) plans, and so on. And these goodies, Romney has no plans to eliminate.

Once these things are taken off the table, the other benefits enjoyed by the rich—deductions for mortgage interest payments, charitable giving, health insurance, and so on—simply aren’t big enough to pay for his huge tax cuts. In fact, even if Romney eliminated all of their other loopholes and benefits—by, for instance, preventing them from claiming any deductions for mortgage payments and charitable giving—then if he were serious about revenue neutrality he would still have to target the non-rich, scaling back some of their tax breaks, too. And once he started down this path, many middle-class families would end up worse off in net terms. Here is the the key passage in the report. (To make it easier to read, wherever the phrase “tax expenditures” occurs, I have substituted “tax breaks and loopholes.”)