I can describe Mitt Romney’s tax policy promises in two words: mathematically impossible.

Those aren’t my words. They’re the words of the nonpartisan Tax Policy Center, which has conducted the most comprehensive analysis to date of Romney’s tax plan and which bent over backward to make his promises add up. They’re perhaps the two most important words that have been written during this U.S. presidential election.

If you were to distill the presumptive Republican nominee’s campaign to a few sentences, you could hardly do better than this statement of purpose from the speech Romney delivered in Detroit, outlining his plan for the economy: “I believe the American people are ready for real leadership. I believe they deserve a bold, conservative plan for reform and economic growth. Unlike President Obama, I actually have one — and I’m not afraid to put it on the table.”

The truth is that Romney is afraid to put his plan on the table. He has promised to reduce the deficit, but refused to identify the spending he would cut. He has promised to reform the tax code, but refused to identify the deductions and loopholes he would eliminate. The only thing he has put on the table is dessert: a promise to cut marginal tax rates by 20 percent across the board and to do so without raising the deficit or reducing the taxes paid by the top 1 percent.

The Tax Policy Center took Romney at his word. They also did what he hasn’t done: They put his plan on the table.

Favorable Conditions

To help Romney, the center did so under the most favorable conditions, which also happen to be wildly unrealistic. The analysts assumed that any cuts to deductions or loopholes would begin with top earners, and that no one earning less than $200,000 would have their deductions reduced until all those earning more than $200,000 had lost all of their deductions and tax preferences first. They assumed, as Romney has promised, that the reforms would spare the portions of the tax code that privilege saving and investment. They even ran a simulation in which they used a model developed, in part, by Greg Mankiw, one of Romney’s economic advisers, that posits “implausibly large growth effects” from tax cuts.

The numbers never worked out. No matter how hard the Tax Policy Center labored to make Romney’s promises add up, every simulation ended the same way: with a tax increase on the middle class. The tax cuts Romney is offering to the rich are simply larger than the size of the (non-investment) deductions and loopholes that exist for the rich. That’s why it’s “mathematically impossible” for Romney’s plan to produce anything but a tax increase on the middle class.

The Romney campaign offered two responses to the Tax Policy Center’s analysis, one more misleading than the other.

First, the campaign called the analysis “just another biased study from a former Obama staffer.” That jab refers to Adam Looney, one of the study’s three co-authors, who served in a staff role on the White House Council of Economic Advisers under President Barack Obama. But the Tax Policy Center is directed by Donald Marron, who was one of the principals on George W. Bush’s Council of Economic Advisers. Calling the Tax Policy Center biased simply isn’t credible — a point underscored by the fact that the Romney campaign referred to the group’s work as “objective, third-party analysis” during the primary campaign.

Then the Romney campaign said, “The study ignores the positive benefits to economic growth from both the corporate tax plan and the deficit reduction called for in the Romney plan.” There’s a reason the study ignores those “positive benefits”: Romney has called for a revenue-neutral corporate tax plan that brings the rate down from 35 percent to 25 percent while also promising to balance the budget. He has not said how he will achieve either goal. Until he does, those positive benefits — if they exist — are impossible to calculate.

Regressive Cuts

If Romney tries to pay for his tax cuts by reducing spending, the results, as the Tax Policy Center notes, would be even more regressive. Romney has promised to increase defense spending and hold benefits steady for the current generation of seniors. The only remaining big spending programs are those that help the poor; that’s where Romney’s cuts would have to be concentrated. Paying for tax cuts for the rich by curtailing programs for the poor is even more of a reverse-Robin Hood act than paying for tax cuts for the rich by cutting the tax expenditures (deductions and the like) of the middle class.

The Center on Budget and Policy Priorities produced its own analysis of Romney’s plan, based on an assumption that Romney pays for half of his tax cuts through spending cuts. The conclusion: By 2022, Romney would need to cut all non-defense, non-Social Security programs by 49 percent. That is not plausible, to say the least.

The Romney campaign has not provided good answers to the questions raised by its own math. But we already knew the Romney campaign didn’t have good answers. If Romney had good answers, he would have made good on his rhetoric and put his plans on the table.

It would be great if Romney could fulfill his promise to cut taxes by trillions of dollars, increase defense spending, keep entitlement spending on pretty much its current path for the next decade, and balance the budget. But as Tyler Cowen, the George Mason University economist, put it in a pithy tweet (though perhaps “pithy tweet” is a tautology), “The proposed Romney fiscal policy just doesn’t make any sense.”

This is not a surprise. Even some Republican policy experts admit in private that Romney’s promises simply don’t add up. To twist Abraham Lincoln’s famous formulation, the Romney campaign has decided it’s better to remain silent and be thought evasive than to reveal your plan and remove all doubt that you’re cutting taxes on the rich while increasing the deficit, raising taxes on the middle class and cutting programs for the poor.

Unfortunately for the Romney campaign, the Tax Policy Center’s analysis has removed all doubt. Romney needs to come up with a way to make his promises mathematically possible — and quick.

Our ideas can save democracy... But we need your help! Donate Now!

Follow Ezra on Twitter @ezraklein. Ezra Klein is the founder and editor-in-chief of Vox.com.