For months, Mitt Romney had been advocating tax cut proposals that would reduce revenues by about $5 trillion over the next decade, and that were heavily tilted toward the rich. Yet he did not explain how he would pay for these cuts, just that he somehow would.

In a recent paper I wrote with two colleagues, we showed that a revenue-neutral plan that met five specific goals that Governor Romney had put forth (reducing income tax rates by 20 percent, repealing the estate tax, the alternative minimum tax, and capital income taxes for middle class households, and enhancing saving and investment) would cut taxes for households with income above $200,000, and—as a result of revenue-neutrality—would therefore necessarily have to raise taxes on taxpayers below $200,000.

This was true even when we bent over backwards to make the plan as favorable to Romney as possible. We considered an unrealistically progressive way of financing the specified tax reductions. We accounted for revenue feedback coming from potential economic growth estimates as estimated by Romney advisor Greg Mankiw. We even ignored the need to finance about a trillion dollars in Romney’s proposed corporate cuts.

Our conclusion was not a prediction about Governor Romney would do as president, it was an arithmetic calculation: all of the promises couldn’t be met simultaneously without resorting to tax increases on households with income below $200,000.

With both candidates referring to the study in the first debate, several responses to the study having been published, new proposals from Governor Romney on the table, and confusing and misleading partisan jabs on both sides of the aisle, it is time to take a new look at this discussion and help readers understand what is going on.

To do that, let’s get out of the hyper-charged world of tax policy for a second.

Suppose Governor Romney said that he wants to drive a car from Boston to Los Angeles in 15 hours. And suppose some analysts employed tools of arithmetic to conclude that “If Governor Romney wants to drive from Boston to LA in 15 hours, it is mathematically impossible to avoid speeding.” After all, the drive from LA to Boston is about 3,000 miles, so to take only 15 hours would require an average of 200 miles per hour. Certainly other road trips are possible—but the particular one proposed here is not.

(Note: this is just an example that uses the logic to be employed; I am not suggesting that Romney has in any way broken a law.)

Especially in this inflamed campaign environment, one can imagine the frenzied responses. The Obama campaign might put ads out that say Romney wants to speed or is going to speed. Romney’s campaign might respond by saying the study is a “joke” and “partisan,” that he supports speeding laws and would never, ever speed, and it is ridiculous to suggest that he would. The Romney campaign and its surrogates might say that the analysts must be wrong because they don’t even know what his road plan is or which car he would drive. Besides, Romney never really said he wanted to go LA, he might want to go somewhere closer; he could get to LA without speeding if he took more than 15 hours; he could get somewhere else in 15 hours without speeding. And so on.

With a few substitutions, this is almost exactly how the tax debate has evolved. Substitute “the various tax cuts Romney has proposed” for “driving from Boston to LA;” substitute revenue-neutrality for “in 15 hours;” substitute “tax increases on households with income below 200k and tax cuts for higher income households” for “speeding” and you have the basic story: Romney can’t do all of the tax cut proposals he has advocated, remain revenue neutral, and avoid taxing households with income below $200,000 or cutting taxes for higher income households.

Substitute “the full Romney tax plan” (which, by the way, does not exist) for the choice or road plan or car and you have the common complaint, “how can you evaluate the specific proposals when the overall tax plan is not even fully specified?” The answer to which is that even with incomplete information, there is enough to understand some of the implications.

Most obviously, despite all of the hoopla and name-calling, no one has proved or really even tried to prove that the analysts’ original calculation was wrong—the proposed trip would require speeding, and Romney’s original tax proposals would require tax increases on households below $200,000.

Romney has now also said that he does not want to raise taxes on the middle class and does not want to cut them for high-income households. Those seem like reasonable goals, but they don’t break the knot. They simply add two more constraints to the list of goals he would like to achieve and makes the list even more impossible (if there is such a thing) to achieve jointly than the earlier list.

Romney campaign surrogates and right-wing media outlets have focused on the idea that new taxes on saving and investment should be imposed. After decades of these same outlets claiming that taxes on saving and investment are bad for the economy, scholars at AEI, Heritage, some academics and the Wall Street Journal editorial page appear lined up behind higher taxes on some forms of interest income, and removal of tax-deferral on some long-term saving products, as a way to finance part of the Romney tax plan. This is an interesting development and should be pursued.

To be clear, though, pursuing this policy wouldn’t be refuting our earlier study, it would be accepting the constraints and conclusions there and finding a way around them.

Likewise, Romney’s recent support of placing a cap on taxapayers’ itemized deductions has the potential to finance some of the tax cuts, and so is a step in the right direction. It remains to be seen, though, whether Romney can develop enough “pay-fors” to cover his tax cuts and not burden the middle class.

Or as one example of what might happen, Alan Viard, a scholar at the American Enterprise Institute noted in the New York Times, suggested that Romney is “going to need to cut rates significantly less than 20 percent if he wants to honor his other goals.” Exactly: something would have to give.

More generally, the basic power of arithmetic is overwhelming in showing that Governor Romney has so far overpromised on the tax side.

You still can’t drive cross country in 15 hours without speeding.