The Joint Committee on Taxation is one of the most respected institutions in Washington. It is to the tax code what the CBO is to the budget: a nonpartisan, impartial arbiter that produces respected estimates of revenues and other figures important to tax policy.

So it's a big deal that they sent Sens. Max Baucus and Orrin Hatch — the chair and ranking member, respectively, on the Senate Finance Committee — a letter (obtained first by Bloomberg) arguing that even if you eliminated almost every tax deduction in the books, you could only afford to cut tax rates by 4 percent before you start adding to the deficit. The full letter is here:

The paper recounts an experiment conducted by the JCT. They supposed that all itemized deductions — things like the charitable deduction, the mortgage-interest break, etc. — were eliminated (though not non-deduction tax breaks — more on that later), along with the Alternative Minimum Tax. That mirrors Romney's desire to cut tax breaks and eliminate the AMT. They also assumed that state and local bonds' interest would start to be taxed, which, as AEI's Matt Jensen has pointed out, makes it easier for the Romney plan to add up.

Finally, JCT assumed that capital gains and other investment income would be taxed at the same rate as regular income, instead of the preferential rates they currently enjoy. That's a big difference from Romney's plan, which proposes eliminating capital gains and other investment taxes for people making less than $200,000, but mirrors the Bowles-Simpson, Domenici-Rivlin and Wyden-Coats tax reform plans, all of which remove the capital preference.

Then JCT asked how low you could cut tax rates under this scenario without increasing the deficit, on net. The answer: not much at all. To keep revenue the same as it'll be next year, when the Bush tax cuts expire, you could only cut rates by 4 percent. Instead of brackets of 15 percent, 28 percent, 31 percent, 36 percent and 39.6 percent, you'd have brackets of 14.4 percent, 26.88 percent, 29.76 percent, 34.56 percent and 38.02 percent. That's not exactly revolutionary, and it's a far cry from the 20 percent cut that Romney wants.

That said, the change is very progressive. People making $10-20,000 a year get their taxes cut by 2.4 percent of income, a 61.4 percent cut relative to their previous burden. By contrast, millionaires see taxes go up 7.1 percent, or 5.5 percent of income:

It's hard to draw conclusions about Romney's or any other real-world plan from the JCT study. For one thing, it didn't eliminate the health insurance or retirement income exemptions, judging that too difficult to model, nor did it cut the Child Tax Credit or Earned Income Tax Credit. Those were on the chopping block in the Tax Policy Center study on the Romney plan, and JCT doesn't only exempt them from cuts in its experiment, it assumes that the expansions of them in the stimulus package and the Bush tax cuts will be made permanent.

Most jarringly, the 4 percent cut is calculated relative to a baseline where almost all the Bush tax cuts expire, rather than the policies in effect today. Romney, by contrast, wants a 20 percent cut relative to the Bush rates, and given that few expect the Bush tax cuts will lapse in their entirety, the relevance of the baseline JCT uses is questionable. But the baseline if anything makes the study too optimistic. Deductions are worth more when tax rates are higher, so you could generate less revenue from cutting them if you used a baseline with the lower, Bush-era rates. So the same study with a more appropriate baseline would come up with even more modest rate cuts. Update - also worth noting that the current policy baseline means the JCT plan wouldn't have to pay for things like the EITC expansion in the stimulus or patching/eliminating the AMT, so the effect is more ambiguous. Thanks to Marc Goldwein at Committee for a Responsible Federal Budget for pointing this out.

That said, the JCT study does drive home one lesson that the discussion of the Romney tax plan taught us: Base-broadening tax reform is really hard. Even if you get rid of popular deductions like the one for mortgage interest, and even if you jack up taxes on investment income, you can't cut rates by all that much. No matter who wins next month, they have a herculean task before them on taxes.