In large measure, what you think about the tenability of Mitt Romney's tax plan depends on what you think his tax reform proposal can do for economic growth.

Optimistic growth estimates, like those used by the Tax Policy Center, have predicted only a mild economic boost from Romney's proposal -- $53 billion of the $360 billion annual cost of the plan would be recouped from higher revenues that result from faster growth. Princeton's Harvey Rosen puts that figure even lower in a paper defending the Republican presidential nominee, at around $25 billion.

But then again, Rosen's estimates assume that the Romney plan speeds up the current growth rate by 3 percentage points. That's an extremely high estimate, and it's based on Rosen's misuse of another analysis of the Romney plan. But even if growth improved by half that figure, it would be an impressive gain. Is there reason to believe that tax reform can really do that?

Bruce Bartlett, the Reagan economic-aide-turned-conservative-apostate, has his doubts. President Reagan's 1986 tax reforms, Bartlett argues, had no notable effect on growth. He cites a literature review by Berkeley's Alan Auerbach and the University of Michigan's Joel Slemrod, arguably the two most respected tax economists in the United States, as well as a paper by Harvard's Martin Feldstein, both of which concluded the same. He concedes that unemployment fell after the reforms but notes that it had started to slide well before then, as the United States was recovering from the 1981-82 recession.

Aye, and there's the rub. A lot of things — from Federal Reserve policy to the price of commodities to government policy – affect unemployment and growth, which makes isolating the effect of a single policy change after the fact extremely difficult. So economists often turn to models to predict the results of a specific policy change, such as the tax code.

And those models suggest that revenue-neutral tax reform could actually have a significant impact on growth in the long-run. The most influential paper on this subject is by Auerbach, David Altig, Lawrence Kotlikoff, Kent Smetters and Jan Walliser. Romney's campaign has cited the paper as support for his tax plan, but the research considers much more dramatic tax policy action than anything Romney has proposed.

The paper builds a model to calculate the effects of replacing the personal and corporate income taxes with five potential alternatives. Three of them are flat taxes. One is a straightforward flat tax with literally no deductions; another adds a standard deduction so that the tax can be considered progressive (and thus most resembles real-world flat tax proposals); and the third has a deduction and also a transition period to ease any fiscal and distributional blow.

The other two are consumption taxes. One is a proportional tax on goods and services, which could take the form of a sales tax or a European-style value-added tax (VAT), which is calculated throughout the goods' production process. The last and perhaps most interesting option is the X tax.

First proposed by David Bradford and recently resurrected by American Enterprise Institute's Alan Viard and Ernst and Young's Robert Carroll, the X tax is a progressive VAT. Just as with regular VATs, businesses pay a tax on their expenses. But under the X tax they also exempt their wage costs, and individuals then pay a progressive payroll tax.

The paper found that all five options boosted growth relative to tax policy in the late 1990s, when the experiment was conducted.

In its purest form, a flat tax has significant, positive effects on growth, but in its common form the tax's impact is considerably less dramatic, especially if paired with a transition period. The real stars here are the consumption taxes. A flat VAT increases long-run growth by 9.4 percent, and an X tax does so by 6.4 percent. That said, a flat VAT would be exceptionally regressive. The authors estimate the effects of each proposal on 12 "income classes," with group 1 being the poorest and group 12 the richest. They also break down the result based on the age of the taxpayer -- from people not born yet who will reach adulthood 54 years after a tax is put in place, to people who are already in their 60s. They find that both the VAT:

Source: Altig et al.

and the flat tax:

Source: Altig et al.

reduce the well-being of most of those in the middle and bottom income classes. The only poor and middle-class people who gain are those born far into the future who would benefit from decades of faster growth.

By contrast, those at the bottom income level gain the most from the X tax:

Source: Altig et al.

If the  X tax, then, is a progressive reform with the potential to boost growth by over 6 percentage points, why aren't people jumping on it?  AEI has embraced the proposal and included it, along with a carbon tax, in the revenue portion of its balanced-budget plan. But the idea hasn't gained much momentum elsewhere.

Some models suggest that base-broadening tax reform, if revenue neutral, could generate growth almost as significant as the models predict for the X tax. Rice University's John Diamond, whose analysis of the Romney tax plan has been touted by Rosen and other supporters, found that base-broadening tax reform, if revenue neutral before growth is taken into account, could spur a 6-point boost in in the economy. Revenue-positive plans, like Bowles-Simpson or Domenici-Rivlin, would likely produce smaller gains, as would reform, like Romney's, which is revenue negative before you take growth into account.

The trouble, of course, is that the Tax Policy Center has proven beyond a reasonable doubt that base-broadening tax reform of the scale Romney is proposing raises taxes on lower-income people and lowers them on people making over $200,000 a year.

So only the X tax promises large gains from faster growth while ensuring that the the levy that people ultimately pay is based on their income levels.