President Obama and legislators are embroiled in a debate over whether and how to punish companies that seek U.S. tax relief by buying a smaller foreign company and legally reincorporating in its country. So-called tax inversions are at a record high, and Obama has suggested it’s not a victimless activity.

“It’s not right,” he said on August 6. “The lost revenue to Treasury means it has got to be made up somewhere, and that typically is going to be a bunch of hard-working Americans, who either pay through higher taxes themselves” or cuts to government services. (Would that some of his donors agreed…)

The inversion debate is a sign of unhappiness with U.S. corporate tax rates, which are the highest in the developed world and tempting companies to jump overseas in the first place. And fixing the tax code, by reducing those onerous rates and plugging loopholes, requires the government to find some new sources of income elsewhere.

Enter federal climate policy, which for years now has been held up as a potential funding source for whatever anyone needs at the moment. Obama’s first budget proposal to Congress, for the 2010 U.S. fiscal year, assumed that a legislated climate policy would bring in $650 billion between 2012 and 2019, helping to reduce federal deficits. The House of Representatives passed a measure in 2009 that died in the Senate months later.

Revenue raised through climate policy, be it an emissions-permit trading scheme or straight-out carbon tax, could really be used to do anything politicians think important – fund clean energy research, aid poor communities reliant on coal mining or burning, or refund it to taxpayers quarterly, as Democratic Representative Chris Van Hollen recently proposed.

Two environmental economists propose that federal income from a carbon tax could help reboot the U.S. corporate tax code. And a rebooted corporate tax code would then have the effect of reducing the cost of the carbon tax to GDP.

Lawrence Goulder, of Stanford University, and Marc Hafstead, of the nonpartisan think tank Resources for the Future, studied how three scenarios might affect GDP: a lump-sum refund of U.S. carbon tax revenue to Americans; using the income to pay for personal income tax cuts; or using it to cut corporate income taxes. The study looked at the potential impacts of a carbon tax of $10 per ton of carbon dioxide (or its heat-trapping equivalent from other greenhouse gases) that rises 5 percent a year, and is levied on industrial energy consumption. The tax itself is the same in each case and all three are “revenue neutral,” meaning that the money that comes in goes right back out the door for some other purpose:

The researchers found that the third option, cutting corporate taxes, reduces the cost of the carbon tax in GDP better than the other two.

The tax would bring in about $50 billion, in 2012 dollars, in its first year (which is 2013, in the research). That would grow past $150 billion in 2040, adjusted for inflation.

Refunding that carbon tax revenue is a politically popular idea among those for whom a carbon tax is a politically popular idea. But if the think tank research holds up, rebates might not be the most economically sensible idea. The carbon tax’s hit to GDP, if the corporate income tax is fixed, is 58 percent lower than the lump-sum refund scenario.

Hafstead published his own blog post on the topic today, which is based on a working paper published with Goulder in October.

The big problem with policy studies, as usual, is the real world. Nearly all Republicans and some Democrats oppose climate policy. And any anticipated dip in GDP is likely to be so intolerable that the whole idea is nixed at the outset.

That’s too bad, because all that carbon dioxide streaming into the atmosphere is basically, among other things, free money.