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For years, chief executives have complained bitterly about the United States corporate tax code, arguing that it is too complicated and that rates are too high. The issue has reached a near boiling point this summer as many large American companies have sought to buy smaller foreign rivals so they can renounce their United States corporate citizenship and reincorporate overseas to lower their tax bills. Others are considering the move, known as an inversion.

Again and again, we hear that these deals are being driven by an effort to make our companies more competitive globally and that unless we “reform” our tax system — which is code for “lower our corporate tax rate” — we will lose business to foreign rivals.

It is a compelling narrative. But it may be wrong.

Edward D. Kleinbard, a professor at the Gould School of Law at the University of Southern California and a former chief of staff to the Congressional Joint Committee on Taxation, makes a captivating argument in an academic paper that the United States tax code — counter to the conventional wisdom — is not impeding global competitiveness. In fact, the opposite is true.

“Despite the claims of corporate apologists, international business ‘competitiveness’ has nothing to do with the reasons for these deals,” he writes. “Whether one measures effective marginal or overall tax rates, sophisticated U.S. multinational firms are burdened by tax rates that are the envy of their international peers.”

What? We’ve been told repeatedly that the United States has the highest corporate tax rate in the developed world — 35 percent — which is higher than the nominal tax rates in places like Ireland (12.5 percent), Britain (21 percent) and the Netherlands (25 percent) and the 24.1 percent average rate of all countries that are part of the Organization for Economic Cooperation and Development.

All of that’s true, but Professor Kleinbard contends that most United States multinational companies don’t pay anywhere near 35 percent. Companies paid, on average, 12.6 percent, according to the Government Accountability Office, which last measured it in 2010, by deliberately stashing piles of cash abroad.

Professor Kleinbard argues that lower tax rates are not driving companies to inversions; instead, he contends it is all the money that companies have overseas — some $2 trillion — and don’t want to bring back to the United States despite protestations by many chief executives that they wish they could.

The provocative paper is worth reading even if you disagree with its conclusions because it helps explain why corporate tax change will be so difficult to accomplish even with the backing of both Democrats and Republicans, who have routinely provided lip service to the idea of lowering rates, but taken no action. Professor Kleinbard’s paper may also help explain why companies themselves may end up lobbying against various corporate tax proposals, even those that lower the statutory rate.

Professor Kleinbard suggests that companies have become so clever with “aggressive tax planning technologies” that many of them are able to take advantage of the current tax system so well that they are more competitive than their foreign rivals. He argues that the American companies are “unencumbered by any of the anti-abuse rules to which non-U.S. multinationals domiciled in jurisdictions with better designed territorial systems might be subject.”

He goes on to argue, referring to generally accepted accounting principles, that “in practice U.S. firms do capture the benefit of operating in lower-tax jurisdictions, both as a cash tax matter and — more important — for purposes of U.S. GAAP, which is the lens through which investors and corporate executives measure a firm’s performance.”

While critics of the current tax system argue that the United States needs to adopt a territorial tax system like most other foreign countries that tax only those profits produced locally, it is unclear whether such a system would actually lower the tax burden for some American multinationals.

Professor Kleinbard makes a tantalizing argument that all that cash “trapped” overseas isn’t really trapped. In fact, he says that some American companies have found a way to use it — in the United States.

“As Apple Inc. demonstrated in 2013, large multinational firms often can access their offshore earnings without incurring a tax cost, simply by borrowing in the United States and using the earnings on the offshore cash to pay the interest costs,” he explained. The tax code allows a company to include interest earned on its offshore cash pile in the United States parent’s income. That “offsets the tax deduction for the interest expense on the firm’s U.S. borrowing, and the firm is left in the same economic position as if it had simply repatriated the cash tax-free.”

None of this is to say that our current tax system is perfect. It isn’t. Despite all Professor Kleinbard’s assertions about the way United States multinational companies use the tax system, he is one of the first to say it needs to be updated. “It is highly distortive and inefficient,” he writes.

There are reasons to change the tax code to help the economy. “But one of the few deficiencies it has avoided is imposing an unfair international business tax competitive burden on sophisticated U.S. multinationals,” he says.

Something to ponder.