Apple Inc. Chief Executive Officer Tim Cook appeared before the Senate Permanent Subcommittee on Investigations this week to defend his company's tax record. The media has focused on how much of Apple's income is earned by subsidiaries that do not claim tax residence anywhere and therefore do not pay tax. That's a problem -- but not the big problem.

The big problem is that the process of determining the taxable U.S. income of a multinational corporation is necessarily complicated and arbitrary. Companies, including Apple, will exploit that arbitrariness to reduce their tax bills, and while we can diminish their flexibility to do so at the margins, we'll never fix the problem entirely. Instead, we should sharply reduce the corporate tax and replace it with higher taxes that are more progressive and easier to collect: taxes on shareholders in corporations.

Apple's story is special because it got its tax rate on foreign income almost down to zero. But even if Apple hadn't managed that, it still could have used garden-variety tax avoidance methods to move its income from the U.S., where our statutory corporate income tax rate is the highest in the advanced world. Apple wouldn't have saved as much money, but the impact on the U.S. Treasury would have been the same.

Professor J. Richard Harvey of Villanova University, in his testimony to the subcommittee this week, described two main ways Apple and other companies move domestic profits abroad.

One is by transferring difficult-to-value intangible assets. Let's say your company has developed intellectual property whose market value is unclear -- the product it supports may be a hit or a flop. Before the product launches, you sell the rights to a foreign subsidiary at a low price, recording only a small profit to the U.S. parent. If the product turns out to be a success, the royalties accrue to the foreign subsidiary, and the profits are not subject to U.S. tax unless you bring them back to the U.S. -- so you leave the money abroad indefinitely. This ability to delay tax on foreign profits is known as "deferral."

The other method is to over-allocate expenses into high-tax jurisdictions. Apple's headquarters are in Cupertino, California, and the company engages in a lot of expensive activities there that support Apple's profit-making operations at home and abroad. For tax purposes, Apple needs to make judgments about what proportion of those expenses count against foreign profits versus domestic ones. If Apple allocates those costs heavily toward U.S. operations, it can show less profitability at home, further reducing its U.S. tax bill.

And indeed, according to Harvey, "Both general and administrative (G&A) expenses and sales, marketing and development (SM&D) expenses as shown on Apple's 2011 consolidating income statement appear to be disproportionately allocated to the U.S." Apple says it earns 24 cents in pre-tax profits for every dollar of U.S. sales, but 36 cents for each dollar of foreign sales. If Apple allocated the above categories of expenses in line with sales, its reported U.S. income would be higher by $2.2 billion a year.

The conservative critique of corporate income tax tends to focus, in part, on our "worldwide" system of corporate taxation: We try to tax U.S.-based companies on their income all over the world, while many other countries tax only domestic operations. So long as U.S. companies can use accounting gimmicks to turn domestic income into "foreign" income, the idea to "only tax U.S. companies on U.S. income" will only deprive the Treasury of money it is legitimately owed.

That's why liberals tend to want to crack down on income-shifting practices. But loopholes don't persist only because big companies have fancy lobbyists and want to keep avoiding taxes. They also persist because the problem of how to allocate a company's profits is legitimately hard. It's difficult to produce rules that stop companies from gaming the system without producing negative side effects.

The most extreme approach, sometimes floated by Democrats, would simply be abolishing deferral of tax on foreign income, meaning that companies could not avoid tax on foreign profits by leaving them abroad. This would make income-shifting strategies useless for U.S.-based multinationals, but Harvey noted a major risk: U.S. companies could expatriate.

Another possible solution, Harvey said, is using fixed formulas to allocate multinationals' profits. For example, if you made 35 percent of your sales in the U.S., you would pay tax on 35 percent of your profits here. But often a company's profitability footprint is legitimately different from its sales footprint, so some firms would be penalized unfairly. U.S. states, which use apportionment approaches like this, have had no success achieving corporate tax uniformity. That non-uniformity doesn't matter a great deal since state corporate tax rates are low, but it would be more of a problem at the international level.

The other expert witness at this week's hearing, Harvard Law Professor Stephen Shay, urged a minimum tax on foreign income. Deferral wouldn't be abolished, but it would be limited on foreign income that was untaxed or taxed at a low rate abroad. Harvey also cited this as a possible approach. But if the minimum tax rate was set pretty low -- say, less than 15 percent -- while companies would have little reason to use Apple-like maneuvers that get taxes on foreign income almost to zero, their likely alternative would be to move income into countries with tax rates between 15 percent and 35 percent. If the minimum rate were set higher, then it would raise real revenue -- but this would be tantamount to abolishing deferral, again encouraging expatriation.

The corporate tax code can still be improved. Harvey discussed many incremental improvements that would make it harder for firms to creatively avoid tax, including making it harder to move intellectual property offshore. But these changes can only go so far, because of two dimensions of problems with corporate tax: (1) the flexibility to shift taxable profits offshore gives multinational firms like Apple an advantage over purely domestic ones, and (2) our practice of taxing actual offshore profits puts U.S.-based multinationals at a disadvantage compared with foreign-based ones. In general, the more you act to fix the first problem, the more you make the second worse.

That's why Harvey said closing loopholes in the U.S. corporate tax code is only a third-best option. His first choice is international cooperation on tax rules that would get countries like Ireland to stop playing ball with Apple and make international tax shifting less profitable. That, as Harvey noted, is unlikely to happen. His second choice is to greatly reduce the corporate income tax and replace it with an alternate source of revenue. He suggested a value-added tax, but noted that is also politically impossible.

But maybe a non-VAT replacement is possible. Republicans hate VATs because they think they encourage government growth, while Democrats dislike that they are regressive. Instead, we should replace lost corporate tax revenue with more taxes on the owners of capital, such as higher capital gains and dividend taxes or a shareholder-level tax on undistributed corporate profits.

In other words, instead of trying to tax Apple, we would tax its shareholders. Individual taxes are simpler than corporate taxes, and it's a lot harder for an individual to shift his tax residence, so we could expect less avoidance.

Unlike a VAT, this change would make the tax code more progressive. The economic incidence of corporate income taxes is ambiguous -- some of the tax is borne by shareholders, but a significant portion is borne by workers in the form of lower wages. Shifting taxes to the shareholders wouldn't just make taxes on returns to corporate investment easier to collect, it would also raise wages in the process. And by lowering the corporate tax rate, it would make the U.S. a more attractive place to invest.

(Josh Barro is lead writer for the Ticker. Follow him on Twitter.)