WASHINGTON — Whoever wins the White House next year will have to deal with an issue of almost-impenetrable complexity and contentiousness: How to tax multinational companies? On the one hand, large global firms — which have never been shy about minimizing their taxes through deft accounting maneuvers — are becoming more aggressive. On the other, so are governments, increasingly desperate to raise tax revenues to pay for aging societies and cover persistent budget deficits.

The latest evidence of the unavoidable collision is the proposed merger between the American drug giant Pfizer and the smaller Irish pharmaceutical company Allergan — a combination that, if realized, would create a firm valued at roughly $160 billion and would legally convert Pfizer into an Irish corporation. The deal is driven in part by tax savings. Ireland’s basic tax rate on corporate income is 12.5 percent compared with a maximum U.S. rate of 35 percent.

The proposed merger attests to a sea change in American corporate attitudes and behavior. A decade ago, it was inconceivable that a huge blue-chip American company would jettison its U.S. legal identity. Smaller firms with lower public profiles might do so — though even that was frowned upon — but it simply wasn’t done by bigger, better-known companies. Pfizer is a long-standing member of America’s corporate elite. Its aggressiveness shows how the taboo has eroded.

Some math helps explain the shift. By 2014, Pfizer had accumulated $74 billion in uncommitted foreign profits that had not been repatriated to the United States, estimates Americans for Tax Fairness, a left-leaning advocacy group. If Pfizer moved the money to the United States, it might potentially be taxed at today’s rate of 35 percent. The bill would be about $26 billion. But the same profits taxed in Ireland might cost only about $9 billion. The $17 billion difference, the company says, could support more drug research, including in the United States where it is now concentrated, or payments to shareholders.

To many, this cold profit-maximization seems unpatriotic and predatory. The move to Ireland would occur mostly on paper. Pfizer says that its “global operational headquarters” would remain in New York while “its principal executive offices” would be in Ireland — whatever that means. The tax switch is called an “inversion.” Here’s how Americans for Tax Fairness characterizes Pfizer’s Irish inversion:

“With an inversion, Pfizer essentially would continue to enjoy all the benefits of being an American corporation but just not pay the taxes required for that privilege. Pfizer would not pay its fair share for its educated workforce; use of our transportation systems; the protections provided by our strong judicial, banking and regulatory systems; and so much more. … “

But pressure on multinationals to generate more tax savings will grow, suggests a report from the McKinsey Global Institute, the research arm of the famed consulting company. From 1980 to 2013, inflation-adjusted after-tax profits for global multinationals more than tripled from $2 trillion to $7.2 trillion, reflecting strong economic growth and expanding profit margins, says McKinsey. Now the boom is ebbing, it argues, as growth slows and new competitors — tech companies and multinationals from emerging-market countries — squeeze profit margins. The result, McKinsey says, is an intensifying corporate competition for global profits.

In this climate, multinationals and governments will spar over how much companies should pay in taxes and to which countries. But this struggle is shrouded in arcane tax and accounting provisions. It’s hard to know what the corporate “fair share” is when it’s not even clear what present tax burdens are. Pfizer puts its effective global tax rate at about 25 percent, but Americans for Tax Fairness claims that the actual rate is closer to 6 percent because much of Pfizer’s reported taxes are “deferred” and will probably never be paid.

There are also practical considerations. As multinationals’ sales move to international markets — about 60 percent of Pfizer’s revenues are outside the United States — the tendency is for jobs and investment to shift abroad as well. Still, many U.S. multinationals continue to coordinate their global operations from huge American headquarters. A 35 percent tax on repatriated foreign profits makes this juggling act harder by discouraging U.S. reinvestment and jobs.

To repeat: This is not a simple problem with an obvious solution. There is a genuine dilemma. If we maximize U.S. tax revenues in the short run, we may minimize the growth of American multinational firms in the United States in the long run, as firms favor expansion abroad.

Robert Samuelson is a columnist for The Washington Post.