[Obama] is the rare president who seems at times to resent indispensability, rather than embrace it. “Free riders aggravate me,” he told me. Recently, Obama warned that Great Britain would no longer be able to claim a “special relationship” with the United States if it did not commit to spending at least 2 percent of its GDP on defense. “You have to pay your fair share,” Obama told David Cameron, who subsequently met the 2 percent threshold.

The similarity of complaints was close enough for Bloomberg View’s Eli Lake to dub it “The Obama-Trump Doctrine.” But this lament is hardly unique to those two men. Andrew Bacevich told the Post’s Glenn Kessler, “Are Europeans free-riders when it comes to security, counting on the U.S. to pick up the slack? Yes, without a doubt.” Nor is this complaint all that new. Indeed, as one Forbes columnist noted last week, “Our post-war alliances are riddled with American whining about how our allies are slacking off.”

As these complaints have been voiced, one chart has inevitably been used to explain the problem. This variant by DefenseOne’s Kedar Pavgi will do the job:

As the chart shows, the United States spends more than 3.5 percent of GDP on defense. Even though NATO members have pledged to spend 2 percent of GDP on defense, only four non-U.S. countries met that target last year.

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So this looks bad for European members of NATO. But before the “free rider” thing calcifies into an accepted story told around the foreign policy campfire, it’s worth considering two small complications to this narrative.

The first complication is that European defense spending is starting to turn around. Indeed, in 2015, U.S. defense spending fell far faster than European defense spending. As Bloomberg View’s Toby Harshaw noted, numerous European countries are ramping up their defense spending in response to Vladimir Putin’s Russia. French diplomat Simond de Galbert wrote in the Atlantic last month: “Although it is very unlikely that all European NATO countries will soon be spending as much as 2 percent of their GDP on defense, as required by NATO, the main European powers are at the threshold (like the United Kingdom and Poland), closely approaching it (France), or taking steps to increase resources allocated to defense (Germany).”

The second and more significant complication is that while the United States does bear a disproportionate cost of military spending, our European allies have borne a disproportionate burden on other aspects of the Western alliance. Consider, for example, the cost of imposing economic sanctions. As de Galbert notes:

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Washington pushed Europeans to put harsh sanctions on Iran, but the United States itself had little leverage on the Iranian economy, having had virtually no trade with the country since 1979. In many ways, it was the European choice to back sanctions that made them so effective —and it was the Europeans who bore many of the costs.

The Iran sanctions are insignificant compared to the joint U.S.-E.U. sanctions against Russia, however. Prior to the imposition of sanctions, European trade with Russia was 10 times the level of American trade. Estimates of the costs of the sanctions to Europe’s economy have ranged as high as $700 billion and 2 million lost jobs. Those estimates are on the very high end; more sober estimates up the cost at roughly 0.4 percent of GDP in 2015. Still, that is a damn sight more than the United States will suffer from sanctions. Oh, and by the way, if you think that Europe paying a greater price for sanctioning Russia is a new phenomenon, go read Michael Mastanduno’s “Economic Containment” for some historical background. Spoiler alert: Europe paid a higher price to enforce the Cold War strategic embargo too.

Despite the cost, E.U. members, particularly Germany, have continued to support the policy.

In the Atlantic, Stephen Sestanovich notes that the Obama administration has done a little free riding of its own:

There is, as Goldberg tells us, just about no foreign leader the president respects more than Angela Merkel. Nor is there one who has done more to help him. (Were it not for Merkel’s support on sanctions against Russia, Obama’s Ukraine policy would barely exist.) No European leader has tried harder to articulate a tolerant, Obama-style approach to the Syrian refugee crisis. Nor has anyone paid a greater price for doing so. Merkel faces both the possible end of her political career and the possible collapse of the European Union. White House aides acknowledge the problem. “If Europe has a 2016 anything like 2015,” one of them has told me, “there won’t be much of Europe left to talk about.” So what has the leader whom Obama respects most, who has done the most for him, who has set out a vision most like his, and who has had the most trouble implementing it, gotten from him in return? The U.S. has admitted a trickle of refugees, NATO-member navies have begun to regulate the migrant flow in Greek and Turkish waters, the Pentagon continues to study the problem of a “safe zone” in Syria — and the White House continues to express doubts about it. Measured against the “existential” crisis facing America’s most important allies, this isn’t much.