As Europe's crisis-struck elected leaders teeter and topple – with the Greek and Italian Prime Ministers headed for the exit today (but not quite gone), Spain's facing certain defeat in an election next week, and the heads of France and Germany too frightened of their electoral futures to speak up – it has fallen to the unelected ones to spell out the true state of affairs.

On Wednesday it was Christine Lagarde, the former French finance minister who heads the Washington-based International Monetary Fund, who said what the heads of state and government dare not express: That the continent is in deep trouble, and it could be pulling the world down into a long depression with it, if drastic measures aren't taken.

And, perhaps symbolically, she had to go halfway around the world to say it.

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"The global economy has entered a dangerous and uncertain phase," she told a Beijing audience in a major speech. Adverse feedback loops between the real economy and the financial sector have become prominent. And unemployment in the advanced economies remains unacceptably high."

She concluded: "If we do not act, and act together, we could enter a downward spiral of uncertainty, financial instability, and a collapse in global demand. Ultimately, we could face a lost decade of low growth and high unemployment."

Of course, her message was aimed at the developing world in general, and at China in particular, and she urged China to increase consumption, to raise the value of its currency and to invest abroad – messages that leaders have repeated for years.

But she was also addressing Europe and the West: This, she noted, is not just economic but political. If the recovery from growth doesn't do something about unemployment, then it could become a political crisis that could trigger worse economic outcomes. (There is little in the austerity plans battering Southern Europe that could build employment in the short run.)

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This starkly political message was being delivered by an unelected official. It joined messages delivered by European Union president Herman Van Rompuy, by European Commission president Jose Manuel Barroso, by European Central Bank chief Mario Draghi – as it appears that elected leaders still do not fully agree on a path forward.

With the fate of millions of hard-pressed voters being left to unelected officials, some of them on the other side of the world, it shouldn't be surprising that many Europeans are taking to the streets.