Is the American Century Over? By Joseph Nye. Polity Press; 152 pages; $12.95 and £9.99.

“AMERICANS have a long history of worrying about their decline,” notes Joseph Nye. Puritans in 17th-century Massachusetts lamented a fall from earlier virtue. The Founding Fathers fretted that the republic they had created might dissipate like ancient Rome. Modern scholars are a gloomy lot, too. Michael Lind of the New America Foundation, a think-tank, has written that, with America’s foreign policy in a state of collapse, its economy ailing and its democracy broken, the American century ended last year.

Mr Nye, a veteran observer of global affairs, is more optimistic. He expects that America will still play the central role in the global balance of power in the 2040s. What, after all, is the alternative?

Europe is hardly a plausible challenger. Though its economy and population are larger than America’s, the old continent is stagnating. In 1900 a quarter of the world’s people were European; by 2060 that figure could be just 6%, and a third of them will be over 65.

By 2025 India will be the most populous nation on Earth. It has copious “soft power”—a term Mr Nye coined—in its diaspora and popular culture. But only 63% of Indians are literate, and none of its universities is in the global top 100. India could only eclipse America if it were to form an anti-American alliance with China, reckons Mr Nye, but that is unlikely: Indians are well-disposed towards Washington and highly suspicious of Beijing.

China is the likeliest contender to be the next hyperpower: its army is the world’s largest and its economy will soon be. (In purchasing-power-parity terms, it already is.) But it will be decades before China is as rich or technologically sophisticated as America; indeed, it may never be. By 2030 China will have more elderly dependants than children, which will sap its vitality. It has yet to figure out how to change governments peacefully. And its soft power is feeble for a country of its size. It has few real friends or allies, unless you count North Korea and Zimbabwe.

Hu Jintao, the previous president, tried to increase China’s soft power by setting up “Confucius Institutes” to teach its language and culture. Yet such a strategy is unlikely to win hearts in, say, Manila, when China is bullying the Philippines over islands in the South China Sea. The staging of the 2008 Olympics in Beijing was a soft-power success, but was undercut by the jailing of Liu Xiaobo, a pro-democracy activist, and the resulting empty chair at the ceremony to award him the Nobel peace prize. “Marketing experts call this ‘stepping on your own message’,” says Mr Nye.

Perhaps the greatest threats to American pre-eminence are domestic. As pundits often point out, young American workers score terribly on cross-country comparisons of numeracy, and Americans are disillusioned with their government. Yet even here, Mr Nye sees hope: 82% of Americans say America is the best place in the world to live. It remains a magnet for foreign talent, and could be an even stronger one if it sorted out its immigration policy. A “long Jeffersonian tradition” says that one “should not worry too much about the level of confidence in government”. Americans may grumble constantly about Washington, but the Internal Revenue Service detects no increase in cheating on taxes, and the proportion of Americans who bother to vote has risen since 2000.

“Leadership is not the same as domination,” says Mr Nye; influence matters more than military might. This short, well-argued book offers a powerful rebuttal to America’s premature obituarists.