American companies have begun to build more R&D facilities in emerging countries, both in response to local government pressure and to be closer to customers. General Electric, which already has research centres in China, India and Germany, announced last year that it would put one in Brazil. This, it says, has not come at America's expense: GE plans to add two more research centres in the United States to the one it runs in upstate New York. Mark Little, the head of GE Global Research, the company's in-house research division, says putting scientists and researchers into other countries enables GE to come up with products it would not have thought of before. For rural Chinese hospitals, more used to doing things manually than in America and Europe, GE designed less-automated MRI machines.

Adam Segal, author of "Advantage: How American Innovation can Overcome the Asian Challenge", says Asia's threat to American technological leadership is overstated. China's research output is soaring, but much of it is poor-quality or based on plagiarism. Chinese companies are seizing market share in solar panels and wind turbines largely because of low manufacturing wages, says Mr Segal: "They have made no major breakthroughs in any of the underlying technologies." R&D spending in India is minuscule.

The real problem for America is not its innovative capacity, but the fact that its benefits go to relatively few. This is illustrated by a recent paper by Michael Spence and Sandile Hlatshwayo, both of New York University. They divided jobs among tradable and non-tradable sectors. Tradable sectors include manufacturing, commodities and services such as finance and engineering that compete globally. Value-added per person, a proxy for productivity, rose sharply in this sector, but the number of jobs actually declined between 2000 and 2008. The opposite was true in the non-tradable services such as government and health care. There real value-added rose only sluggishly, but employment expanded significantly. Behind this, says Mr Spence, is the trend of American multinationals to keep the highest value-added activities at home while shifting lower value-added activities, such as manufacturing, abroad.

Qualcomm, a developer of mobile-phone chips and technology based in San Diego, earns roughly 40% of its revenue from licensing and royalty fees for technology developed primarily in America, where three-quarters of its employees work. Last year it spent $2.5 billion, or roughly 20% of revenue, on R&D for such projects as developing Mirasol, an easy-to-read, energy-efficient phone display. Paul Jacobs, the company's boss, complains about high corporate-tax rates and the difficulty of getting immigrant visas for foreign-born engineers and scientists, but maintains that America is not about to be superseded as a centre for innovation. In California Qualcomm has access to the best college graduates and a pool of ideas and recruits generated by a nexus of established and start-up companies.

But Qualcomm has done no manufacturing of its own since selling its last handset plant in 2000. Although Mirasol was developed in America, the displays will be made in Taiwan, which has the skills, the suppliers and the economies of scale.

These findings present a dilemma for America's policymakers. Raising federal R&D spending and easing immigration for foreign-born PhDs would boost innovation and company successes, but would not produce many jobs. Mr Spence and Mr Atkinson would like to see government incentives aimed at strategic manufacturing sectors. But such policies have a poor track record. And in any case Congress is in no mood to pay for them, no matter what Mr Obama says.