The software that entrepreneur Terence Swee ships around the world was developed in Singapore, but you would never know it.

His company, Muvee Technologies, which creates software that automatically edits videos to the beat of a music soundtrack, is vague about the exact address of its headquarters. It uses American English in its ads and holds sales on Thanksgiving rather than Chinese New Year. Its office is retrofitted with a 1950s-style American diner. “We don’t explicitly state that we are from Singapore,” he says. “The world is still more comfortable buying software from the USA.”

Singapore is known for being hospitable to innovation. But underneath the success lurks an identity crisis: it has never had a blockbuster invention or technology it can call its own.

That’s a stain on what’s otherwise a Cinderella story of how a small island—less than half the size of London—transformed itself from a colonial backwater into one of the world’s most affluent, most fully wired places in a single generation. That rise is attributed to luck and smart planning by a government that has plowed billions into infrastructure, R&D subsidies, and tax breaks to lure multinational corporations.

Yet Singapore’s own ideas and startup companies are struggling to define themselves in the shadow of big names that have set up shop on its shores, such as Google, Hewlett-Packard, and Procter & Gamble. There’s no company that jumps out as a Singaporean success in the same way that South Korea’s Samsung or Japan’s Sony does. Despite heavy investment in biomedical research, there’s still no Nobel Prize, either. The country’s most famous entrepreneur may actually be Eduardo Saverin, the Facebook cofounder who renounced his U.S. citizenship and took up residence in a snazzy Singapore penthouse.

That there’s no distinctly Singaporean brand of innovation looks to some like an unintended consequence of too much government stimulation. Business leaders now publicly wonder whether Singapore’s top-down approach, its obsession with standardized tests, and its law-and-order ways (bubble-gum sales are banned) are leading to a society that can produce no truly significant new ideas.

Such cultural clichés, however, fail to touch on the most important of Singapore’s economic realities: the country’s tiny size. That, say entrepreneurs and government officials, means Singapore must cater to global standards and markets or doom its businesses to irrelevance. In other words, the very same pragmatism that put Singapore on the international map may now explain why it doesn’t stand out.

“It makes no sense to attempt a Yelp or a GrubHub for Singapore—the scale is just too small,” says Darius Cheung, a 31-year-old who sold a mobile security company, tenCube, to McAfee in 2010. “So startups are forced to choose other kinds of innovation that can achieve larger scale across borders, such as something that is truly culture- and location-agnostic.” Cheung’s most recent venture, an English-language phone app called BillPin, lets friends track shared expenses like rent bills and movie tickets. It’s the kind of thing that could get big, but only if it tops similar apps being written in San Francisco, New York, or London.

Singapore’s economic takeoff began in the 1960s, after the country gained independence. Already attractive for its purposeful multiculturalism and open-door economic policies, it added government incentives for technology enterprises, including in aerospace and biomedical research. The government has designated $12.9 billion to fund R&D from 2010 through 2015, or about $2,500 for each of its five million people.

“Whenever one of my corporate clients around the world is thinking about establishing a new research hub in Asia, Singapore is always on the shortlist,” says Andrew Taylor, a managing director at the Boston Consulting Group. In a 2010 study Taylor coauthored, he ranked it as the most “innovation friendly” country in the world, ahead of the United States and Israel. Scores of multinational companies now do R&D in Singapore.

But in terms of actual innovation—output of ideas—the record is more mixed. While Singapore has become influential in some scientific fields and the number of patents has grown greatly, much of that activity is not driven by Singaporean companies. Foreign companies such as Hewlett-Packard and Micron Technology account for 15 of the top 20 patent winners in Singapore, and for over half of all intellectual-property claims, according to the National University of Singapore. That is much higher than the proportion seen in Japan, Korea, or Taiwan.

The presence of multinationals has also acted as a disincentive to would-be entrepreneurs, who may find it hard to turn down a high-status office job with an American-sized salary. Swee, the video editing entrepreneur, admits he’s seen as a bit unusual for politely refusing the overtures of headhunters. “There are so many people who could have formed the next generation of tech innovators but decided to take on managerial jobs in regional sales offices of the multinational corporations,” he says.

Singapore has lately been trying to give more encouragement to its nascent entrepreneurial class. As part of a plan to double the number of local companies with at least $80 million in revenue by 2020, aiming for a total of 1,000, it is offering a mix of direct financing, grants, and state-run venture capital. “Singapore is a small country,” Teo Ser Luck, minister of state for trade and industry, said in a speech this August, delivered in a fashionable mix of Mandarin and English. He thinks smaller companies “must think global at an early stage if they want to grow.” Similarly, the government’s current priority for biomedical startups is to fund those that have “scalability for the global market,” an agency website says.

Some say that in setting global goals Singapore is missing the chance to formulate its own distinctive type of innovation—one aimed more narrowly, perhaps within Asia. “The key to developing innovation is plugging into the ecosystem and networks around us, but we haven’t fully exploited our natural connections to the regional backyard,” says Wong Poh Kam, director of the National University of Singapore Entrepreneurship Center.

The government has typically placed bets with name-brand U.S. universities. For example, Singapore-Stanford Biodesign, a collaboration with Stanford University, trains innovators in medical technology. But Singapore hasn’t formed such partnerships with Universitas Indonesia or the University of the Philippines. Those untapped, underdeveloped markets could be the real opportunity for disruptive technology, Wong thinks. He blames the oversight on the “cultural attitudes of strategic planners,” which he says “are colored by where they have been schooled—namely, places such as Harvard and MIT.”

For Singapore’s technology entrepreneurs, at least, the lack of a blockbuster Singaporean invention or product isn’t any reason not to keep thinking globally. Just the opposite, says Swee, whose company now has 60 employees. “If you cannot compete with the best in the world,” he says, “you shouldn’t exist.”