A slight acceleration in Chinese economic growth at the end of last year is reinforcing the common narrative that China’s expansion is a threat to other nations, including the US.The bigger danger over the medium term, however, may be a slowdown in Chinese growth — which appears to be more likely than most US-based commentators seem to realise.China, after all, is fast approaching income levels associated with the “middle-income trap,” the point at which many other countries have moved from rapid to sluggish growth.This trap opens up for several reasons, including that economies expand disproportionately, at early stages of development, by shifting workers from agriculture to manufacturing. At some point, though, the gains from such shifts disappear, and new sources of growth are needed. China appears to be near this point.The middle-income trap typically occurs at two income levels: about $10,000 in per-capita income, and again at about $15,000.This is based on the most recent data, assembled by economists Barry Eichengreen of the University of California at Berkeley, Donghyun Park of the Asian Development Bank and Kwanho Shin of Korea University, and published this month by the National Bureau of Economic Research.Chinese income per capita amounted to slightly more than $7,000 in 2010. At an average growth rate of 7 percent a year from 2010 onward, China would hit the lower threshold by 2015. And as the authors note, “slowdowns are more likely in economies with high old age dependency ratios, high investment rates that may translate into low future returns on capital, and undervalued real exchange rates that provide a disincentive to move up the technology ladder.These patterns will presumably remind readers of current conditions and recent policies in China.”One thing that can help determine whether a country escapes the middle-income trap and continues to grow rapidly is its level of inequality, a recent study by researchers at the Chinese Academy of Sciences and Stanford University showed. More unequal societies, with less-inclusive institutions, have greater difficulty sustaining growth.This message is also at the heart of a more comprehensive analysis in “Why Nations Fail,” a recent book by economists Daron Acemoglu of the Massachusetts Institute of Technology and James Robinson of Harvard University.Comparing nations that have escaped the middle-income trap with those that have gotten stuck in it, the researchers from the Chinese Academy of Sciences and Stanford concluded that graduating countries had low inequality, with Gini coefficients of less than 40 percent. (The Gini coefficient equals zero if everyone has the same income, and 100 percent if one person has all the income and everyone else has none.)China’s Gini coefficient is about 50 percent and rising. “To be clear,” the researchers write, “we are not saying that there is an absolute causal link between inequality and stagnation in growth when a country reaches middle income.However, we are saying that if in the very near future China does not address income inequality and — even more so — human capital inequality, China will have to try to accomplish what no successful graduate has ever done since Second World War: make the transition from middle to high income with high levels of inequality.”What would be the consequences if China falls into the trap?According to Yasheng Huang, a professor of management at MIT, slower growth could destabilise China’s internal political economy. That, in turn, could prove to be the far larger risk for other nations.In a similar vein, China specialist Susan Shirk of the University of California at San Diego warns that it is China’s “internal fragility, not its growing strength, that presents the greatest danger.”And Aaron Friedberg, a professor of politics and international affairs at Princeton University, writes that a less prosperous China “may be a less effective competitor in certain respects, but it could also prove to be less predictable, more aggressive, and hence even more dangerous and difficult for the United States and its allies to manage.”Friedberg says weak leaders in China might be tempted to rally popular support by confronting other countries.Slower growth in China is not inevitable, but it is a greater — and more dangerous — possibility than many in the US may realise.(Peter Orszag is vice chairman of corporate and investment banking at Citigroup Inc. and a former director of the Office of Management and Budget in the Obama administration. The opinions expressed are his own.)