Even China? Could the world’s economic juggernaut, having grown an average of 10 percent annually for three decades, face a slowdown or what for China would be a recession? Does it have a real estate “bubble” about to “pop”? What would be the global consequences? Treasury Secretary Timothy Geithner visits China and Japan this week. These questions form a backdrop. With Europe’s slump and America’s sluggish economy, a sizable Chinese slowdown would be bad news.

China inspires ambivalence. Its policies — especially its undervalued exchange rate — are skewed to give it an advantage on world markets. This has cost jobs in the United States, Europe and developing countries. Still, China is now such a powerful economic force that an abrupt slowdown would ripple beyond its borders. Trade would suffer. China’s protectionism might intensify to offset job loss. If surpluses of steel and other commodities were dumped on world markets, prices and production elsewhere would fall.

There are warning signs. Economist Nicholas Lardy of the Peterson Institute cites three. First, Europe’s slump has weakened China’s trade; Europe buys about a fifth of its exports. Second, housing is showing signs of a bubble and is deflating. Finally, China’s government will have a harder time deploying a stimulus than during the 2008-09 financial crisis. Government debt rose from 26 percent of gross domestic product in 2007 to 43 percent of GDP in 2010.

How all this affects China’s growth is controversial. “Most likely, China will have a soft landing,” says Justin Yifu Lin, the World Bank’s chief economist. “Growth goes to 8 percent or 8.5 percent.” That’s down from about 9 percent in 2011. Government debt is still low enough to permit ample stimulus, Lin thinks. Many forecasts agree.

But skepticism is mounting. The Japanese securities firm Nomura sees a one-in-three possibility of a “hard landing” — a drop in growth to 5 percent or less. To Americans, now experiencing annual economic growth around 2 percent, this may seem fabulous. But for China’s modernizing economy and huge labor force, a 5 percent growth rate would raise unemployment and social discontent. The adverse GDP swing would roughly equal the U.S. decline in the 2007-09 recession.

Housing may settle who’s right. China has vastly overinvested in housing, argues Lardy in a new book (“Sustaining China’s Economic Growth After the Global Financial Crisis”). The main reason, he says, is that financial policies prevent savers from realizing adequate returns on their money. The stock market is seen as rigged. Government regulations keep interest rates on bank deposits — the main outlet for savings — low. From 2004 to 2010, they were less than inflation. Frustrated savers invest in housing, where prices are not regulated.

The result seems a classic speculative bubble. People buy because they believe prices will go up; and prices go up because people buy. A 2010 survey found that 18 percent of Beijing households owned two or more properties; another 2010 survey of all cities found that 40 percent of purchases were for investment. Many units, Lardy reports, are vacant because rents in Beijing, Shanghai and other major cities are low.

Unfortunately, booms breed busts. Buyers ultimately recognize that rising prices reflect artificial demand. Purchases slow. Prices fall. New building declines. The process feeds on itself. With modest imbalances, the result is a correction. Otherwise, there’s a crash.

Which does China face? A popped real estate bubble could exert a big drag. Housing construction exceeds 10 percent of GDP. That’s historically high, says Lardy. At a similar stage of economic development, Taiwan’s housing investment was 4.3 percent of GDP. In the recent U.S. real estate boom, housing peaked at 6 percent of GDP. In China, housing stimulates much consumer spending (furniture, appliances) and accounts for 40 percent of steel production, notes Lardy. Land sales are also a big revenue source for local governments. All would suffer from a housing bust.

There are mitigating factors. Outside Beijing and Shanghai, it’s unclear that housing prices are “out of line with household income growth,” says economist Eswar Prasad of Cornell University. Chinese buyers also typically make large cash payments for their properties. Compared to United States, a housing bust is less likely to become a banking crisis as mortgages sour.

Whatever happens, China’s economic model is reaching its limits, as Lardy argues. It has relied on exports, promoted through the controlled exchange rate, and investment, including housing, subsidized by cheap credit. Meanwhile, Chinese savers have been punished by the low returns on deposits. This dampens their incomes and consumption spending. The trouble is that the global slowdown threatens exports and housing’s excesses threaten investment. Unless China can switch to stronger consumption spending, its economy will slow — or it will achieve growth by becoming even more predatory toward other countries.