WASHINGTON — President Obama has declared the economic crisis over — and for the United States, maybe it seems that way. But most other countries, not so much. Their recoveries are faltering. The obvious question is whether the global weakness will infect the U.S. expansion. This is a crucial footnote to Obama’s optimism.

Two major reports — one from the World Bank, the other from its sister organization, the International Monetary Fund — recently lowered estimates for global economic growth in 2015. Said the IMF: “The United States is the only major economy for which growth projections have been raised.”

Consider the bleak landscape. Japan is in recession. Unemployment in the eurozone (the 19 countries using the euro) is a scary 11.5 percent. Unhappily, the IMF expects only meager eurozone growth of 1.2 percent in 2015. Even this could be optimistic if the Greek election triggers a new debt crisis. Assuming the IMF forecast is reached, growth would still be a third of the predicted U.S. rate (3.6 percent).

Led by China, so-called “emerging-market countries” have disappointed. They were expected to replace the United States as the world economy’s main engine of growth. The theory was simple. The material wants of their burgeoning middle classes could be met with known products and technologies. So: Their appetite for raw materials (iron ore, copper, corn) and advanced technology goods would stimulate the broader global economy.

It hasn’t worked as imagined. From 2005 to 2012, emerging-market economies averaged annual growth of 6.5 percent. Now, the IMF projects their growth in 2015 at 4.3 percent. Until recently, China’s growth averaged about 10 percent a year. In 2014, it was 7.4 percent, and the IMF predicts 6.3 percent for 2016. It might go lower.

What spoiled the theory? For one, it ignored the reality that many emerging-market countries — including China — depended on export-led economic growth. This meant the crisis hit them hard. “When you rely on trade, you die when there’s no demand,” says World Bank economist Ayhan Kose. And demand from the United States and Europe slumped badly. Global trade is now growing at about half its pre-crisis rate, says the World Bank.

For a while, the emerging-market slowdown was obscured because many countries took action that initially offset lost exports. In 2008, China announced a 4 trillion yuan stimulus, which — adjusted for the size of its economy — was roughly twice President Obama’s stimulus.

Although this temporarily sustained growth, it left a legacy of high debt — much of the plan was financed by loans to companies and localities — and dubious investment projects. There are “unsold apartment buildings, steel mills running at 50 percent of capacity, new airports in minor cities and underutilized highways,” says economist David Dollar, the U.S. Treasury’s chief representative in China from 2009 to 2013. China’s government and private debts have zoomed from 156 percent of gross domestic product (a measure of its economy) at the end of 2007 to 251 percent in mid-2014, reports the World Bank.

All in all, stagnation advances. Because China is the largest buyer of raw materials, its slowdown has abetted surpluses of many commodities — not just oil but also grains and metals. Prices have declined. Although this helps consumers, it hurts Brazil, Australia and other producers, especially in Latin America. Low prices will deter new investment. Meanwhile, Europe and Japan hope that their central banks’ bond-buying (so-called “quantitative easing”) will revive their floundering economies.

Think now how this might imperil the U.S. recovery. One channel is weaker exports; other countries buy less of what we make. Another is reduced profits from foreign operations of American multinationals. These represent about a third of total U.S. corporate profits. The danger is indirect. Weaker profits might depress stocks, leading to less consumer spending because shareholders feel poorer.

A stronger dollar compounds these threats: In the second half of 2014, the U.S. dollar rose 10 percent against major currencies. This makes our exports more expensive and our imports cheaper. It dampens foreign profits, because profits are reported in dollars and profits earned in foreign currencies (euros, yen) translate into fewer dollars. Finally, a stronger dollar makes it costlier for foreigners to visit the United States — and cheaper for Americans to go abroad.

None of this is conclusive; it’s merely suggestive. The consensus seems to be that these foreign vulnerabilities won’t derail the American recovery. “Exports are only 13 percent of GDP,” says the consulting firm IHS. “Strong domestic demand” will protect a faster recovery. Perhaps the healthier U.S. recovery will even spread abroad.

But we should hold the happy talk. The economic crisis is worldwide. It won’t be “over” while its near universality persists. Until this changes, we’re exposed to foreign surprises, for good and ill.

Robert Samuelson is a columnist for The Washington Post.