* World economic growth on divergent paths
* Steady growth in Asia, slow in U.S.; euro zone sinks
* Confidence slumps but economic activity improves
* Financial contagion remains a serious risk
WASHINGTON, Nov 7 (Reuters) - Europe is the largest trading partner for the United States and for China, and its financial system is deeply interwoven with world finance. Until euro-zone leaders draw a line under their debt crisis, risks of upheaval spreading through the global economy will remain high.
So far, the United States and China have shown a welcome resilience to turmoil from Europe, revealing a disconnect between sentiment and what is happening in the real economy.
The United States has seen a slow but steady improvement in its labor market. It has added 367,000 jobs in the private sector over the last three months, a slightly faster pace than the 301,000 gain in the May-July period and enough to lower the unemployment rate a notch to 9 percent, a six-month low.
Factory workers put in longer hours last month and incomes edged upward, which will support retail spending in the months ahead. Capital spending by U.S. businesses also is surging and productivity ticked upward in the third quarter as labor costs eased.
"I think it's a sign of a more robust economy than we've been giving it credit for. Some of the underlying fundamentals are fairly strong," said Karl Schamotta, senior strategist at Western Union Business Solutions. "It's not a fantastic recovery, but it's good given what's going on globally."
The improvements in the U.S. outlook come even as Europe slides into recession, political upheaval in Greece and Italy stymie their reform efforts and uncertainty remains over exactly how euro-zone leaders will structure a bailout plan.
Stock markets worldwide slumped again in the past week, adding to steep third-quarter losses. Investors found no comfort in a G20 summit where leaders of the world's largest economies delivered a statement of growth principles but failed to put to rest concerns over containing Europe's debt crisis.
Nervousness that financial contagion could spread from Europe through the banking system is likely to continue weighing on asset prices, feeding into already depressed business and consumer sentiment.
Usually when confidence is shaken for months on end, it undermines economic growth. The Reuters/University of Michigan sentiment survey is stuck at low levels and is expected to remain there, at 60.9, when the latest data is released on Friday.
Yet businesses continue investing and consumers have begun replacing goods. Nigel Gault, U.S. economist at IHS Global Insight, said pent-up demand among the better-off U.S. consumers, who have jobs and retain positive equity in their homes, is helping insulate the United States from damage from Europe.
Even if U.S. trade data due on Thursday shows exports to Europe slumping, Gault said it would shave only about six-tenths of a percentage point from overall U.S. growth -- not enough to tip an economy now growing at a 2 to 3 percent annual rate back into recession. September numbers are expected to show the U.S. trade deficit widened to $46.0 billion from $45.6 billion.
ASIA HOLDS UP
China likewise would not necessarily be doomed if Europe slips into a recession, although it is certainly feeling the pinch.
A government report last week showed the manufacturing sector weakened in October and new export orders contracted. Data on Thursday is expected to show October exports rose 16.5 percent from a year earlier, which would be somewhat slower than September's 17.1 percent rise.
South Korea provided an early glimpse into how Asia's exporters fared in October. Its shipments to Europe tumbled 20 percent from a year earlier in the Oct. 1-20 period.
The last time China's European exports recorded a year-on-year decline was in February, which is typically a slow month because of the Chinese New Year celebration.
But trade is not China's sole economic growth engine. In fact, exports subtracted from China's gross domestic product over the first three quarters of 2011.
"China is modernizing. Forty percent of China's GDP growth is from consumption and that will increase; 40 percent is from investment in plant and equipment. It is becoming a self-sustaining process and China can sell right through this," said Carl Weinberg, chief economist at High Frequency Economics.
Additionally, China, unlike most advanced economies, has room to ramp up government spending or ease credit conditions if its outlook worsens. Inflation pressures are easing, which should give the People's Bank of China more maneuvering room.
Data on Wednesday is expected to show the consumer price index rose 5.5 percent in October from a year earlier, moderating from September's 6.1 percent annual increase.
That would still leave inflation well above Beijing's 4 percent target, which suggests interest rate cuts are unlikely. But China's leaders have been dropping hints that they will selectively ease credit conditions, particularly for small- and mid-sized companies that have had trouble borrowing.
Absent the wild card of a bank failure in Europe that unleashes fresh financial contagion, it points to a world economy on divergent paths: Slow growth in the United States, steady growth in Asia and Europe sinking.