As of 4:00 p.m. Eastern time in the US Thursday afternoon, or 7:00 a.m. Friday morning in Sydney, the S&P/Australian Securities Exchange 200 Index (ASX) was poised to open almost 1 percent higher on the last trading day of the week.

US equity indexes, including the S&P 500, the Dow Jones Industrial Average and the Nasdaq Composite, all closed up more than 1 percent Thursday, while the S&P/Toronto Stock Exchange Composite added about 0.6 percent.

Rallies abound because recent data–from North America as well as emerging Asia–suggest stabilization, at least, for countries critical to global growth, including the US, still the world’s biggest economy, and China, still the most important engine of expansion.

In the US, the revamped report from the research unit of payroll processor Automatic Data Processing Inc (NYSE: ADP) showed that 158,000 private-sector jobs were added in October, up from a revised 88,200 in September.

(The September revision from 162,000 resulted from a change that better aligns this survey’s approach with the methodologies employed by the monthly employment report proffered by the US Dept of Labor.)

It’s the biggest gain for the ADP Research Institute survey since February. Of the 158,000 jobs created, 144,000 came from services and 14,000 from goods production, of which 23,000 were construction jobs. But manufacturing jobs contracted by 8,000.

Because the data ADP Research Institute relies upon are derived from the actual payroll slips its parent processes, this should be an accurate measure of employment.

The website The Daily Jobs Update provided further reason for confidence in the Bureau of Labor Statistics’ monthly non-farm payroll report due out Friday morning, as its research found that “over the past three weeks, the year-over-year growth rate of federal withholding-tax collections was a respectable 4.72 percent.”

In addition, US manufacturing expanded more than forecast, consumer confidence rose to a four-year high, and fewer Americans filed claims for unemployment benefits.

The Institute for Supply Management’s factory index rose to a five-month high of 51.7 in October from 51.5, The Conference Board’s sentiment index increased to 72.2, the highest since February 2008, and  applications for jobless benefits fell by 9,000 to 363,000 in the week ended Oct. 27, the Labor Dept reported.

This is all positive for the US, of course, and for the global economy, which, for better or worse, still relies upon America and its consumers as a “market of first and last resort” for goods of all types.  A stabilizing and improving US labor market is good for US consumption, which in turn is good for the global exporters. These are the simple building blocks of a sustainable recovery.

As for the Middle Kingdom, the National Bureau of Statistics of China and the China Federation of Logistics and Purchasing reported Thursday that the official manufacturing Purchasing Managers Index (PMI) rose to 50.2 in October to 50.2, up from 49.8 in September.

PMI readings below 50 show contraction, while readings above 50 indicate expansion. October’s marked the first official PMI “expansion” reading since July.

China’s official Purchasing Managers’ Index rose to 50.2 in October, up from 49.8 in September, suggesting an increase in manufacturing activity.

Meanwhile, the “unofficial” PMI report from HSBC rose to 49.5 in October from 47.9 in September. This was better than the HSBC Flash China PMI of 49.1 that we discussed in this space last week.

The difference between the official and expanding PMI and the unofficial and still-contracting-but-getting-better HSBC PMI suggests that large manufacturers in China (read: state-owned enterprises, or SOEs) have started to expand their manufacturing activities, while medium and small enterprises (read: privately owned) continue to keep their powder dry.

The HSBC survey is based on data compiled from monthly replies to questionnaires sent to purchasing executives in over 430 manufacturing companies–but not SOEs. Both it and the official reading do, however, lend further evidence to the case that China is at least stabilizing.

The rise in the final HSBC PMI compared to the flash reading is encouraging because it confirms to some extent the more bullish tone established by the “expanding” official reading and it could suggest accelerating growth within the month.

As for implications for future policy, the ruling Chinese Communist Party will hold its 18th Congress meeting on Nov. 8 for the once-a-decade leadership handover. Membership of the Politburo Standing Committee is likely settled at this point, which leaves room Mainland leaders to re-focus on the economy.

Recent data provide some confirmation that China’s efforts to boost the economy, including the acceleration of large projects beginning last spring, have begun to take effect and likely argue against more significant stimulus. But further easing of reserve requirements by the Peoples Bank of China may be in the offing. Growth is not yet assured and officials, new to office, have no room for complacency.

Already half a decade ago, in 2007, China surpassed Japan as Australia’s largest trading partner. The Middle Kingdom is the largest destination for exports from the Land Down Under, and it’s the largest source of Australian imports. Overall Australia is China’s eighth-largest trading partner.

Despite the recent slowdown, China’s growth plan for 2011 through 2015 period and its increasingly surging demand for commodities such as iron ore and coal will continue to spur growth in Australia.

Although demand for minerals has softened in the short term, Chen Yuming, China’s Ambassador to Australia, recently asserted that “from a long-term perspective, it is unnecessary for us to worry about the Chinese economy and its demand or to hold any doubts about the closer bilateral economic and trade relations between China and Australia.”

“China will continue to be the growth engine of the Australian and global economies in the next five years,” said Mr. Chen in early October.