* U.S. nonfarm payrolls rise 157,000 in January * Unemployment rate ticks up to 7.9 percent from 7.8 percent * Average hourly earnings rise four cents * Factory activity picks up in January, consumer morale up * Reports show sluggish economic recovery on track By Lucia Mutikani WASHINGTON, Feb 1 (Reuters) - U.S. employment grew modestly in January and job gains in the previous two months were larger than first reported, a counterpunch to recent data that suggested a tepid economic recovery had stalled at the end of last year. Adding to that optimism, separate reports on Friday showed factory activity hit a nine-month high in January as new orders rebounded, while car and truck sales surged and consumer confidence perked. The reports, which helped propel U.S. stock markets to their highest levels in more than five years, contrasted markedly with a government report earlier in the week that said the economy shrank unexpectedly in the final months of 2012, albeit for what most economists consider fleeting reasons. "It is clear that the economy has a forward momentum. Most pistons in the economic engine are firing, pointing to sustained economic growth," said Sung Won Sohn, an economics professor at California State University Channel Islands. Employers added 157,000 jobs last month and 127,000 more jobs were created in November and December than previously reported, the Labor Department said. Revisions performed each January to the prior year's data showed the labor market was healthier in 2012 than initially thought. While the unemployment rate rose 0.1 percentage point to 7.9 percent, the closely watched report showed an increase in hourly earnings and solid gains in construction and retail employment. Separately, the Institute for Supply Management said its index of national factory activity rose to 53.1 last month, the highest level since April, from 50.2 in December. A reading over 50 suggests expansion in the manufacturing sector. Activity was boosted by a bounce back in orders and inventories, as well as gains in employment. That offered hope manufacturing will continue to support the economy. The fairly upbeat reports sparked a rally on Wall Street, with the Dow Jones industrial average touching its highest level since mid-October 2007 and the Standard & Poor's index rising to a five-year high. The dollar rallied against the Japanese yen, while U.S. Treasury debt prices fell marginally. OUTPUT CONTRACTION SEEN AS A FLUKE A third report on Friday showed consumer sentiment on the rise even as households faced up to smaller paychecks as some federal taxes rose on Jan. 1. The economic growth picture was also brightened by reports showing several automakers, including General Motors Co and Ford Motor Co scored better-than-expected sales in January. The flurry of upbeat reports followed Wednesday's surprise contraction in gross domestic product in the fourth quarter, and as a group should ease worries that the United States was at risk for recession. GDP contracted at a 0.1 percent annual rate in the fourth quarter, largely because of a plunge in defense spending and slowdown in the pace of inventory accumulation. Superstorm Sandy, which hit the East Coast in late October, also weighed on output, a drag that should lift this quarter and could be replaced by new spending linked to rebuilding projects. "Underneath the surface, the fourth-quarter economy was really pretty good despite all the defense cuts. I think the private sector is leading the way," said Jack Ablin, chief investment officer at BMO Private Bank in Chicago. Still, the pace of job growth is too slow to absorb the roughly 22.7 million Americans who are either unemployed or working part-time while hoping for full-time work. Economists say employment gains in excess of 250,000 a month over a sustained period are needed to make a significant dent in the jobless rate. The Federal Reserve on Wednesday left in place a monthly $85 billion bond-buying stimulus plan, saying economic activity had "paused" in recent months. "The report keeps the Fed clearly in play to continue their easy monetary policy," said Eric Stein, portfolio manager at Eaton Vance Investment Managers in Boston. The Labor Department's annual benchmark revisions, going back to 2008, found the level of employment as of March 2012 was 422,000 higher than previously reported. That helped to push the average job growth for 2012 to 181,000 a month from 153,000 previously. MODEST JOB GROWTH Those steady gains, if sustained, could help the economy weather the headwinds of higher taxes and lower government spending. A payroll tax cut expired on Jan. 1 and automatic spending cuts will kick in in March unless Congress acts. January's job gains all came in the private sector. Hiring was broad-based, as it was in December, and declines in public sector employment were small. The goods-producing sector showed a third month of solid gains, and manufacturing employment advanced for a fourth straight month. Construction payrolls increased 28,000, adding to December's healthy 30,000 gain. Since hitting a low in January 2011, construction employment has grown by 296,000. Fully one-third of those gains have taken place in the last four months alone. Though the level of construction jobs remains about 2 million below its peak in 2006, further improvement is expected this year as the housing market recovery gains momentum. Housing is expected to support the economy this year, taking over the baton from manufacturing, as many Americans buy and start to furnish and renovate houses. Within the vast private services sector, retail jobs rose by a solid 32,600 jobs after rising 11,200 in December. Retail employment has now risen for seven straight months. Education and health payrolls added 25,000 jobs in January after employment grew by the most in 10 months in December. Government payrolls dropped by 9,000 last month after falling 6,000 in December. The pace of cuts is moderating as local government layoffs, outside education, subside. Average hourly earnings rose four cents last month and were up 2.1 percent in the 12 months through January. That followed a similar gain in December. "It may be that we are now getting to a point in the labor market where we are going to see an upward creep in average hourly earnings," said John Ryding, chief economist at RDQ Economics in New York. "That's going to be good for the consumer and they need help because they are being whacked by the payrolls tax increase." The length of the workweek for the average worker was steady at 34.4 hours for a third straight month.