* Fourth-quarter gain in output biggest in 3-1/2 years
* Factory production beats forecasts in December
* Weather hits housing starts, drop smaller than expected
* Housing permits slip on decline in single-family units
WASHINGTON, Jan 17 (Reuters) - U.S. industrial output rose at its fastest clip in 3-1/2 years in the fourth quarter as factory activity closed out the year on a strong note, a sign of the economy's brightening prospects.
Manufacturing production rose a stronger-than-expected 0.4 percent in December after an out-sized 1.0 percent increase the prior month, a Federal Reserve report on Friday showed.
That helped push overall output at the nation's factories, mines and utilities up 0.3 percent last month. Economists polled by Reuters had expected factory output to rise 0.3 percent, while the gain in overall industrial production matched forecasts.
"It adds to the evidence that the fourth quarter was a good one," Gus Faucher, a senior economist at PNC Financial Services in Pittsburgh. "It also provides further evidence that the slowdown in employment growth in December was a fluke."
For the fourth quarter as a whole, industrial production advanced at a 6.8 percent pace, the largest quarterly increase since the second quarter of 2010.
Fourth-quarter growth is shaping up to be far stronger than economists had anticipated, with estimates ranging as high as a 3.9 percent annual rate. But that does not seem to have inspired U.S. households.
A separate report showed the Thomson Reuters/University of Michigan's preliminary reading on the overall index on consumer sentiment slipped to 80.4 early this month from 82.5 in December.
Job growth slowed sharply in December, largely blamed on cold weather that blanketed large parts of the country. At the same time, incomes barely grew, sapping household morale.
Frigid temperatures also helped to put a dent in homebuilding last month. Groundbreaking for new homes dropped 9.8 percent to a seasonally adjusted annual rate of 999,000-unit pace in December, another report from the Commerce Department showed.
It was the largest percentage decline since April, but housing starts were coming off a six-year high reached in November and the decline was smaller than economists had expected. For all of 2013, starts increased 18.3 percent to an average of 923,400-units, the highest since 2007.
PAYBACK FOR STRONG NOVEMBER
"We suspect weather played a large role in the soft headline number and some of the weakness could be payback for the strong November print," said Mark Vitner, a senior economist at Wells Fargo Securities in Charlotte, North Carolina.
"With weather and the seasonal adjustment process likely pulling the headline lower, we could see another soft print in January. Even if we see two successive downbeat months it does not mean the housing recovery has faltered."
Groundbreaking for single-family homes, the largest segment of the market, fell 7.0 percent to a 667,000-unit pace in December. Starts for the volatile multi-family homes segment declined 14.9 percent to a 332,000-unit rate.
Starts in the Midwest, which experienced unseasonably colder weather, tumbled 33.5 percent, suggesting the weather might have weighed on home building in the region last month.
Residential construction has been on the rise after a brief lull last year in the wake of a run-up in mortgage rates.
Increasing household formation and a tight supply of houses has been boosting home building, which in turn is supporting the labor market.
Permits to build homes fell 3.0 percent in December to a 986,000-unit pace. It was the second straight month of declines. They were weighed down by a 4.8 percent drop in permits for single-family homes. Multifamily sector permits were flat.
"In all likelihood, single-family permits will also shake off their torpor, as inventories remain low and household formation continues to generate demand for housing," said Guy Berger, an economist at RBS in Stamford, Connecticut.
For all of 2013, permits increased 17.5 percent to an average of 974,700-units, also the highest since 2007.
The report on industrial output showed that industry employed 79.2 percent of its capacity in December - the most since June 2008. Still, capacity use remained 1 percentage point below its long-run average, the Fed said.