(Reuters) - Employment improved and housing prices rose in most major U.S. metropolitan areas in the final quarter of 2012, but output sputtered, according to a report released on Thursday by the Brookings Institution.

The study found that among the 100 largest areas, 78 posted job gains during the fourth quarter, while job growth rates accelerated in 57 metropolitan areas.

Still, employment levels returned to where they were before the 2007-2009 recession in only 14 metropolitan areas. Six of those areas were in Texas: Austin, Dallas, El Paso, Houston, McAllen and San Antonio.

Most metropolitan areas started 2013 with brighter job pictures than the year before. In January, 227 out of all 372 metropolitan areas in the country had unemployment rates lower than January 2012, and the rates were unchanged in 21 areas, according to the Bureau of Labor Statistics. Meanwhile, 306 metropolitan areas gained jobs over the year.

Home prices have been rising in recent months and were up an average of 0.3 percent across the country during the fourth quarter when adjusted for inflation, according to the report from Brookings, an independent research group based in Washington, D.C. In major metropolitan areas, which typically encompass at least one large city and its surrounding suburbs, the average rise was more than double that - at 0.8 percent.

Altogether, home prices increased in 85 out of the largest 100 areas during the fourth quarter.

Brookings found the strongest improvements were in the areas that suffered the most economic damage from the housing crisis: Nevada's Las Vegas, Arizona's Phoenix, Florida's Cape Coral, California's Stockton, and Idaho's Boise. There, the increases were all around 3 percent or more.

Rising home prices are seen as an indicator of the economic recovery gaining momentum.

For local governments that use property taxes as their chief sources of revenue, the upswing will curb the major budget cuts that cities and counties have made in recent years.

Still, when it comes to economic activity, not much has changed for the typical metropolitan area. In a little less than half - 45 - output grew during the quarter, while in 55 metro areas, or slightly more than half of them, output fell.

"This marked a surprising decline in the rate of output growth from prior quarters, due overall to reduced inventories and defense spending," Brookings said.