Parts of the oil-rich economy in Texas are showing signs of slowing down, but still outperforming the rest of the nation, the Dallas Federal Reserve said.

A survey from the Texas Alliance of Energy Producers said the number of jobs lost in the state as a result of the depressed oil economy may be worse than initially forecast. Lower crude oil prices have hurt the corporate profits for many companies with headquarters in Texas. When the downturn began in mid-2014, the alliance expected no more than 50,000 jobs would be lost in the state, but its latest forecast gave a conservative estimate of around 56,000.

A survey from the Dallas Federal Reserve found mortgage debt in the district declined about 1 percent year-on-year, while auto loan debt burdens increased. Aggregate consumer debt, a metric used to indicate consumption rather than investment, climbed 5.7 percent year-on-year.

"While the expansion was less robust than during the prior year, it nonetheless exceeded the national rate of 1.8 percent," the bank said.

In its so-called Beige Book, the federal reserve said job cuts in the energy sector were spilling over to white-collar employment. New home construction, meanwhile, was restrained by labor shortages, mostly in the Dallas-Forth Worth area.

Wages for workers in the state are flat and demand for workers in the oilfield is depressed.

"At current pricing and demand, the financial positions of many energy firms continued to deteriorate, particularly smaller firms," the bank said.

A drilling productivity report from the U.S. Energy Information Administration finds the Permian shale basin in Texas is one of the few expected to report increased production under current market conditions. From November to December, the Eagle Ford shale basin in Texas is expected to decline the most in terms of overall barrels, with about 78,000 barrels per day disappearing by December.