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Economists forecast that the index which gauges activity in the sector was positive this month, at 1.5, up from -1.5 in October. If that happens, it would be the first time since December 2014 that the index reads above zero.
The downturn has mostly been due to the oil-price crash, which hurt the energy producers.
"Job losses from the oil sector are having a negative effect on tax revenues in Texas," said the October release. "This puts pressure on government spending at the state and local level. High-paying manufacturing jobs are being replaced with lower-paying minimum wage service sector jobs."