Very few Americans have enjoyed steadily rising pay beyond inflation over the last couple of decades, a shift from prior years in which the working and middle classes enjoyed broad-based wage gains as the economy expanded.

Why it matters: Now, executives of big U.S. companies suggest that the days of most people getting a pay raise are over, and that they also plan to reduce their work forces further.

Quick take: This was rare, candid and bracing talk from executives atop corporate America, made at a conference Thursday at the Dallas Fed. The message is that Americans should stop waiting for across-the-board pay hikes coinciding with higher corporate profit; to cash in, workers will need to shift to higher-skilled jobs that command more income.

Troy Taylor, CEO of the Coke franchise for Florida, said he is currently adding employees with the idea of later reducing the staff over time "as we invest in automation." Those being hired: technically-skilled people. "It's highly technical just being a driver," he said.

The moderator asked the panel whether there would be broad-based wage gains again. "It's just not going to happen," Taylor said. The gains would go mostly to technically-skilled employees, he said. As for a general raise? "Absolutely not in my business," he said.

whether there would be broad-based wage gains again. "It's just not going to happen," Taylor said. The gains would go mostly to technically-skilled employees, he said. As for a general raise? "Absolutely not in my business," he said. John Stephens, chief financial officer at AT&T, said 20% of the company's employees are call-center workers. He said he doesn't need that many. In addition, he added, "I don't need that many guys to install coaxial cables."

Because of the changes coming, AT&T is pushing employees to take nano-degree programs to prepare them for other jobs — either at AT&T or elsewhere.