The Federal Reserve pushed back against the narrative that the U.S. has a worker shortage, saying Friday in a report to Congress that "it's difficult to see" signs of labor constraints weighing on businesses.

The Fed Board of Governors' monetary policy report acknowledges that "it is possible that labor shortages have arisen in certain pockets of the economy," a complaint voiced recently by businesses.

"However, even at the industry level it is difficult to see much evidence of emerging supply constraints," the report concludes.

If there were a worker shortage, the report noted, the industries with low unemployment would be seeing larger wage gains, as employers bid to find people to fill positions. That isn't happening in even the hottest sectors, such as leisure and hospitality.

Also, the report noted, monthly job gains have been much higher than would be expected if there were a worker shortage.

The commentary on the possibility of a worker shortage came in a special note in the Fed's semi-annual monetary policy report to Congress. Newly installed Chairman Jerome Powell is set to testify on the report next week.

In the note, Fed officials wrestled with the question of whether the labor market is truly "tight." With the unemployment rate the lowest it's been since the turn of the century, at 4.1 percent, some analysts have suggested that the jobless rate can't go any lower without the Fed risking higher inflation. The Fed has suggested that it will raise interest rates to prevent the possibility of spiking inflation, but will do so slowly.

In other parts of its report, the Fed suggested that the country appears to be "near or a little beyond full employment," even though the country does not have worker shortages.

The special note considered the possibility that the unemployment rate may not fully reflect the state of the jobs market, as there may be people forced into part-time work or are outside of the official labor force — that is, not actively looking for jobs. But even judged by those metrics, the note concludes, the labor market is relatively tight.