WASHINGTON (Reuters) -U.S. firms were shedding more than 11,000 jobs a week through late October, payroll processor ADP said on Tuesday in its latest real-time estimate of job market trends.

Though an ADP report last week estimated the U.S. overall added 42,000 jobs in October versus the month before, the new estimates show how hiring trends are evolving on a week-to-week basis - in this case pointing to further weakening in a labor market being closely monitored by Federal Reserve policymakers.

"The labor market struggled to produce jobs consistently during the second half of the month," said Nela Richardson, ADP's chief economist. ADP recently began issuing weekly payroll estimates as a way to augment its monthly jobs report.

The data could reinforce some Fed policymakers' arguments that developing job market weakness warrants further reductions in the U.S. central bank's benchmark interest rate. The Fed reduced its policy rate by a quarter of a percentage point at each of its last two meetings. Investors expect it to deliver another quarter-percentage-point cut at its December 9-10 meeting.

ADP's payroll data is among several private-sector sources that policymakers have referred to as an alternative - if not a full substitute - to the official statistics that have been missing during the current U.S. government shutdown.

If the shutdown ends this week, a possibility after the U.S. Senate's passage of a temporary funding bill, Fed policymakers should see the flow of data from the Bureau of Labor Statistics resume in time for their next meeting, even if some reports are still missing.