WASHINGTON (Reuters) -The U.S. unemployment rate remained stable at around 4.3% in October according to a Chicago Federal Reserve bank economic model that uses private data to estimate the jobless rate even in the absence of government statistics that have been unavailable since the start of an ongoing federal shutdown.

The last official unemployment report was for August and also showed the jobless rate at 4.3%. A Chicago Fed estimate for September put the number, unrounded, at 4.34%, and at an unrounded 4.35% for August.

The Chicago Fed noted that the government shutdown would over time make its own model less reliable since it uses the official unemployment rate as a baseline, then estimates the change in the jobless rate each month using a variety of private-sector sources that line up well with different aspects of the job market. Since the September unemployment rate was unavailable, the Chicago Fed said it used its own prior "real time" estimate as the baseline - a possible source of error that could compound the longer the shutdown lasts.

Over 1 to 3 months, however, Chicago Fed economists said the impact was "likely to be modest." 

The October estimate is consistent with other data, such as a slight rise in unemployment claims still being reported by state unemployment agencies, suggesting the U.S. job market has cooled but is not collapsing. 

The Fed meets this week and is expected to reduce the benchmark interest rate by a quarter of a percentage point in part to insure against a sharp rise in unemployment. 

(Editing by Toby Chopra and Chizu Nomiyama )