The job market appears to have softened in recent months. Fiscal austerity has begun to take a toll on job creation. —ADP report

The Bureau of Labor Statistics announced on Thursday that it will not be releasing a jobs report on Friday due to the government shutdown. In the meantime, economists have been looking to other indicators that are providing mixed messages about the health of the American economy.

The jobs report is usually released the first Friday of every month. It is an important economic indicator that Wall Street looks to for information about the direction the economy is moving.

MJ Lee at Politico said the reports have been receiving extra attention lately because the markets are looking "for signs of when the Federal Reserve might start pulling back on its bond-purchasing program, also known as quantitative easing."

With a lack of employment information coming from the government, some eyes are turned toward a private sector measure of jobs produced by payroll processor Automatic Data Processing Inc. and forecasting firm Moody's Analytics.

The ADP report "is what people will gravitate to, and they'll put a lot more stock in it," Kevin Grady, president of Phoenix Futures and Options, told CNBC. "I don't think there's a direct correlation between the jobs number but I do think people will be trading off that number."

The news from the ADP report wasn't heartening, reported Kathleen Madigan and Ruth Mantell at the Wall Street Journal. The ADP report showed that the private sector gained 166,000 jobs in September, which was below analyst expectations of a 178,000 increase in jobs.

"The job market appears to have softened in recent months. Fiscal austerity has begun to take a toll on job creation," the report said.

But economists are also looking at the initial unemployment claims — also known as jobless claims — that the Department of Labor released on Thursday. That data suggested good economic news, according to University of Michigan economist Justin Wolfers at Bloomberg. It showed initial unemployment claims from the last month averaged 305,000, down from 332,000 the previous month. Wolfers added that initial claims were down to pre-recession levels and at their lowest level since May 2007.

But until the government shutdown ends, the markets may be left in the dark as to the jobs situation in America, including the impact of the shutdown itself on the labor economy. As Wolfers put it, "Ironically, a direct effect of the current budget battles is that they limit our ability to track the broader economic effects of, you guessed it, the budget battles."