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In this May 29, 2013 photo, job seeker Craig Cline of Lincolnwood, Ill., right, meets with Jeremy Skeeters, left, and Lindy Hammel, of Aflac Insurance Co. during a career fair in Rolling Meadows, Ill. The U.S. economy added 175,000 jobs in May, a gain that shows employers are hiring at a still-modest but steady pace despite government spending cuts and higher taxes, according to the Labor Department, Friday, June 7, 2013. (AP Photo/M. Spencer Green)
Washington, D.C.

The government shutdown may have affected October's jobs numbers. But not how you think.

For weeks, the White House had braced for a dour report on hiring, with economists and aides lowering expectations and blaming last month's partial shutdown for the inevitable bad news to come.

Then Friday's numbers materialized: Employers appeared to have ignored the shutdown and hired away, to the tune of 204,000 jobs in October.

The shutdown, it seemed, had had no effect.

Not so fast.

In the height of irony, the 16 days of federal worker furloughs and government disruptions may have helped, not hurt, the improved jobs picture.

Typically, jobs numbers are announced on the first Friday of the month. Because of the shutdown, the Bureau of Labor Statistics delayed the release of the jobs numbers by one week to allow more time to collect payroll and household data. That extra time resulted in an above average response rate for payroll data.

So, not to get hung up on numbers, but the average participation rate by employers in payroll surveys for the nine months before October was 76.4 percent. That meant that in subsequent months, as more data was collected, the hiring numbers were adjusted, often upward.

In October, with an extra week to collect data, the participation rate was 83.5 percent, the highest ever.

A robust hiring number, to some economists, now felt slightly inflated.

"It seems that when the initial response rate is high, the initial payroll number is often, though certainly not always, stronger than the prior trend," Ian Shepherdson, chief economist at Pantheon Macroeconomics, wrote in a research note.

In other words, if the jobs numbers in prior months were based on a lower participation rate, a stronger participation rate would skew the number up.

"Tentatively, we think the effect of this could explain all the overshoot in payrolls," Shepherdson wrote.

As a result, some economists are predicting that when the October numbers are updated, they might be in for a downward revision and that November could yield a lower number as well.

"Businesses may have inadvertently counted employment for an extra week," said Mark Zandi, chief economist at Moody's Analytics. "That could juice up the number. That may mean that we actually get surprised next month with a much weaker number."