Jobless Americans (Tim Boyle/Bloomberg)

The most recent government jobs report showed that the U.S. economy gained 114,000 jobs in September. That was encouraging. But as we emphasized last week, the report came with a lot of caveats. The margin of error on the number of payroll jobs gained in September was plus or minus 108,293.

But history can also tell us how the government's estimate for September jobs is likely to change in the months ahead. That number will be revised twice as the Bureau of Labor Statistics gathers fuller data. And, as Matt Yglesias notes, the BLS estimates often change dramatically over the course of those two subsequent revisions. Since 1979, the final revision has been, on average, about 57,000 jobs higher or lower than the initial report:

It does appear that the BLS is getting better at estimating. The average report in the 1980s was off by 72,150 jobs, while the average report in the 2000s was off by 48,060.

But estimation suffers a lot during downturns. The average error during a downturn is 89,321, and usually the initial estimate of jobs lost is too low. During the recent financial crisis, for instance, the initial BLS estimates each month underestimated job losses by, on average, 50,000 per month. All told, the initial monthly reports underestimated job losses by 950,000.

Let me repeat that — almost a million job losses were not counted in those initial reports. That, arguably, was a major reason why fiscal and monetary stimulus failed to get us back to our level of employment. The Obama administration and the Federal Reserve just didn't know the full extent of the jobs crisis in 2009.

But the silver lining is that, since the downturn ended, the economy has been gaining jobs faster than the initial monthly reports suggest. Since June 2009 — when the recession officially ended — revisions have, on average, added about 30,000 jobs to the initial estimate. That adds up to 1.1 million more jobs than the reports initially counted.

The figures get one final look-through, called a "benchmark revision."* The revision for 2011 found an even bigger discrepancy. That report concluded that we gained 386,000 more jobs between April 2011 and March 2012 than previously estimated, whereas the monthly revisions found a gain of only 340,000 additional jobs. So if September's jobs report fits the pattern, it's likely to get revised up — just as August and July did before it.

Now, this doesn't mean the recovery is going well, just that it's going less terribly than we initially thought. Between July 2011 and July 2012, we added an average of 155,000 jobs a month, which, according to the Hamilton Project's handy calculator, gets us back to full employment …never (or at least not before 2025). But the initial estimates found an average gain of 126,000 jobs, a much more anemic pace.

So take Friday's report with a grain of salt. If the recovery to date is any indication, the 114,000 number could very well be too low.

Further reading

- How the BLS computes these numbers

- Matt Yglesias on revisions

- BLS revision data

- Ezra on whether this time could have been different

- Brad on benchmark revisions

- The Hamilton Project's employment calculator

*Correction: I initially said that the monthly numbers aren't updated with the benchmark revisions. That's wrong; they are. I apologize for the error.