It’s much more likely that we’re undercounting job growth at small businesses than overcounting it.

Barack Obama’s weak first presidential debate was almost immediately followed by a Bureau of Labor Statistics Employment Situation Summary showing a huge drop in the unemployment rate in September and decent job growth. In the era of social media and rabid partisanship, that swiftly led to a conspiracy theory spearheaded by former GE CEO Jack Welch, who alleged that “these Chicago guys will do anything” to win, “can’t debate so change numbers.”

Welch wasn’t kidding around, and has been joined to one degree or another in his criticisms by Donald Trump, Weekly Standard’s Jay Cost, and others in the conservative media firmament. Washington Examiner’s Conn Carroll came up with the inventive idea that unemployed Obama supporters are lying to surveyors to make their candidate look better.

This kind of nonsense is scarcely worth refuting beyond the observation that even Richard Nixon couldn’t pull this kind of manipulation off despite putting considerable effort into it. Given the post-Nixon safeguards at BLS, cooking the books without any leaks would be a mind-boggling feat.

While the allegations of a BLS conspiracy are absurd, the possibility of a BLS error certainly isn’t. Estimating the total quantity of employment in the United States is hard. The only problem for people wanting to wield the BLS’s mistakes as a weapon against the administration is that the error is more likely in the other direction. Rather than overcounting September jobs, the BLS may well have been undercounting jobs, especially at new small businesses.

If you pay a lot of attention to economic data, you’ll see that for many indicators, a lag of one or two months for gathering and processing is by no means rare. That’s just how long it takes to estimate things properly. But there’s sufficient public interest in the jobs data that the BLS does a quickie initial estimate right near the end of every month. It should come as no surprise that despite the job counters’ best estimates, the results are not incredibly accurate. In fact, the “margin of error” on initial number is about 100,000 jobs. On average, the two rounds of revisions that occur in the two months after the initial number lead to a change of a bit over 50,000 jobs relative to the initial estimate.

In other words, it would be a remarkable coincidence if these initial figures turned out to be right on the money.

There’s considerable reason to think that the economy is growing a bit stronger than the official data reflects, and that summertime job growth was stronger than the BLS knew. The main reason for this is that in addition to standard statistical error, the BLS’s “establishment survey”—the poll of employers that forms the basis for the canonical jobs number—seems to feature systematically correlated errors. In particular, when employment is shrinking it undercounts the pace of the shrinkage and when employment is rising it undercounts job growth.

That’s because an establishment survey counts hires and fires at existing firms. If an elementary school hires an extra teacher or a Wal-Mart decides it can get by with one fewer cashier, the establishment survey finds that. But if a restaurant shuts down, there’s nobody left to survey. If you leave your job to start selling a new smartphone app, they won’t know you’re there to be surveyed. If the economy’s in a steady state, these survey issues don’t matter because business births and deaths even out in a way the normal statistical adjustments account for. But in an economic crash, the number of firm births plummets and the number of firm deaths soars leading the government to undercount the scale of pain. In a recovery, the reverse happens. But over time as the BLS adjusts its counts, these problems tend to go away.

In that vein, the most optimistic sign in the September jobs report wasn’t the drop in the unemployment rate found in the household survey, it was the upward revisions to the July and August payroll data. Upward revisions indicate that we may be in a growth phase featuring systematic undercounting. Indeed, on Sept. 27 the BLS announced the results of a re-benchmarking exercise and said that as of March 2012 they’d been missing almost 400,000 jobs that should have been counted. If you assume miscounting on the same scale since March, that would explain why unemployment suddenly looks lower. A summer economy that was stronger than it appeared could also help explain conservative frustration that Romney’s economy-focused anti-Obama message didn’t seem to be working very well.

It’s possible, of course, that this is all just wishful thinking. Further revisions could show no change in the payroll number or even revise it downward. It’s dangerous to rely too much on initial estimates, and equally dangerous to assume you know the direction of revisions. But what we do know for sure is that if the economy is recovering at a relatively robust pace, we would only see that in the rearview mirror. Especially because a large share employment growth is going to come from new small businesses that are invisible to government surveys.