Private nonfarm payrolls for the U.S. increased a better-than-expected 163,000 in July, according to the ADP Employment Report. The consensus forecast was looking for a substantially lower 125,000 gain, according to Briefing.com. Is the relatively upbeat news a sign that we could see another upside surprise in Friday’s official report from the Labor Department on the state of the jobs market? It’s a thought worth considering.

Consider how the ADP monthly payrolls estimates compare with the government’s establishment survey over the past year (see first chart below). Note that the ADP numbers have exceeded the Labor Department’s figures since March. History suggests that the difference between the two series tends to be random over the longer term. In that case, we shouldn’t expect to see an ongoing positive bias in favor of the ADP data. In short, it’s time for the Labor Department’s payrolls estimate to move closer, if not exceed, the ADP report. Will the July update be the month for convergence?

For a bit of statistical support for thinking optimistically, let’s compare the monthly difference between the ADP and Labor Department estimates over the last 10 years. The second chart below shows the difference in the monthly net change in the ADP number less its counterpart via government figures. For example, ADP advises that private payrolls added a net 172,000 jobs in June vs. an 84,000 gain that month via the Labor Department’s tally. The difference is 88,000 (172,000 less 84,000). Tracking the monthly difference through time shows a largely random fluctuation around zero–weakly stationary, in econometric-speak. That’s a good sign for thinking that there’s minimal bias in one data series relative to the other. As such, we should expect any positive or negative bias to close… eventually and perhaps soon. Given that a positive bias in favor of the ADP numbers has prevailed since March, it’s reasonable to wonder if the gap is poised to close, or at least narrow. If July’s the month, that implies a much stronger employment report on Friday relative to June’s disappointing update.

But let’s not go overboard. Even if the Labor Department reports a net gain in jobs last month on par with the ADP figures, the rise would still fall under the heading of slow growth. But stronger slow growth is at least better than suffering the opposite change.

“This is another resilient outcome,” says Sean Incremona, an economist at 4Cast Ltd, about today’s ADP report. “It does show that things are chugging along and this is pretty respectable.”

Hold that thought as we await confirmation (or rejection) in Friday’s update.

This post originally appeared at The Capital Spectator and is posted with permission.