The unemployment rate fell to 8.1% in April despite terrible payroll numbers. On the one hand, it seems like a lower unemployment rate has to be good news. On the other hand, many commentators have pointed out that the numbers are flat out misleading. What the heck is going on here?

First of all, the total number of jobs that are added on a month-to-month basis is anything but nailed down. As Morgan Housel pointed out in his coverage of the April jobs report: "[I]nitial reports need to be taken with a grain of salt. Statistically, the margin of error in monthly jobs reports is plus or minus 100,000, so April may have been much better or worse than it looked."

To underscore that point, the April report adjusted March's job tally up to 154,000 from 120,000 and bumped February's total up by 19,000 to 259,000. Those handy with a calculator may note that the adjustment to March is a near 30% increase. That's hardly a rounding error.

The unemployment rate is an even more interesting case. For anyone trying to get a handle on the overall employment situation, focusing on the unemployment rate is like judging a house by just visiting the master bathroom. A fancy commode might tip you off that it's a nice house, but you'd be crazy to draw a conclusion based on that alone.

Recently, some of the media has made more of an effort to shine a light on the nuances -- or, rather a nuance -- of the unemployment rate. Specifically, media reports have noted that a decline in the unemployment rate coupled with lackluster jobs growth doesn't mean that the employment picture is sneakily getting better, but rather that workers are dropping out of the labor force. The standard interpretation is that the unemployment rate is misleading and it would be far higher if we didn't have this issue of workers throwing up their hands and giving up altogether.

While the math checks out there, it's still not really the full picture. Echoing the thoughts of a number of other economists and econo-bloggers, the Atlanta Fed's Dave Altig noted recently that a good part of the decline in the labor force participation rate (or LFPR, as he writes) actually stems from more than just workers getting fed up with not being able to find jobs. He notes:

The decline in the LFPR, now at its lowest level since the early 1980s, is itself being influenced by a confounding mix of demographic change and other behavioral changes that nobody seems to understand …

When he says "demographic change," what Altig is referring to is the fact that as our population ages -- think baby boomers -- there should be a shift to a lower labor force participation rate. In addition, as higher education increases in necessity, teens opting for college rather than work can also impact the LFPR -- as The Fool's Housel pointed out in his coverage.

If we think about factors like these, we can't help but consider that some decline in the LFPR may be good. Thinking in terms of our quality of life and the future of our economy, we want older workers to be able to retire and we want kids to be able to put off entering the labor force so that they can get further education. So we don't necessarily want to rip our hair out over the decline in the labor force participation rate.

Put that all together and you can end up with this:

That's from the Fed Bank of Atlanta and shows an adjusted LFPR that takes into account the demographic changes that would likely be going on -- maybe to an even greater extent --even if we weren't stuck in a sluggish economy.

As is obvious from the chart, even with the adjustment, LFPR has declined markedly since the recession started. But considering this more nuanced view of the LFPR highlights three things:

  1. Concerns that "real" unemployment is vastly higher because the workforce should be larger are only half truths. Since the labor force participation rate was trending down prior to the recession, any estimate of "real" unemployment that uses the pre-recession LFPR is misleading at best.
  2. The number of average monthly payroll additions we need to meet the Fed's targeted 7.5% unemployment rate by the end of 2013 depends a lot on assumptions of the LFPR. The Atlanta Fed's Altig proposes a LFPR range of 63.6%-65.1%, which would require monthly job additions ranging from 144,036 to 304,260.
  3. Most importantly, it reminds us once again that sound bites are quick, easy, and readily digestible, but often of very little informational nutrition. It's easy enough to point out that labor force participation is falling and that's contributing to the lower unemployment rate, but as a guidepost for government policy or a measure of economic progress, it's critical to understand the bigger picture.

But regardless of whether the story is told fully and properly (it probably won't be), the employment picture will play a big role in this year's election. And as much as I wish it was possible to divorce stock-picking and politics, all too often it's just not. Some of my fellow Fools, however, have some ideas how you may be able to profit from the upcoming election. To check out their picks, grab a free copy of our special report: "These Stocks Could Skyrocket After the 2012 Presidential Election."